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The U.B.C. recordings collection : a traffic flow study 1971

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THE U . B . C . RECORDINGS C O L L E C T I O N : A T R A F F I C FLOW STUDY b y JOHANNES KRAMAR I n g e n i e u r ( g r a d . ) , F r i e d b e r g P o l y t e c h n i c / G e r m a n y 1 9 6 7 W e l d i n g E n g i n e e r , I n s t i t u t e f o r I n s t r u c t i o n a n d R e - s e a r c h o f W e l d i n g T e c h n o l o g y , M a n n h e i m / G e r m a n y 1 9 6 7 A T H E S I S SUBMITTED IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF B U S I N E S S ADMINISTRAT ION IN THE FACULTY o f COMMERCE AND B U S I N E S S ADMINISTRAT ION We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE U N I V E R S I T Y OF B R I T I S H COLUMBIA M a r c h 1 9 7 1 In presenting th is thesis in par t ia l fu l f i lment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shal l make i t f reely avai lable for reference and study. I further agree that permission for extensive copying of th is thesis for scholar ly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publ icat ion of th is thesis for f inancia l gain shal l not be allowed without my written permission. Department of Commerce and Bu s i ne s s A d m t n f s t r a t l o n The University of B r i t i s h Columbia Vancouver 8, Canada March 15, 1971 The U . B . C . R e c o r d i n g s C o l l e c t i o n r e p r e s e n t s a s e r v i c e n e t w o r k w i t h d i f f e r e n t s e r v i c e c e n t e r s w h i c h i n - c l u d e t h e I n f o r m a t i o n d e s k , t h e s h e l v e s , a n d t h e l i s t e n i n g r o o m . A r r i v a l s t o t h e s y s t e m f o l l o w a r a n d o m t r a f f i c p a t t e r n . The u n i t s f l o w i n g i n t h e n e t w o r k a r e d e f i n e d a s j o b s r e q u i r i n g s e r v i c e f r o m t h e s e r v i c e s t a t i o n s . The p r o b a b i l i s t i c j o b r o u t i n g s a r e c o n s i d e r e d t o be a s t a t i o n - a r y f i n i t e - s t a t e M a r k o v C h a i n d i s c r e t e In t i m e . F i e l d . w o r k was d o n e d u r i n g t h e summer s c h o o l a n d d u r i n g t h e r e g u l a r w i n t e r t e r m . The e s s e n t i a l t r a f f i c o b s e r v a t i o n s w e r e o b t a i n e d by q u e s t i o n n a i r e s . A f i r s t a n a l y s i s o f t h e o p e r a t i n g c h a r a c t e r i s t i c s was made u s i n g a g r a p h i c a l m e t h o d s h o w n i n t h e d i a g r a m s 1 a n d 2; a t t h i s , t h e r e c o r d i n g s c o l l e c t i o n was c o n s i d e r e d t o be a s e r v i c e f a c i l i t y w i t h a l a r g e number o f s e r v i c e c h a n n e l s . By t h i s m e t h o d , k n o w l e d g e c o u l d be g a i n e d a b o u t t h e n u m b e r o f a r r i v a l s d u r i n g a d a y , t h e number o f s i m u l t a n e o u s c u s t o m e r s i n t h e s y s t e m a n d i n t h e l i s t e n i n g r o o m , t h e t i m e s p e n t f o r s e r v i c e , t h e r e g u l a r i t y a n d c h a n g e s i n a r r i v a l a n d s e r v i c e s t a t i s t i c s , a n d t h e r e g u l a r i t y o f d e p a r t u r e s . I t became e v i d e n t t h a t t h e d i s t r i b u t i o n o f t h e i n t e r a r r i v a l t i m e s , b o t h . , t o t h e r e c o r d i n g s c o l l e c t i o n ( s h e l v e s a n d I n f o r m a t i o n d e s k ) a n d t o t h e l i s t e n i n g room a s w e l l , f i t a n e g a t i v e e x p o n e n t i a l d i s t r i b u t i o n f u n c t i o n . The d i s t r i b u t i o n o f t h e s e r v i c e t i m e s a s s o c i a t e d w i t h t h e r e c o r d 1ngs c o l 1 e c t i o n c o u l d be i d e n t i f i e d a s e x - p o n e n t i a l l y d i s t r i b u t e d , w h i l e t h e s e r v i c e t i m e d i s t r i b u t - i o n o f t h e l i s t e n i n g room f o l l o w s an e m p i r i c a l d i s t r i b u t - i o n f u n c t i o n ( s e e d i a g r a m s 3 t o 1 0 ) . The b a s i c a l l y o b s e r v e d s t a t i s t i c s w e r e a p p l i e d i n a s i m u l a t i o n . The s i m u l a t i o n was p e r f o r m e d w i t h t h e " G e n e r a l P u r p o s e S i m u l a t i o n S y s t e m / 3 6 0 , ( G P S S / 3 6 0 ) " In t h r e e v a r i a t i o n s i n o r d e r t o o b t a i n e m p i r i c a l d a t a u n d e r m o d i f i e d a r r i v a l r a t e s a n d o n e o r two d e s k s e r v e r s , r e s p e c t - i v e l y . The d a t a o f i n t e r e s t was g a t h e r e d In t a b l e s / t h e I n f o r m a t i o n c o n t e n t o f t h e t a b l e s was p l o t t e d i n g r a p h s ( s e e c o m p u t e r o u t p u t ) . D a t a o f s i g n i f i c a n c e h a s b e e n u s e d f o r t h e d e s c r i p t i o n o f t h e t r a f f i c b e h a v i o r o f e a c h s i n g l e s e r v i c e c e n t e r a n d was d i s p l a y e d i n t h e d i a g r a m s 11 t o 1 3 . The f l o w m o d e l p r e d i c t e d t h a t c o n g e s t i o n may a p p e a r a t t h e i n f o r m a t i o n d e s k a n d i n t h e l i s t e n i n g r o o m . The s i m u l a t i o n h a s c o n f i r m e d t h i s p r e d i c t i o n . U n d e r l a s t i n g r u s h h o u r c o n d i t i o n s , j o b s r e - q u i r i n g s e r v i c e a t t h e i n f o r m a t i o n d e s k may s p e n d j . a b o u t 3 t o h t i m e s t h e i r a c t u a l s e r v i c e t i m e i n q u e u e w a i t i n g f o r s e r v i c e . T h i s r e s u l t h a s b e e n o b t a i n e d u n d e r t h e g e n e r a l a s s u m p t i o n o f a f i r s t - i n f i r s t - s e r v i c e o r d e r o f a 1 H . a r r i v i n g desk j o b s . However, In p r a c t i c e , the observed rush t r a f f i c l a s t s only about two hours between 12:00 and 2 :00 . Consequently, a r r i v i n g jobs r e l a t e d to re- s h e l v i n g of recordings may be b u f f e r e d and s e r v i c e d at times of lower t r a f f i c . Thus, the ac t u a l waiting time in queue w i l l be lower. In the case of a second s e r v e r on duty, the w a i t i n g time in queue drops down s i g n i f i c a n t l y . It w i l l not exceed the s e r v i c e time (see diagram 11). The s e r v i c e at the shelves s t o r i n g the re c o r d - ings Is problemless. The maximum number of jobs at the i shelves does not reach the s e r v i c e c a p a c i t y . The average s e r v i c e times are constant under v a r i e d c o n d i t i o n s . In d e c i d i n g what fs an adequate number of t u r n - t a b l e s , there is a c o n f l i c t between high u t i l i z a t i o n rate and s a t i s f i e d customers. The c o n f l i c t s i t u a t i o n becomes evident under extreme t r a f f i c c o n d i t i o n s , f o r inst a n c e , when the peak t r a f f i c exceeds the provided c a p a c i t y , or c o n v e r s e l y , when the equipment i s i d l e because of low t r a f f i c . A s a t i s f y i n g approach depends upon the range and weight of the appearing t r a f f i c f l u c t u a t i o n s . As i t is shown, the i n t e n s i t y of a r r i v a l s v a r i e s c o n s i d e r a b l y d u r i n g the i n t e r v a l of a day. However, the range of f l u c t u a t i n g a r r i v a l rates s t i l l increases by c o n s i d e r i n g d i f f e r e n t days of a week or d i f f e r e n t seasons, such as the summer '.' s e s s i o n o r t h e w i n t e r t e r m . An a c c e p t a b l e s o l u t i o n o f an a d e q u a t e number o f t u r n t a b l e s I n s t a l l e d may l e a d t o a c o m p r o m i s e b e t w e e n ' p e r f e c t ' e q u i p m e n t u t i l i z a t i o n a n d ' c o m p l e t e l y ' s a t i s f i e d c u s t o m e r s . D e p e n d i n g on t h e p u r s u e d p o l i c y / i t may f a v o u r o n e o r t h e o t h e r i n t e r e s t . CHAPTER PAGE I G E N E R A L I T I E S : THE SYSTEM UNDER STUDY 1 II A N A L Y S I S OF THE OPERATING C H A R A C T E R I S T I C S k . 1 . D e t e r m i n a t i o n o f S i g n i f i c a n t T r a f f i c C h a r a c t e r i s t i c s h 1 . 1 D e s c r i p t i o n o f t h e t e c h n i q u e e m p l o y e d k 1 . 2 The t r a f f i c f l o w d u r i n g t h e summer t e r m . 9 1 . 3 C o m p a r i s o n o f t h e t r a f f i c f l o w o b s e r v e d d u r i n g t h e summer s e s s i o n a n d t h e w i n t e r t e r m 16 I I I THE T R A F F I C FLOW MODEL 27 1 . t h e S t a t i s t i c a l P r o p e r t i e s o f t h e C o n t i n u o u s F l o w M o d e l 29 2 . The J o b R o u t i n g M o d e l a s a F i n l t e r - S t a t e M a r k o v C h a i n 32 TABLE OF CONTENTS (cont'd) CHAPTER PAGE 2.1 The expected number of visits to state (j) before a customer will leave the service system, given, he Is in a present state i i) 3 7 2.2 The probability, a customer ever will v i s i t state (j) ....... 39 2.3 Markov Renewal Process 1+8 3. Restrictions of the Markov Assumptions in the Model 55 IV SIMULATION OF THE MODEL 7..".. 5 8 V MEASUREMENT AND EFFECTS OF STATISTICAL PROPERTIES ON THE SERVICE NETWORK UNDER VARIOUS SIMULATION CONDITIONS T.LS 63 1. The Information Desk 63 2. The Shelves 67 3. The Listening Room 69 CHAPTER BIBLIOGRAPHY . . ..' APPENDIX W 1. Tables 2. Computer Output LIST OF TABLES TABLE PAGE I Maximum values describing the t r a f f i c characteristics of the recordings collection during the summer term 1970 ... Ik II Maximum values describing the t r a f f i c characteristics of the recordings collection during the winter term 1970 ... 16 III The average arrival rates of the system and of the listening room on an average day in the winter term 72 IV Cumulative number of customers entering or leaving, respectively/ the system at certain t imes(summer term) ....... 78 Cumulative number of customers entering or leaving, respectively, the listening room at certain times (summer term) ... TABLE PAGE VI Cumulative number of customers e n t e r i n g or l e a v i n g , r e s p e c t i v e l y , the system at c e r t a i n times (winter term) 80 VII Cumulative number of customers e n t e r i n g or l e a v i n g , r e s p e c t i v e l y , the 1 Isten1ng room at c e r t a i n times (winter term) .. 81 VIII D i s t r i b u t i o n of elapsed time between a r r i v a l s to the recordings c o l l e c t i o n 82 JX D i s t r i b u t i o n of s e r v i c e time in the recordings c o l l e c t i o n 83 X D i s t r i b u t i o n of elapsed time beween a r r i v a l s to the l i s t e n i n g room ... 8k XI D i s t r i b u t i o n of s e r v i c e time con- c e r n i n g the l i s t e n i n g room 85 LI ST OF F I G U R E S F I G U R E PAGE 1 The p h y s i c a l p l a n t of the s e r v i c e f a c i l i t i e s of the recordings c o l l e c t i o n and the corresponding channels of the job flows 3 2 Operating t r a f f i c c h a r a c t e r i s t i c s shown in a schematic graph 6 j l The determination of the r e p r e s e n t a t i v e a r r i v a l and departure curve 8 k The continuous flow model of the complex s e r v i c e system with f i v e s t a t e s , numbered 1 to 5 28 5 The e m p i r i c a l l y observed flow of jobs represented by 100 customers r e q u i r i n g s e r v i c e from the system dur i n g a time i n t e r v a l of ca. 100 minutes 30 6 The flow model showing the s t a t e t r a n s i t i o n p r o b a b i l i t i e s 33 FIGURE PAGE 7 The probability tree showing the possible paths 0̂ 8 A sample function of transitions into state (f) k8 9 The transition from state (I) to two alternative successive states j ( l ) and j(2) . .. 50 10 The simulation model 50 11 Graphical display of the interrelations "Service Center","Recordings Collection", "Service System" - 62 12 The average utilization rate vs. the probability that every customer will find a vacancy in the listening room - 73 13 Anticipated simulation map 7k FIGURE PAGE jti Map of I n d i f f e r e n c e curves 76 15 D e c i s i o n f i e l d of the model 77 L I S T OF DIAGRAMS DIAGRAM PAGE 1 The t r a f f i c c h a r a c t e r i s t i c c u r v e s o f t h e r e c o r d i n g s c o l l e c t i o n d u r i n g t h e summer t e r m 10 2 The t r a f f i c c h a r a c t e r i s t i c c u r v e s o f t h e r e c o r d i n g s c o l l e c t i o n d u r i n g t h e w i n t e r t e r m 15 3 I n t e r a r r i v a l t i m e d i s t r i b u t i o n ( r e c o r d i n g s c o l l e c t i o n ) 19 k C u m u l a t i v e I n t e r a r r i v a l t i m e d i s t r i b u t i o n ( r e c o r d i n g s c o l l e c t i o n ) 20 5 S e r v i c e t i m e d i s t r i b u t i o n o f t h e r e c o r d i n g s c o l l e c t i o n w i t h o u t c o n - s i d e r a t i o n o f t h e s e r v i c e t i m e In t h e l i s t e n i n g room ; 2 1 6 C u m u l a t i v e s e r v i c e t i m e d i s t r i b u t - i o n o f t h e r e c o r d i n g s c o l l e c t i o n w i t h o u t c o n s i d e r a t i o n o f t h e s e r v i c e t i m e In t h e l i s t e n i n g room 22 DIAGRAM PAGE 7 I n t e r a r r i v a l t ime d i s t r i b u t i o n ( 1 i s t e n i ng room) 23 8 C u m u l a t i v e i n t e r a r r i v a l t ime d i s t r i b u t i o n ( l i s t e n i n g room) . . . . 2k 9 S e r v i c e t ime d i s t r i b u t i o n ( 1 i s t e n i n g room) 25 10 C u m u l a t i v e s e r v i c e t ime d i s t r i b u t - i on ( l i s t e n i n g room) . , 26 11 The average number o f a r r i v a l s / 1 0 m in . to the i n f o r m a t i o n desk and the ave rage t r a n s i t t i m e / j o b as a f u n c t i o n ; : o f the number o f a r r i v a l s to the system/10 m inu te s 6k 12 F u n c t i o n a l i n t e r r e l a t i o n s h i p s c o n c e r n i n g the l i s t e n i n g rcom . . . . 68 ACKNOWLEDGEMENT I am grateful to a number of people for advice and help in the development of my thesis work. I would like to express my thanks to Prof. Larry George, Prof. Shelby Brumelle, and Prof. Hartmut Will for their guidance and the atmosphere of cb-operation. Also, I owe thanks to Prof. Bernhard Schwab for his perceptive comments. I am indebted to Mr. Basil Stuart-Stubbs, the manager of the U.B.C. Main Library, and to Mr. Doug Kaye, the manager of the U.B.C. Recordings Collection, for the readiness to help they offered in the preparation of the study during the f i e l d work. My appreciation extends to a l l persons who f i l l e d in my questionnaires, and in particular to al l those who have patiently corrected my composition and grammatical errors. Johannes Kramar GENERALITIES: THE SYSTEM UNDER STUDY The recordings col 1 e c t i o n of the U.B.C. L i b r a r y houses more than f i f t e e n thousand recordings of a l l kinds which may be played in the Wilson L i s t e n i n g Room wi t h - out charge or may be borrowed f o r an annual f e e . The t r a f f i c flow study of the recordings c o l l e c t - Ion i n c l u s i v e of the l i s t e n i n g room i n c l u d e s : a) the a n a l y s i s of the s e r v i c e system In i t s o p e r a t i n g c h a r a c t e r i s t i c s , b) the p r e s e n t a t i o n of a t r a f f i c flow model, c) the s i m u l a t i o n of the model under changing t r a f f i c c o n d i t i o n s , d) the a p p l i c a t i o n of the e s s e n t i a l s i m u l a t i o n e x t r a c t to provide a measurement and e v a l u a t - ion method of the achievment of each s i n g l e s e r v i c e f a c i 1 I t y . The recordings col 1 ect ion, as a s e r v i c e system, c o n s i s t s of three f a c i l i t i e s o f f e r i n g d i f f e r e n t customer s e r v I c e s : a ) A t t h e i n f o r m a t i o n d e s k , m a i n s e r v i c e s a r e t o p r o v i d e I n f o r m a t i o n c o n c e r n i n g t h e r e c o r d i n g s c o l l e c t i o n , i n c l u d i n g new a p p l i c a t i o n s f o r m e m b e r s h I p ; a n d t o s t o r e a l l r e t u r n e d r e c o r d s . b ) The r e c o r d s h e l v e s t h e m s e l v e s a r e an I n f o r m a t - i o n s o u r c e a n d s u p p l y t h e r e c o r d i n g s e i t h e r f o r t a k i n g *h.ome 'brr'-"'ri,.^ c ) f o r l i s t e n i n g on t h e t u r n t a b l e s I n s t a l l e d i n t h e 1 ? s t e n I n g r o o m . The s y s t e m ' s i n p u t Is a s e r i e s o f a r r i v i n g j o b s r e p r e s e n t e d by t h e a r r i v i n g p a t r o n s , e a c h r e q u i r i n g a number o f s e r v i c e o p e r a t i o n s a t t h e s e r v i c e f a c i l i t i e s . The s y s t e m ' s o u t p u t i s c o m p r i s e d o f c o m p l e t e d s e r v i c e s o r s a t i s f i e d c u s t o m e r s , r e s p e c t i v e l y . The f l o w o f j o b s among t h e s e r v i c e f a c i l i t i e s Is I l l u s t r a t e d b e l o w : F i g u r e 1 : the p h y s i c a l p l a n t of the s e r v i c e f a c i l i t i e s of the recordings c o l l e c t i o n and the correspond- ing channels of the job flows A N A L Y S I S OF THE OPERATING C H A R A C T E R I S T I C S The r e c o r d i n g s c o l l e c t i o n Is a s e r v i c e f a c i l i t y w i t h a j l a r g e n u m b e r o f s e r v i c e c h a n n e l s . S i m u l t a n e o u s l y , a c e r t a i n number o f j o b s may be i n t h e s y s t e m ' s s e r v i c e o c c u p y i n g i t s s e r v i c e c a p a c i t i e s . F o r i n s t a n c e , t h e l i s t e n i n g room o f f e r s 23 t u r n t a b l e s i n s t a l l e d , a n d a t t h e s t o r i n g s h e l v e s , s e r v i c e i s s e l f - o p e r a t e d . The o n l y s i n g l e c h a n n e l s e r v i c e s t a t i o n i s t h e i n f o r m a t i o n d e s k . 1 . D e t e r m i n a t i o n o f S i g n i f i c a n t T r a f f i c C h a r a c t e r i s t i c s 1.1 D e s c r i p t i o n o f t h e t e c h n i q u e e m p l o y e d t h e n u m b e r o f a r r i v i n g c u s t o m e r s d u r i n g a d a y , t h e number o f s i m u l t a n e o u s c u s t o m e r s , t h e t i m e s p e n t f o r s e r v i c e , t h e r e g u l a r i t y a n d c h a n g e s In a r r i v a l a n d s e r v i c e s t a t i s t i c s , t h e r e g u l a r i t y o f d e p a r t u r e s w i l l be e v a l u a t e d i n a g r a p h i c a l m e t h o d . We w a n t t o u s e a g r a p h t o c o m p r e h e n d t h e t r a f f i c d a t a w h i c h was o b t a i n e d by t h e n u m e r o u s a n s w e r s o n t h e q u e s t I o n n a I r s . F u r t h e r m o r e , I t Is o u r o b j e c t i v e t o g e n e r a l i z e ( . " ' " t h e o b s e r v e d t r a f f i c f l o w i n a f o r m , t h a t we m i g h t be a b l e t o l e a r n a n e x - The o p e r a t i n g C h a r a c t e r i s t i c s s u c h a s : p e c t e d b e h a v i o r o f t h e s e r v i c e s y s t e m u n d e r s t u d y . The g r a p h u s e d s h o w s on i t s a b s c i s s a t h e c u r r e n t h o u r s o f t h e d a i l y p u b l i c a c c e s s t o t h e r e c o r d i n g s c o l l e c t i o n . The o r d i n a t e r e c o r d s t h e c u m u l a t i v e number o f c u s t o m e r s g o i n g I n t o t h e s y s t e m a n d I n t o t h e l i s t e n i n g r o o m , r e s p e c t i v e l y . The c u m u l a t i v e number o f c u s t o m e r s may be r e c o r d e d a t a n y c o n v e n i e n t t i m e i n t e r v a l . The s m a l l e r t h e I n t e r v a l b e t w e e n t h e r e c o r d i n g s , t h e m o r e a c - c u r a t e Is t h e o b s e r v a t i o n t h a t c a n be made f r o m a n a l y s i s o f t h e m e a s u r e m e n t s . The r e q u i r e d i n f o r m a t i o n was o b t a i n e d u s i n g a q u e s t i o n n a i r e . T h i s f o r m was p r e s e n t e d t o e a c h a r r i v i n g c u s t o m e r a t t h e e n t r a n c e w i t h t h e r e q u e s t t o r e t u r n i t a t t h e e x i t . D u r i n g t h e s e e v e n t s , t h e a r r i v a l a n d d e - p a r t u r e t i m e c o u l d be n o t e d on t h e f o r m . A l s o , i f t h e c u s t o m e r v i s i t e d t h e l i s t e n i n g r o o m , he f i l l e d i n t h e a p p r o p r i a t e a r r i v a l a n d e x i t t i m e . The o t h e r i t e m s o f t h e q u e s t i o n n a i r e a s s i s t e d t o d e t e r m i n e w h a t k i n d o f s e r v i c e f a c i l i t i e s t h e p a t r o n s h a d u s e d . F r o m t h e I n f o r m a t - i o n s h e e t s , a l l r e q u i r e d d a t a c o u l d be o b t a i n e d f o r f u r t h e r e v a l u a t i o n . A t c e r t a i n t i m e s , t h e c u m u l a t i v e number o f c u s t o m e r s who e n t e r e d t h e r e c o r d i n g s c o l l e c t i o n a n d t h e l i s t e n i n g r o o m , r e s p e c t i v e l y , ts=: r e p r e s e n t e d by t h e a r r i v a l c u r v e s . S i m i l a r l y , t h e d e p a r t u r e c u r v e s show t h e c u m u l a t - i v e c u s t o m e r s t h a t l e a v e a f t e r t h e i r s e r v i c e c o m p l e t i o n . The a r r i v a l c u r v e a n d t h e d e p a r t u r e c u r v e w i t h i n a c o - o r d i n a t e s y s t e m and t h e p a r a m e t e r s d e r i v e d f r o m i t a r e o u t l i n e d i n t h e s c h e m a t i c g r a p h b e l o w : F i g u r e 2: O p e r a t i n g t r a f f i c c h a r a c t e r i s t i c s s h o w n i n a p p e a r t o demand s e r v i c e . I t v a r i e s d u r i n g t h e s u c c e s s i v e t i m e s o f a d a y . The a r r i v a l r a t e may be o b t a i n e d f r o m t h e s l o p e o f t h e a r r i v a l c u r v e f o r a n y t i m e i n t e r v a l u n d e r c o n s i d e r a t i o n . I f a d e s i r e d t i m e i n t e r v a l i s s e l e c t e d , t h e s l o p e o f t h e e n t r a n c e c u r v e b e t w e e n t h e b e g i n n i n g a n d t h e e n d o f t h e i n t e r v a l g i v e s t h e a r r i v a l r a t e d u r i n g t h a t I n t e r v a l . S i m i l a r l y , t h e r a t e o f s e r v i c e Is t h e r a t e w i t h w h i c h c u s t o m e r s a r e d i s c h a r g e d f r o m t h e s e r v i c e . I t a l s o v a r i e s d u r i n g t h e d a i l y s e r v i c e p e r i o d a n d c a n be d e t e r m - DUI?A7lO^ O F service F=ER10IX TIME a s c h e m a t i c g r a p h The a r r i v a l r a t e i s t h e r a t e a t w h i c h c u s t o m e r s i n e d In t h e same way a s t h e a r r i v a l r a t e . A t a c e r t a i n t i m e o f i n t e r e s t , t h e s i m u l t a n e o u s number o f c u s t o m e r s i n s e r v i c e f o l l o w s f r o m t h e v e r t i c a l d i s t a n c e b e t w e e n t h e a r r i v a l a n d t h e e x i t c u r v e . The : a r r i v a l c u r v e s h o w s t h e c u m u l a t i v e number o f c u s t o m e r s t h a t h a v e e n t e r e d . The number o f c u s t o m e r s t h a t h a v e l e f t i s g i v e n by t h e e x i t c u r v e . T h u s , t h e d i f f e r e n c e b e t w e e n t h e two v a l u e s m u s t be t h e number o f c u s t o m e r s t h a t r e m a i n In s e r v i c e a t t h e moment In q u e s t i o n . An a v e r a g e t i m e s p e n t f o r s e r v i c e may be o b t a i n e d by t h e h o r i z o n t a l d i s t a n c e b e t w e e n t h e e n t r a n c e a n d e x i t c u r v e . I f we k e e p t r a c k g r a p h i c a l l y o f a l l a r r i v a l s ( t Ime/cummu1 a t I v e number o f c u s t o m e r s ) a n d r e g i s t e r t h e t i m e s p e n t f o r s e r v i c e ( t ) o f e a c h c u s t o m e r ( n ) , t h e n we c may o b t a i n an a v e r a g e s e r v i c e t i m e a s s o c i a t e d t o t h o s e n c u s t o m e r s by 1 n t = - - — ;>_> t c c , a v g . n u m b e r o f n c u s t o m e r s c=i We i n t e r c o n n e c t a l l p o i n t s o f a r r i v a l s a n d o b t a i n t h e a r r i v a l c u r v e ; t h e p o i n t s o f a v e r a g e s e r v i c e t i m e s l i e on t h e e x i t c u r v e , s u c h a s i t i s shown i n t h e s k e t c h b e i o w : C u R R E N r -SERVICE TiMI Figure 3: The determination of the representative arrival and departure curve Thus, the smoothed curves of the arrivals and the exits represent a generalized description of the t r a f f i c be- havior during the current service time. We compare * V those t r a f f i c characteristics observed on dlffernt days of aWek and realize a strong similarity in the customer's behavior. The comprehended data of a week's observation Is shown In diagram 1. We assume, this generalized graph represents the t r a f f i c flow during the summer term, and ana 1 ogously, the graph shown In diagram 2 may represent the t r a f f i c during the winter term. In proceeding to determine how much time an average customer will spend for service when he arrives at the current time t c of a day, f i r s t we examine the arrival curve. We realize, it will be the n-th customer on t h e a v e r a g e . L o o k i n g h o r i z o n t a l l y a c r o s s , t o t h e a r r i v a l c u r v e , i t c a n be n o t e d t h a t t h e n - t h c u s t o m e r w i l l l e a v e a t t i m e t c + . H e n c e , we c a n e x p e c t t h a t t h e n - t h c u s t o m e r w i l l s p e n d a t o t a l o f ( t c - t c + r ) ) = t p m i n u t e s f o r s e r v i c e . G e n e r a l l y , t h e h o r i z o n t a l d i s t a n c e b e t w e e n t h e a r r i v a l a n d e x i t c u r v e Is a g r a p h i c a l r e p r e s e n t a t i o n o f how l o n g c u s t o m e r s s p e n d a t a n y s i n g l e p o i n t . The l o n g e s t a n d s h o r t e s t t i m e s p e n t i s r e p r e s e n t e d by t h e l o n g e s t a n d s h o r t e s t h o r i z o n t a l l i n e s b e t w e e n t h e two c u r v e s . The t o t a l number o f c u s t o m e r s , r e a d i l y o b t a i n e d f r o m t h e c u r v e s , Is I n d i c a t e d by t h e h i g h e s t p o i n t s on b o t h ; - , t h e a r r i v a l a n d t h e e x i t c u r v e s , a n d may be r e a d on t h e v e r t i c a l s c a l e . The d u r a t i o n o f t h e d a i l y s e r v i c e p e r i o d i s i n d i c a t e d on t h e h o r i z o n t a l s c a l e . 1 . 2 The t r a f f i c f l o w d u r i n g t h e summer t e r m U s u a l l y , f e w e r s t u d e n t s a t t e n d summer s c h o o l . B u t summer s c h o o l s t u d e n t s m i g h t h a v e more l e i s u r e t h a n s t u d e n t s o f t h e r e g u l a r w i n t e r t e r m . S u c h c i r c u m s t a n c e s may s i g n i f i c a n t l y a f f e c t t h e b e h a v i o r o f v i s i t s o f t h e r e c o r d i n g s c o l l e c t i o n . D i a g r a i B 1 s h o w s t h e a p p r o x i m a t e t r a f f i c c h a r a c t e r i s t i c s d u r i n g t h e summer s e s s i o n 1 9 7 0 . The i n - q u i r y t o o k p l a c e i n t h e f i r s t week o f J u l y .  F r o m t h e s y s t e m a r r i v a l c u r v e o f d i a g r a m 1 , we c a n d e t e r m i n e t h r e e a r r i v a l r a t e s i n t h e t i m e per iods b e t w e e n 9 : 0 0 a n d 12 : 0 0 , 12 : 00 and 2 : 0 0 , and 2 : 0 0 and 5 : 0 0 . A t 9 : 0 0 , 1 2 : 0 0 , 2 : 0 0 , a n d 5 : 0 0 , t h e r e w e r e 0 , h O , 9 7 , a n d ] h S c u m u l a t i v e c o u n t e d c u s t o m e r s i n t h e s y s t e m / as o b t a i n e d f r o m e x a m i n a t i o n o f t h e a r r i v a l c u r v e . T h u s , U 0 , 5 7 , a n d bS c u s t o m e r s had e n t e r e d t h e r e c o r d i n g s c o l l e c t i o n d u r i n g t h e c o r r e s p o n d i n g t i m e p e r i o d s o f 1 8 0 , 1 2 0 , and 180 m i n u t e s . The s l o p e a t a n y p o i n t o f t h e s y s t e m ' s a r r i v a l c u r v e Is o b t a i n e d by d i v i d i n g t h e number o f c u s t o m e r s s e r v e d by t h e r e s p e c t t v e 1 t i m e p e r i o d . H e n c e , i n t h e a v e r a g e , t h e r e a r r i v e d 1 80 57 120 U8 180 = 1 c u s t o m e r / 4 . 5 m i n u t e s = 1 c u s t o m e r / 2 . 1 m i n u t e s = 1 c u s t o m e r / 3 . 7 5 m i n u t e s d u r i n g t h e p e r i o d s e x a m i n e d . The l e n g t h o f t h e i n t e r v a l m u s t be s h o r t when t h e s l o p e c h a n g e s r a p i d l y o r t h e r e w i l l be a n a v e r a g i n g o f d i f f e r e n t a r r i v a l r a t e s . The b e h a v i o r o f t h e e x i t c u r v e i s a f f e c t e d by p e r i o d i c c h a n g e s d u r i n g t h e m o r n i n g . The c u s t o m e r s a r e g o i n g t o l e a v e t h e r e c o r d i n g s c o l l e c t i o n b e t w e e n 9 : 3 0 a n d t h e b r e a k a t 1 0 : 3 0 w i t h an a v e r a g e d e p a r t u r e r a t e of 1 customer/3.3 minutes. After the.10:30 break, the departure rate slows down but Increases again shortly before the 11:30 break. Obviously, the students either leave for :' •'• - classes or for early lunch starting at 11:30. However, the average departure rate decreases to 1 customer/8.7 minutes between 10:30 and 11:30. This/results in a maximum number of simultaneous customers (8) in the system at 11:30, as the average arrival rate does not diminish during the same Interval. After 11:30, the visitors to the recordings collection may leave for lunch. The exit rate increases to 1 customer/k.1 minutes. :~; X- From 12:15 t i l l about 2:00, rush hour takes place, the exit rate goes up to 1 customer/2.2 minutes, which Is about equivalent to the arrival rate of 1 customer/2.1 minutes during the same Interval. This, indicates that there is a high t r a f f i c flow into and out of the recordings col 1ectIon. Under these circum- stances, of course, the number of simultaneous customers and the time spent in the system are about constant. After this period, the exit rate decreases again to 1 customer/3.2 minutes. Within the few minutes before t h e 5 : 0 0 c l o s i n g t i m e , t h e r e m a i n i n g c u s t o m e r s l e a v e a n d o n c e a g a i n c r e a t e a k i n d o f r u s h t r a f f i c ( 1 c u s t o m e r / l . 3 6 mi n u t e s ) . I t c a n be s e e n t h a t t h e maximum number o f s i m u l t a n e o u s c u s t o m e r s a p p e a r a t 1 1 : 3 0 (8 . ; c u s tome r s ) , a t 1 : 3 0 ( 1 3 c u s t o m e r s ) , a t 3 : 0 0 ( 1 2 c u s t o m e r s ) , a n d a t 4 : 1 5 ( 1 3 c u s t o m e r s ) , r e s p e c t i v e l y . The l o n g e s t t i m e s a r e s p e n t b e t w e e n 1 0 : 3 5 and 1 1 : 2 0 ( 4 5 m i n u t e s ) a n d 2 : 4 5 a n d 3 : 3 0 ( 4 5 m i n u t e s ) . On t h e a v e r a g e d a y Inv i the 1 9 7 - s u m m e r , 145 c u s t o m e r s h a v e b e e n s e r v i c e d . The g r a p h c o n c e r n i n g t h e l i s t e n i n g room c a n be i n t e r p r e t e d i n a s i m i l a r w a y . I t r e p r e s e n t s t h e d a t a w h i c h wa&;:^ r e c o r d e d s i m u l t a n e o u s l y u n d e r t h e same c o n d i t i o n s . In t h e s u m m a r y , t h e t a b l e o u t l i n e s t h e maximum d a t a o f t h e t r a f f i c f l o w i n t o t h e r e c o r d i n g s c o l l e c t i o n a n d a d j o i n i n g l i s t e n i n g r o o m : PARAMETER TIME INTERVAL SYSTEM LISTENING ROOM 1. A r r i v a l Rate (cust./tIme) 12:00-2:00 1 cust./2.1 min 12:00-4:45 1 cust./7.9 min 2. Departure Rate (cust./tIme) 12:00-2:00 1 cust./2.2 min. 4:45-5:00 .1 cust./1.4 min. 12:00-4:30 1 cust./8.7 min 4:30-5:00 1 cust./3 min. 3. Number of SImultaneous Cus tomers 11:30 8 customers 11:45 6 customers 1:30 13 customers 7 customers 3:00 12 customers 8 customers 4:15 13 customers 9 customers 4. Time Spent = S e r v i c e TI me 10:35-11:20 45 minutes 10:40-1.1:50 70 minutes 2:45-3:30 45 minutes 3 :00-4:30 90 minutes 5. Avg. To t a l # of Cust. Servjced/Day 145 customers 52 customers Table I: Maximum values d e s c r i b i n g the t r a f f i c c h a r a c t e r - i s t i c s of the recordings c o l l e c t i o n d u r i n g the summer term 1970 0 5 ."r ' ; i . .i .... i. • i 11 ..'•,! • l;.v:!:; : •I • -0 O • I r']''M j:i;|;;:.:j::i:|]!:i{':;! h i ' . S l i r ; : j !U U • i h ' i r l i i i ! !i.li!!LL!i!b.6,'--is-:dIo • •7.-|: : . : I : ' : . r::: • i : . - • UUOOJ-: ' US} Si' (';;: j jU!3}'SA;S;::j:::; : ~ : ! : r u j ' " Q u a d s ' : i ; < r i " ^ V / J j ^ ijiij ' i ' l r n i j i i |:ii;|lU3,'jS;/J'S;: UlOO.i: * is:; (. m i | i Jj,:j : .: ,U:l |::SjJ,3UJO.43,1 10;. j ::: l - -" -1 -1:" :. :t .; I:::I!'H::!:!:: i l l : ' : : ! : : :|': ,|;. . j . :. i. . j;: i(j <? A'Uia.i; uv i ,3U!; 4;; i : ! I i;: i : •i: • i . ^ • i a v i : ; : i ' : . • ! i! i;:;.!;!i!!'M!»Wi1ui''b'ci!!:iii n ijiiiiijj •tiii^'ji l i l i i ' i i i i l i l j i i j j j j i j j j i j i i i j i j i j l r v<Y:\v-:, \ 'irM'ir;TiTrnlir;i'liiTn"""'}nfrnr i;!i!iMii;;ii|i! f J.lJiii! |:::; ! : : :! ....i... • ...Ttii!ii:Tn ii.!4lli JliU !!!n!!;!|!!!i ' i i i i l ' iH ! l l i : ! i jjjjjii: iiil!':!' l i l i i i i i i i i i ! -••••'•••-:;:::iZr:i:r*"-.'- : i : •:::.. r 'Ji IlLi UiJilliiliUi! iLLi'*?^L£.?;ii::.: rrf~ • : i i : : - [ - i T | ; n ^ : ^ - Li I7'-'; j % I •: •: ̂^^xN;vH # t j W WLiLTLiL •: i : i iLL ' L L P ti '"L L i l W P j nr. ; ! ; ; ; r: vr. ;|.;.'L;.pi;i:.:i:.jCi/.N.:..!0p.L liiii .i-re::.:!:,::; ;(Ti cv:.:::; m Iii iii ill i i i I'fill 11n i 11 i llSr!! 1̂ 1 H i III l̂ i j I=t ;t i j !̂ '"cr ::: i • i i ! i ! i ! ! ; : ! l , , . , i ! : i : ; ; ; J ! i i i ! ! ; ! ..;: |:.:: .iilj::;; HI : '.Ji'.\; 11 . i'.; 11' ; .l;.:.iii'Ji 1.3 Comparison of the t r a f f i c flow observed dur i n g the summer s e s s i o n and the winter term The approximate t r a f f i c c h a r a c t e r i s t i c s are shown In diagram 2 durin g the winter term 1970. The data r e s u l t s from an i n q u i r y d u r i n g the l a s t week of September 1970. The corresponding maximum values are: PARAMETER TIME INTERVAL SYSTEM LISTENING ROOM 1. A r r i v a l Rate ( c u s t . / t i m e ) 12:00-2:00 1 _c.u.s_t..Xl-.-D3 12 :30-l:30 1 cust./I.67 min 10:30-11:45 1 cust./2.27 min 2. Departure Rate ( c u s t . / t ime) 12:15-2:30 1 c u s t . / l m i n 11:15-2:30 1 cust./2.1 min 3. Number of SImu1taneous Cus tomers 11:00 21 customers 20 customers 11:45 24 customers 21 customers 1:45 25 customers 22 customers 4. Time Spent =ServIce Time 9:45-10:45 60 minutes 10:30-11:15 45 minutes 11:50-12:^5 55 minutes 4:00-5:00 60 minutes 4:50-5:30 40 minutes 5. Avg. T o t a l Number of Customers Servi ced/Day 380 customers 182 customers Table II: The maximum values d e s c r i b i n g the t r a f f i c c h a r a c t e r i s t i c s of the recordings c o l l e c t i o n d u r i n g the winter term 1970 A c o m p a r i s o n o f t h e summer a n d w i n t e r t r a f f i c f l o w s r e v e a l e d t h e f o l l o w i n g : 1 . The n u m b e r s o f c u s t o m e r s p e r d a y d e m a n d i n g s e r v i c e f r o m t h e r e c o r d i n g s c o l l e c t i o n d u r i n g t h e w i n t e r t e r m i s a m u l t i p l e o f t h o s e i n t h e summer s e s s i o n . C o n s e q u e n t l y , t h e a r r i v a l r a t e , t h e d e p a r t u r e r a t e , a n d t h e number o f s i m u l t a n e o u s c u s t o m e r s a r e a l s o m u l t i p l e s . Of c o u r s e , t h e u t i l i z a t i o n r a t e o f t h e s e r v i c e f a c i l i t i e s w i l l be h i g h e r d u r i n g t h e r e g u l a r w i n t e r t e r m t h a n In t h e s u m m e r . B u t a l s o , I f t h e r e Is a n y c o n g e s t i o n l n t h e s e r v i c e s y s t e m , t h e n t t w i l l become o b v i o u s i n t h e r u s h h o u r s d u r i n g t h e w i n t e r t e r m . 2. D e s p i t e t h e d i f f e r e n t t r a f f i c v o l u m e s o f t h e summer a n d w i n t e r t e r m s , a f u n d a m e n t a l t r a f f i c f l o w b e h a v t o r c a n be g e n e r a l i z e d f o r b o t h s e a s o n s . a ) The b r e a k s b e t w e e n t h e U n i v e r s i t y l e s s o n s i n f l u e n c e s i g n i f i c a n t l y t h e b e h a v i o r o f t h e c u s t o m e r s a r r i v i n g o r l e a v i n g . T h i s c a n be g e n e r a l l y o b s e r v e d , e s p e c i a l 1y d u r i n g t h e f i r s t h a l f o f t h e d a y . F o r i n s t a n c e , t h e a r r i v a l r a t e d e c r e a s e s s h o r t l y b e f o r e t h e b r e a k s b u t I n c r e a s e s d i s t i n c t l y d u r i n g a n d s h o r t l y a f t e r t h e b r e a k s . In c o n t r a s t , t h e d e p a r t u r e r a t e I n c r e a s e s some m i n u t e s b e f o r e t h e b r e a k b u t d e c r e a s e s a g a i n a f t e r t h e b r e a k . T h i s o b s e r v a t i o n I s v a l i d f o r t h e t r a f f i c f l o w o f t h e s y s t e m a n d o f t h e l i s t e n i n g room as w e l l . I t i nd i c a t e s / t h a t s t u d e n t s u s e t h e b r e a k b e t w e e n two l e s s o n s o r a f o l l o w i n g f r e e h o u r f o r a v i s i t t o t h e r e c o r d i n g s c o l l e c t i o n . T h e y a r r i v e d u r i n g a n d s h o r t l y a f t e r one b r e a k a n d l e a v e j u s t b e f o r e o r d u r i n g t h e n e x t b r e a k . b ) The t i m e I n t e r v a l o f t h e maximum t r a f f i c f l o w , as i t i s i n d i c a t e d by t h e maximum a r r i v a l r a t e a n d d e p a r t u r e r a t e , w i l l a p p e a r r o u g h l y b e t w e e n 1 2 : 0 0 a n d 2 : 0 0 . c ) The maximum n u m b e r o f s i m u l t a n e o u s c u s t o m e r s In t h e r e c o r d i n g s c o l l e c t i o n c a n be e x p e c t e d a t 1 1 : 0 0 - 1 1 : 4 5 a n d a t 1 : 3 0 - 1 : 4 5 . d ) On t h e a v e r a g e , c u s t o m e r s t h a t a r r i v e n e a r 1 0 : 3 0 w i l l s p e n d t h e m o s t t i m e ( 45 m i n u t e s ) o f a n y c u s t o m e r s a r r i v i n g . T h o s e who e n t e r t h e l i s t e n i n g room a t t h a t t i m e I n t e n d t o u s e t h e l i s t e n i n g u n i t s p r o v i d e d f o r a p p r o x i m a t e l y 60 m i n u t e s on t h e a v e r a g e . tro-pin OS IP. (0- <0- cu ::<u:: FLcf ffE. +P-- £<U- ::Q-: -uv( : 0 : :©a </>- - - C - "tE 3S ::<tt : « 1 :Q3: -tit fig:  ^ 4 -Ttl- in? sxponen r-e r a repuenc -V- +++? +++4, ++++ 2.5. irre- (TO HEESfcEE! :S.e#,V: j i i j i f t i cons _ce: itie rme: t mrt ttS: o# t3t |-t)Ut:lrpn ne :e+if 1+tOjt ̂::t:R§Effi ipnjie: record icn:g ST£ <?: ithe l i s t e n jhec 4+ icng- :hput- KOOtTV 1 J 1 ) t %J. _ nl UJ I'- • ) -4 s r+ L ' CJ ^. 1 - u/ Lb a - l i J -r i ?!• -U-- 1 Kn- - ) > u 1 1 1 1 1 — to • fa 1 1 vu ifi > • '< ll F i i • c i r t t •1 h* _ J •Vi- OJ * i ' O •fc)1 r= —! -rti •*f UJ Gj- i Li k) 1 T i r Tr 11 i _ iii T | >• • rt \- +J-| UJ uv fD- # O 1 F -J. 1 t/j - 1- c - CSl -uJ - = O M £ • 1 1 T T TT ro -vD • - LI 1 -1 * L r | -jui- i •(/> i u 1 \ ! r l rl i •UJ 1 C/f-r 4-> -F tJ -Tl \l m-t f I 1 I 1 L I J 4H • ; j G> 4- ; i 1 i f fu I M -1 O -> - (>)- - * « 11 l i 11 4-̂ • _i— • Y\ > f I I . c in 1 t 1 T -^T T < 1 T Q 3 - T c- o • 1 L rr ) 9 3 i a J r < 3 O A 1 f 1 Lur \ 3 / \ c 1  _ 1 I 1 1 \ o: i . i . "KV [ >» u T in • : o m ; ; r r [, flj L iJ. | J iL It 1 c tn: ". i m 4) •rr-1 1 m 1 • N CX " C OJ t " - CJ- -QJ. J_l til I U •l 1 . B! i • ±~ 4(U4 1 T i j i r ( J n •rr-c a en n- : ; - 1 1 [ .1. fU L.' +. J 4-J T-i T"i 4_) c 31 i. J ; : I ) 0 m tr .si: • U 4L rfi : : r J I : | n I .•tn >- I r— ! | -u I 10 H L L x L C |! r 1 .u • | n > r • U m i fa A 1 • i 1 m i i_ C 3 11 • • 1 ra 1 11 i ] M i"> <JT "(TT1 1 I .1 ^rr LI | m T T • r r 1 i -C3%- • i 1 •—t LYV J. Il t l o uanl 1 ii r o -/Vi - J . J: _'_L n iC   THE T R A F F I C FLOW MODEL F u n d a m e n t a l l y , t h e s e r v i c e p r o c e s s o f t h e r e - c o r d i n g s c o l l e c t i o n c a n be f o r m u l a t e d a s a n e t w o r k o f s e r v i c e s t a t i o n s w i t h a s t o c h a s t i c I n p u t o f j o b s . E a c h I n p u t Is c o m p o s e d o f t h e j o b d e p a r t u r e p r o c e s s f r o m t h e p r e v i o u s s e r v i c e s t a t e s . In d e t e r m i n i n g t h e t r a f f i c b e - h a v i o r o f t h e j o b s t h r o u g h t h e n e t w o r k , t h e c u s t o m e r s who r e q u I r e j s e r v I c I n g In t h e d i f f e r e n t s t a t e s f o l l o w more t h a n o n e p a t h t h r o u g h t h e n e t w o r k w i t h a p r o b a b i l i s t i c b e h a v i o r . N e v e r t h e l e s s , e a c h a r r i v i n g j o b t o t h e s y s t e m Is d e s c r i b e d by a c o m p l e t e l y o r d e r e d j o b r o u t I ng, wh I c h s p e c i f i e s t h e s e r v i c e c e n t e r s r e q u i r e d t o c o m p l e t e l y p r o c e s s t h e j o b a n d t h e u n i q u e s e q u e n c e In w h i c h t h e y m u s t be e m p l o y e d . The j o b t r a f f i c f l o w o f t h e n e t w o r k c a n be s h o w n In a c o n t l n u o O s f l o w m o d e l . The n o d e s r e - p r e s e n t t h e d i f f e r e n t s e r v i c e s t a t i o n s w i t h t h e f o l l o w i n g n o t a t i o n : 1 [" a r r i v a l s t o t h e s y s t e m 2 I n f o r m a t i o n d e s k 3 s h e l v e s k l i s t e n i ng room 5 d e p a r t u r e s Figure 4: The continuous flow model of the complex s e r v i c e system with f i v e s t a t e s , numbered 1 to 5 The l i n k s c onnecting the nodes i n d i c a t e the p o s s i b l e job flows. For instance, some routings through the may be used In a sequence such as: flow mode 4 £ c y c l e c y c l e |\ <4=> c y c l e c y c l e >=̂ 1 - 2 - 4 - 5 1 - 3 - 4 - 5 1 - 2 - 3 - 4 - 5 1 - 3 - 2 - 4 - 5 1 - /:2 - 4 : £ - 5 l - / : 3 - 4 : / - 5 1 - /:2 - 3 - 2:1 1 - /:3 - 2 - 3:/ 4 4 5 5 e t c . 1. The Statistical Properties of the Continuous Flow Model The flow model is used to study the spread of arriving jobs to different states of the complex service system. The continuous job flow goes from state 1 and ends in state 5. Empirical observations have been made using a questionnaire. For convenience, the approximate behavior generally observed is shown by 100 customers requiring service from the recordings collection ?n several states. The parameters of the probabilistic flow model are: a) The p a r t i a l f l o w s (Fjj's, number of jobs/ti me unit) which give the flows through the relevant links, for Instance, from state (I) to state ( j ) , b) The v o 1 u me s of service demand during a , considered time period (Vj, number of jobs serviced during a time interval) originated by the jobs arrived in each state ( 1 ) . maximum flow VJ = volume of service demand In state ( I ) , ( 1=1,2, .. .5) F.. = partial flow of jobs from state ( I ) J to state (j ), (j=2,3,'i,5) *•) The partial flows Fo^ and F^? could not be observed reliably with the question- naire used. For this purpose, an addition- al more detailed inquiry would have been necessary. Figure 5: The empirically observed flow of jobs re- presented by 100 customers requiring service from the system during a time interval of ca. 100 minutes (system's arrival rate = =1 customer/minute) . As t h e f l o w m o d e l s h o w s , o u t o f 100 p a t r o n s a r r i v i n g w i t h i n a c e r t a i n t i m e p e r i o d ( s t a t e 1 ) , 36 o f t h e m w i l l demand s e r v i c e i n t h e f i r s t s t e p f r o m t h e I n f o r m a t i o n d e s k ( s t a t e 2 ) , a n d 6k o f t h o s e c u s t o m e r s w f l l r e q u i r e s e r v i c e f r o m t h e s h e l v e s ( s t a t e 3 ) . In a s e c o n d s t e p , c u s t o m e r s b e i n g s e r v i c e d e i t h e r a t t h e i n f o r m a t i o n d e s k o r a t t h e s h e l v e s , may m i g r a t e t o a l t e r n a t i v e a c c e s s i b l e s e r v i c e c e n t e r s I f t h e y r e q u i r e a d d i t i o n a l s@r^i<£© f r o m t h e r e . A j o b e n t e r i n g s t a t e 5 ( d e p a r t u r e s ) means t h a t t h e r e i s no l o n g e r a n e e d f o r s e r v i c e f r o m t h e s e r v i c e s y s t e m . A f t e r t h e d e p a r t u r e o f a l l 100 c u s t o m e r s , t h e n u m b e r o f j o b s s e r v i c e d i n e a c h s t a t e i s s t a t e d by t h e v o l u m e o f t h e s e r v i c e demand V j . T h i s demand g i v e s an i n d i c a t i o n a b o u t t h e r e - l a t i v e f r e q u e n c y o f t h e u s e o f e a c h p a r t i c u l a r s e r v i c e f a c i l i t y , an u n b a l a n c e d u s a g e o f t h e s e r v i c e u n i t s w i t h i n t h e s e r v i c e c o m p l e x , o r t h e o r i g i n o f c o n g e s t i o n . The o b s e r v e d j o b f l o w s i n d i c a t e an a p p r o x i m a t e l y b a l a n c e d s e r v i c e demand f o r t h e u s e o f t h e I n f o r m a t i o n d e s k ( 1 1 2 d e m a n d s ) a n d t h e s h e l v e s (98 d e m a n d s ) . The u s e o f t h e l i s t e n i n g room s e e m s t o be r e l a t i v e l y l i g h t (52 demands ) ; S /fHowever , i t m u s t be t a k e n i n t o a c c o u n t t h a t t h e c a p a c i t y o f t h e l i s t e n i n g room Is l i m i t e d by t h e 23 l i s t e n i n g u n i t s i n s t a l l e d . T h i s c a p a c i t y l i m i t a t i o n m i g h t be a r e a s o n f o r c o n g e s t i o n . F o r e x a m p l e , i f 100 customers will pass through the system for service in a time period of about 2 hours of the top t r a f f i c , a demand of 52 services will be created for the listening room. A listening time of ca. -53 minutes on the average will be available for each listening room customer. The playing of one single side of a LP-record takes about 25 minutes. Thus, the time available for each customer may be just sufficient. for listening to both sides of one record. if any congestion will appear within the complex service system, then It will become obvious along the path of maximum job flow which is routing 1-3-4-2-5. 2. The Job Routing Model as a Finite-State Markov Chain We may consider the job routing model by studying an embedded Markov Chain in the study of the complex service system. The basic concepts of the Markov Chain are determined by the "state" of the system and the "state transition". The state jpf,~the..system Is the particular service f a c i l i t y or the exit and departure state currently occupied by the customer. The system changes its state when the customer trans Its from one state to the next specified state. There are five states In the system numbered from 1 to 5. The time between transitions is a random variable determined by the service time distributions related to each single service center. Hence/ we may consider the system to be a finite-state, continuous-time process. If the system has an embedded Markov Chain, then the probability of a transition to state (j) at the next transition, given that the system now occupies state ( i ) , is a function only of (i) and (j) and is not altered by additional knowledge concerning its past behavior. In other words, we may specify a set of conditional probabilities pjj that a system which now occupies state (i) will occupy state (j) after its next transition. A corresponding transition diagram of the system, showing the states and the transition probabilities In the graph below, is derived from the original flow model: Figure 6: The flow model showing the state transition probab11i t ies The graph, f o r Instance, makes p l a i n that when a customer is in s t a t e (2) there Is a 2k% chance to go to s t a t e (3) a f t e r the s e r v i c e completion In the present s t a t e , or to migrate to s t a t e (4) or to s t a t e (5) with the p r o b a b i l i t i e s of 3% and 73%, r e s p e c t i v e l y . A complete d e s c r i p t i o n of the process can be s t a t e d by the t r a n s i t i o n matrix P and by the i n i t i a l p r o b a b i l i t y v e c t o r ( 1 ) ; the l a t t e r determinates the s t a r t i n g s t a t e of the process. The rows of the matrix sum to 1: s S p ? j = they are composed of the t r a n s i t i o n p r o b a b i l i t i e s of a customer in s t a t e ( i ) (row) going to another s t a t e ( j ) (column). The t r a n s i t i o n to a f o l l o w i n g s t a t e ( j ) may happen In n steps (n=l,2,... ). The one-step t r a n s i t i o n matrix P of the process Is given by: s t a t e a f t e r t r a n s i t i o n (n+1) 1 2 3 4 5 st at e af te r tr an si ti on  ( n)  1 0 .36 .64 0 0 st at e af te r tr an si ti on  ( n)  2 0 0 .24 .03 .73 st at e af te r tr an si ti on  ( n)  3 0 .36 0 .50 .14 st at e af te r tr an si ti on  ( n)  k 0 .79 .13 0 .08 st at e af te r tr an si ti on  ( n)  5 0 0 0 0 1 The I n i t i a l s t a t e p r o b a b i l i t y v e c t o r (1) Is (1,0,0,0,0). The t r a n s i t i o n m a t r i x r e p r e s e n t s an a b s o r b i n g c h a i n w i t h t r a n s i e n t s t a t e s f rom 1 t o k and an a b s o r b i n g s t a t e denoted by 5. As l o ng as the p r o ce s s Is In the t r a n s i e n t s e t o f s t a t e s , t t w i l l make s t a t e t r a n s i t i o n s t i l l the a b s o r b i n g s t a t e ts r e a c h e d . Once e n t e r e d the a b s o r b i n g s t a t e , the p r o ce s s w i l l s t a y the re . The p r o b a b i l i t y t h a t such a s t a t e Is e n t e r e d tends t o 1 w i t h an I n c r e a s i n g number o f t r a n s I t t o n ' s t e p s . The m a t r i x v e r s i o n o f an a b s o r b i n g c h a i n agg rega t - ing the t r a n s i e n t and e r g o d l c s e t o f the s t a t e s Is P = I* 7 S t ^ \r " s p i n h I 1 0 ^ where the s u b m a t r t c e s can be I n t e r p r e t e d such a s : 1. Reg ion ( r - s ) . ( s ) = s u b m a t r i x 0: The s u b m a t r i x c o n s i s t s e n t i r e l y o f 0 ' s . 2. Reg ion ( s ) . ( s ) = s u b m a t r i x 0: The p roce s s s t a y s In t r a n s i e n t s t a t e s ; t h a t means, each s t a t e can be reached f rom each o t h e r s t a t e , a n d each s t a t e can be l e f t a g a i n . 3. Region ( s ) . ( r - s ) = submatrix R: represents the process t r a n s i t i o n s from t r a n s i e n t to e r g o d i c s t a t e s . 4. Region ( r - s ) . ( r - s ) = submatrix I: The process has reached the e r g o d i c set of s t a t e s and remains t h e r e . The r e s p e c t i v e submatrix Is represented by an i d e n t i t y matrix of the a p p r o p r i a t e dimensions. Thus, we can w r i t e our t r a n s i t i o n matrix P ?n the new c a n o n i c a l form: 5 1 0 0 0 . 0 1 0 0 .36 .64 0 2 .73 0 0 .24 .03 3 .14 .0 .36 0 .50 4 .08 0 .79 .13 0 where the regions 1,0,R, and Q have been marked o f f . Finally, we will make use of the transition probability matrix for the following questions: 2.1 What is the expected number of visi t s to any state (j) before a customer will leave the service system, given, he is in a present state (i) ? 2.2 What is the probability, a customer ever will v i s i t any state (j) ? Additionally, we will consider briefly the expected number of transitions up to time t which Is represented by a 2.3 Markov Renewal Process. 2.1 The expected number of visi t s to state (j) before a customer will leave the service system, given, he is In ajpresent state (i) We say, the mean of the total number of times the process is In a particular transient state (j) is n../ given, the process starts in state (I). n.. = ET̂ number of vi s i t s to (j) | start tn state ( = i S P(lnvstate (j) on n-th s t e p l ^ a r t i n ^ = l , j + Q f j . + C Q 2 ) j j + (Q 3 ) | j + . . . + To c o m p u t e o n e e l e m e n t n j j , we may a d d u p t h e o r i g i n a l p o s i t i o n ' s c o n t r i b u t i o n , r e p r e s e n t e d by t h e l - m a t r i x , p l u s e a c h o f t h e s t e p s ' c o n t r i b u t i o n i n a c c o r d a n c e t o t h e t r a n s i t i o n p r o b a b i l i t i e s o f t h e Q - m a t r l x . A new e n t r a n c e t o a r e g a r d e d t r a n s i e n t s t a t e c o n t r i b u t e s t o o u r mean o f f r e q u e n c y o f v i s i t s . I f t h e n e w l y o c c u p i e d s t a t e i s a b s o r b i n g , I t c o n t r i b u t e s n o t h i n g , s i n c e t h e p r o c e s s w i l l n e v e r l e a v e a g a i n t h i s s t a t e . We d e t e r m i n e a l l p o s s i b l e r i j j ' s In t h e N - m a t r i x ; N = I + Q + Q 2 + Q 3 + . . . The e x p r e s s i o n I + Q + Q 2 + Q 3 + . i s s u m m a b l e t o ( l -Q)" 1 ; t h u s N = ( I - Q) - 1 1 ) We a p p l y t h e s e r e s u l t s t o o u r e x a m p l e : i-a)> i 2 3 4 1 0 0 0 •0 .36 1 •0 .36 • 0 . 7 9 •0.64 •0.24 1 • 0 . 1 3 0 - 0 . 0 3 - 0 . 5 0 1 1 ) J o h n Kemeny a n d L a u r i e S n e l l , F i n i t e M a r k o v C h a i n s , V a n N o s t r a n d C o m p a n y , I n c . , Nw. Y o r k 1 9 6 3 , p g . 45 f f . The Inverse matrix Is: 1 2 3 4 1 1.125 0.978 0.523 0 1.283 0.335 0.206 0 1.036 1.340 0.701 0 1.148 0.438 1.253 In a proof, the m u l t i p l i c a t i o n of the (l-Q) matrix with Its Inverse (N) has to r e s u l t in the I d e n t i t y ma t r i x I : We see from the N-matHx that, f o r inst a n c e , i f the process s t a r t s in s t a t e ( 2 ) , then It w i l l be tn the same s t a t e (2) an average of 1.283 times, but 0.335 times in s t a t e (3) and 0.206 times in s t a t e ( 4 ) , e t c . S i m i l a r examples e a s i l y can be chosen from the N-matrix. 2.2 The p r o b a b i l i t y , a customer ever w i l l v i s i t s t a t e ( j ) We may wish to know, f o r example, the p r o b a b i l i t y that the customer w i l l be in s t a t e (2) a f t e r n t r a n s i t i o n s i f we know he is In s t a t e (2) at the beginning of the n-t.r.ans 111 on process. For t h i s reason, we d e f i n e a s t a t e probabI11tyIT.(n), the p r o b a b i l i t y that the system w i l l occupy state (j) after n tr a n s i t i o n s , or TTj ( n ) , (n = l , 2, . . .k) = Prob. process in state (j) at n-th t rans i t i on Considering a l l possible realizations of the process, we may employ a probability tree which states a l l possible paths. We obtain the following graphic representation i f we assume the process starts in state (2) for example: 1. trans. 2 . trans • 14 2 4 5 -2 3 -5 •73 process in state (j) after 2 transitions probabI1. p. _. . - *- 0.1101 < S - - J - 0.004 ~- 0.12 ^ 4 i s — 0 . 766 ' / / Figure 7: The probability tree showing the possible paths To f i n d t h e p r o b a b i l i t y o f a c e r t a i n o u t c o m e In n s t e p s ( n = l , 2 , . . . k ) , we a d d t h e w e i g h t s o f a l l p o s s i b l e p a t h s l e a d i n g t o t h i s r e s u l t . The n - t h p o w e r o f t h e o n e - s t e p t r a n s i t i o n m a t r i x s t a t e s t h e c o n d i t i o n a l p r o b a b i l i t i e s t h a t , g i v e n . , , t h e p r o c e s s s t a r t e d i n s t a t e ( f ) , ( r o w s o f t h e . m a t r i x ) , i t w i l l a f t e r n s t e p s be i n s t a t e ( j ) , ( c o l u m n s o f t h e m a t r i x ) . T h i s f o l l o w s f r o m 2 I . ( n ) = 1 i = i 1 T t ( n+l) = JE7 TT , ( n ) p , . , n = 0 , l , 2 , . , . J i»i 1 'J I f we d e f i n e a row v e c t o r o f s t a t e p r o b a b 1 1 1 1 1 e s T ( n ) w i t h e l e m e n t s " j ( n ) , t h e n TT ( n + 1 ) = *T(n)P' , n = 0 , 1 , 2 , . . . S i n c e by r e c u r s i o n " ( l ) = T r ( 0 ) P " (2 ) = ^ ( 1 ) P = 0) P 2 ^ (3 ) = T (2 ) P = T( o) p3 In g e n e r a l , ( n ) = w " ( 0)P n , n = 0 , 1 , 2 , . T h u s , we f i n d t h e p r o b a b i l i t y t h a t t h e s y s t e m o c c u p i e s e a c h o f I t s s t a t e s a f t e r n t r a n s i t ? o n s , T ( n ) , by m u l t i p l y i n g t h e I n i t i a l s t a t e p r o b a b i l i t y v e c t o r M(l) by t h e h - t h p o w e r o f t h e t r a n s i t i o n m a t r i x P . L e t us I l l u s t r a t e t h e s e r e s u l t s by a p p l y i n g t h e m t o o u r e x a m p l e . F o r i n s t a n c e . I f t h e p r o c e s s s t a r t s In s t a t e ( 1 ) , i t w i l l be i n s t a t e (k) a f t e r 2 t r a n s i t i o n s w i t h a p r o b a b i l i t y o f 0 . 3 3 0 8 i n a c c o r d a n c e t o t h e P 2 - m a t r i x . The c a l c u l a t i o n i s : . 0 . 3 6 . 6 4 . 0 . 0 0 0 . 2 4 . 0 3 . 7 3 0 . 3 6 0 . 5 0 . 1 4 0 . 7 9 . 1 3 0 . 0 8 0 0 0 0 1 0 . 3 6 . 6 4 . 0 0 0 . 2 3 0 4 . 0 8 9 . 3 3 0 8 . 3 5 2 4 0 0 . 2 4 . 0 3 . 7 3 0 . 1 1 0 1 . 0 0 4 . 1 2 . 7 6 6 0 . 3 6 0 . 5 0 . 1 4 0 . 3 9 5 . 1 5 1 4 . 0 1 0 8 . 4 4 2 8 0 . 7 9 . 1 3 0 . 0 8 0 . 0 4 6 7 . 1 9 . 0 8 9 . 6 7 4 9 0 0 0 0 1 o o 0 P 2 = 0 1 ;a I n , t h e 3 - s t e p , o r g e n e r a l , t h e n - s t e p p r o b a b 1 1 i t ? e s c a n be I n t e r p r e t e d s i m i l a r l y . W i t h a n I n c r e a s i n g n u m b e r o f t r a n s i t i o n s , t h e p r o c e s s t e n d s t o be i n t h e f i n a l s t a t e ( 5 ) w i t h o u t a n y r e g a r d f r o m w h i c h o r i g i n a l s t a t e t h e p r o c e s s s t a r t e d . T h i s t r e n d c a n be e a s i l y o b s e r v e d by t h e P n - m a t r ! c e s s u c h a s : P3 a 0 .2924 .0983 .0501 .5591 0 .0962 .0420 .0053 . 8565 0 .0630 .0962 .0875 .7532 0 .1383 .0228 .0962 . 7427 0 0 0 0 1 0 .0748 .0766 .0579 . 7902 0 .0193 .0238 .0239 .9330 0 .1040 .0265 .0499 .8197 0 .0842 .0457 .0155 .8546 0 0 0 0 1 0 .0143 .0065 .0065 .9723 0 .0049 .0022 .0020 .9909 0 .0090 .0055 .0046 .9811 0 .0077 .0039 .0045 .9839 0 ' 0 0 0 1 We w a n t t o know t h e p r o b a b i l i t i e s ; a c u s t o m e r e v e r w i l l v i s i t a n y c o n s i d e r e d s t a t e ( j ) i f he s t a r t s f r o m a s t a t e ( t ) . f n j s h a l l be t h e p r o b a b i l i t y t h a t , s t a r t i n g f r o m s t a t e ( 1 ) , t h e f i r s t r e t u r n t o s t a t e ( i ) o c c u r s a t t h e n - t h t r a n s i t i o n . We s a y f j j " P J J A2) ( 2 ) . ( 1 ) f . . = P . . " f . . P . . J J J J J J J J r ( n ) _ ( n ) Al) „ ( n - l ) . ( 2 ) „ ( n - 2 ) f ( n - l ) . r . . - p . . - t . . p . . - t . . p . . - . . . - t . . p . . J J J J J J J J J J J J J J J J In g e n e r a l * ( n ) _ ^ f ( k ) n ( n - k ) f ( 0 ) _ , f j j " f J J P J J ' f J J " 1 r ( n ) _ „ ( n ) An-k) ( n ) J J ~ j J " £ i - J J J J I f t h e s y s t e m s t a r t s In s t a t e ( I ) , and we a r e I n t e r e s t e d In t h e f i r s t p a s s a g e t h r o u g h s t a t e ( i ) , t h e n - ( n ) ( n ) y An-k) ( n ) 9 . ' j ' j K=2 J J A p p l i e d t o o u r c a s e , t h e f j j ^ " p r o b a b i l i t i e s a r e i d e n t i c a l t o t h e P j j ' s . We o b t a i n t h e f ( n ) - p r o b a b i l i t i e s by 2 ) W. F e l l .e_r-,-- I n t r o d u c t I on t o P r o b . T h e o r y , W i l e y & S o n s , ' " ' I n c . " , New Y o r k 1 9 5 7 , P ; 352 f . ( 2 ) 0 . 2 3 0 4 . 0 8 9 0 . 3308 . 3524 0 . 1 . 1 0 1 . 0 0 4 0 . 1 2 0 0 . 0 3 6 0 0 . 3 9 5 0 . 1 5 1 4 . 0 1 0 8 . 3 0 2 8 0 . 0 4 6 8 . 1 8 9 6 . 0 8 8 7 . 5 9 4 9 0 0 0 0 0 T h a t m e a n s , i f t h e p r o c e s s s t a r t s f o r e x a m p l e i n s t a t e ( 1 ) , t h e f i r s t r e t u r n i n 2 s t e p s t o s t a t e ( 1 ) w i H n e v e r o c c u r , h o w e v e r , i t w i l l go t h e f i r s t t i m e t o t h e s t a t e s ( 2 ) , ( 3 ) , ( 4 ) , and ( 5 ) w i t h t h e p r o b a b i l i t i e s o f 2 3 % , 9 % , 3 3 % , a n d 3 5 % . We o b s e r v e , t h e p r o c e s s t e n d s t o be i n t h e ^ . f i n a l s t a t e ( 5 ) a f t e r n>2 t r a n s i t i o n s ; t h e p r o b a b i l i t i e s d i m i n i s h t h a t t h e p r o c e s s w i l l be i n t h e s t a t e s ( 2 ) , ( 3 ) o r ( 4 ) , as I t i s shown In t h e f\V a n d f.V m a t r i c e s f\V - P.V - fiV P.V - f.V P<7> 'J 1J U JJ 1J JJ : ( 3 ) . _ 0 . 2 5 2 8 . 0 0 1 5 . 0 5 0 0 . 5 5 9 1 0 . 0 9 6 2 . 0 0 6 0 . 0 0 5 0 . 0 9 0 5 0 . 0 2 3 4 . 0 9 6 2 . 0 4 3 0 . 3 1 0 4 0 . 0 5 1 4 . 0 0 3 1 . 0 9 6 0 . 0 6 7 8 0 0 0 0 0 = P (4) U f ( l ) n ( 3 ) " T, . P . . > J JJ - <\v (2) , (3 ) P . . ~ f . . JJ • J (1) P . . JJ 0 .0.149 .0015 .0286 0720 0 .0072 .0002 .0105 0870 = 0 .0269 . 0035 .0010 1800 0 .0031 .0045 . 0070 1119 0 0 0 0 0 FI n a i l y , t h e p r o b a b i i i 11es t h a t a c u s t o m e r w i n v i s i t a s t a t e ( j ) , (=2,3, . . . 5 ) g i v e n , he f r o m a n y s t a t e ( i ) , (1=1,2, . . . 5 ) I s e x p r e s s e d by t h e sum o f f » , = ̂ L i f ( ? ^ . F r o m o u r r e s u l t s , we may o b t a i n ( n ) 'J mi 'J w h i e h I s 4- ( n ) ; f n ^ f n 'J n=l 'J 0 . 8581 . 7320 .4094 .9735 0 .2135 . 2503 . 1655 .9435 0 . 8035 .2511 .5548 .9332 0 . 8913 .3272 . 1923 .8546 0 0 0 0 1 Because of the n e g l i g i b l e c o n t r i b u t i o n of the p r o b a b i l i t y that a customer w i l l v i s i t a s t a t e the f i r s t time a f t e r n>4 t r a n s i t i o n s , we may o b t a i n ft- = J?: F ! - } °N T H E B A S L S °F F , . =S F { ^ ) • i j i s in an approximation: f , . = f\? ̂  = I j " - - l I j 0 .86 .74 .41 1 0 .22 .26 .17 1 0 .81 .26 .66 1 0 .90 .33 .20 1 0 0 0 0 1 In our case, every customer w i l l a r r i v e in s t a t e (1) as there is no a l t e r n a t i v e a r r i v a l s t a t e in the system regarded. Thus, we may c o n s i d e r j u s t the f^. , ( j = 2,3,4,5) from the f i r s t row of the matrix above as here are presented the p r o b a b i l i t i e s of ever going to any s t a t e ( j ) , given, the customers s t a r t in s t a t e ( 1 ) . 2 . 3 M a r k o v R e n e w a l P r o c e s s We may be I n t e r e s t e d In t h e e x p e c t e d number o f t r a n s i t i o n s o c c u r r i n g In e a c h p a r t i c u l a r s t a t e , a n d In t h e s y s t e m a s w e l l , up t o t i m e T . Our q u e s t i o n Is d e s c r i b e d by a M a r k o v r e n e w a l p r o c e s s w h i c h r e g i s t e r s t h e n u m b e r s o f t r a n s i t i o n s I n t o e a c h s t a t e In a c e r t a l n t i m e i n t e r v a l ( 0 , T ) , when t h e t r a n s i t i o n t i m e s o f t h e e v e n t s a r e I n d e p e n d e n t l y d i s t r i b u t e d p o s i t i v e r a n d o m v a r i a b l e s w i t h known p r o b a b i l i t y p a t t e r n . A t y p i c a l s a m p l e f u n c t i o n o f t r a n s i t i o n s I n t o s t a t e ( 1 ) t s s k e t c h e d b e l o w : / n , ( T ) . 6 5 4 3 2 1 + - 0 t . — t . t 1 + t 2 - ^ k t 1 + t2*t3-< K t 1 + t2 + t3 + tt| — -t1 + t2 + t3+tI+ + t5 V F i g u r e 8 : A s a m p l e f u n c t i o n o f t r a n s i t i o n s I n t o s t a t e ( I ) In our case, the times between the successive transitions are random variables denoted by t. . , where the index (I) referres to the regarded service state; the second index (k) indicates the k-th successive ?ntertransition time which elapsed between the (k - l)-th and k-th transition. If nj(T) represents the number of transitions into state ( i ) , (1=1,2,...5) during the time interval 0 to T, then ^n j (T),TM)| is a general renewal process (renewals = transitions into the same state) considering the particular state (1). We want; to determi ne the expected number of transitions into each state (i) up to time T. Therefore, we define f i r s t the distribution of the amount of time until the next transition occurs in relation to each service state. The following sketch shows a state (i) and two alternative successive states j ( l) and j(2), or In general j(x),(x=l,2). Given, the process occupies state (1) at the present time, from there it will migrate either to state j ( l ) or to state j(2) with the probabilities of p..... or P..,0̂ : I] (2) a f t e r s e r v i c e completion tn s t a t e ( i ) , the next t r a n s i t - ion w i l l occur i n one of the succes- s i v e s t a t e s j ( x $ , (x=l,2) with a probab i11ty of p IJ(x) Figure;,;,9: The t r a n s i t i o n from s t a t e ( i ) to two a l t e r n a t i v e s u c c e s s i v e s t a t e s j ( l ) and j ( 2 ) We d e f i n e the f o l l o w i n g : A t r a n s i t i o n •> is the job flow from the p r e s e n t l y occupied s t a t e ( I ) , (1=1,2,...5) to the s u c c e s s i v e s t a t e ( j ) , (j=2,3,4,5); the t r a n s i t i o n occurs tnto s t a t e ( j ) . t j ( x ) •> ts the p r o b a b i l i t y that the next t r a n s i t i o n w i l l be i n t o s t a t e j ( x ) , given that the process has j u s t , entered s t a t e ( I ) : ' i j C x) = p ( ] " > J ( x ) 1 ] ] Ij (x) > is the p r o b a b i l i t y that a f t e r making a t r a n s i t i o n i n t o s t a t e ( I ) , t h e p r o c e s s n e x t makes a t r a n s i t i o n i n t o s t a t e j ( x ) In a n amount o f . t i m e <_ T . p (T ) > 0 , I , j ( x ) = 1,2, . . . 5 , U < x ) T > 0 5~! P = l f - ? ( x ) i , j ( x ) = 1,2, . . . 5 F ( T ) > i s t h e c o n d i t i o n a l p r o b a b i l i t y t h a t i j ( x ) t h e j , o b w i l l t r a n s i t w i t h i n an amount o f t i m e ( T ) , g i v e n t h a t t h e p r o c e s s h a s j u s t e n t e r e d s t a t e ( I ) a n d w i l l n e x t e n t e r o n e o f t h e s u c c e s s i v e s t a t e s j ( x ) . -F-' , ( T ) = prtime< T | ! - - > J ( x ) l - i j ( x ) L — J T j ( x ; F l j ( x ) = p l j ( x ) F , . , s h o w s t h e " d I s t r I b u 1 1 on o f t h e I n t e r t r a n s i t i o n l j ( x ) t i m e s (= t h e a m o u n t o f e l a p s e d t i m e u n t i l t h e n e x t t r a n s i t i o n o c c u r s . I n s t a t a . j ( x ) , g i v e n t h a t t h e p r o c e s s h a s j u s t e n t e r e d s t a t e ( 1 ) ) . The f n t e r t r a n s i t ! o n t i m e s r e l a t e d t o a n y s t a t e ( j ) a r e d e t e r m i n e d by t h e a r r i v a l p r o c e s s and t h e s e r v i c e p r o c e s s i n t h e p r e v i o u s s t a t e ( I ) , t h e r o u t i n g p r o b a b i l i t i e s f r o m s t a t e ( ? ) t o s t a t e ( j ) , a n d by p o s s i b l y o c c u r r i n g c o n g e s t i o n c o n d i t i o n s i n s t a t e ( j ) . In o r d e r t o d e t e r m i n e t h e d e n s i t y f u n c t i o n o f t h e I n t e r t r a n s i t i o n t i m e s In a n y s t a t e ( i ) , we d e f i n e H j ( . ) by : H . ( T ) = 2 J F . . , , ( T ) . p , . , . = J S p . . , ( T ) 1 j« 0 , J ( X ) ! J ( X ) fr0 • J c x ) T >_ 0 i = a n y s t a t e ; ( 1 , 2 , . . . 5 ) j ( x ) = a n y s u c c e s s i v e s t a t e o f ( 1 ) , ( j ( x ) = 2 , 3 , 4 , 5 , , ) I f we r e g a r d o n e p a r t i c u l a r s t a t e ( 1 ) , t o e a c h p o s s i b l e t i m e I n t e r v a l ( t ) w h i c h e l a p s e s b e t w e e n two a r r i v a l s , we may a s s o c i a t e t h e p r o b a b i l i t y d e n s i t y o f i t s o c c u r r e n c e . We d e n o t e t h e p r o b a b i l i t y by h . ( t ) : d h . ( t ) = H . ( t ) , f o r t>0 1 1 d t f h j ( t ) = 1 t=0 We o b t a i n t h e d e n s i t y f u n c t i o n s H . ( t ) ' s o f t h e I n t e r - t r a n s l t l o n t i m e s f o r e a c h s e r v i c e s t a t e by s i m u l a t i o n ( s e e c o m p u t e r o u t p u t ) . T h o s e s i m u l a t e d r e s u l t s c o n s i d e r t h e s e r v i c e c o n d i t i o n s o f t h e p r e c e d i n g s t a t e s a n d t h u s p r o v i d e t h e d e n s i t y f u n c t i o n o f t h e a c t u a l i n t e r - t r a n s l t i o n t i m e s . We a s s u m e t h e s i m u l a t e d d e n s i t y f u n c t i o n s i n t h e f o l l o w i n g . I f we c o n s i d e r a l l s u c c e s s i v e t r a n s i t i o n s o f t h e s t a t e ( ! ) d u r i n g t h e t i m e I n t e r v a l ( 0 , T ) i n a c h a i n , t h e f i r s t t r a n s i t i o n w i l l h a v e b e e n © c c u r e d a f t e r t i m e i n t e r v a l t ^ j . j w i l l h a v e b e e n p a s s e d , t h e s e c o n d t r a n s i t i o n a f t e r t i m e t - ^ j j + t 2 ( p , a n d t h e y - t h t r a n s i t - Ion a f t e r t i m e ^ t ^ ( f ) . L e t N j ( T ) be t h e e x p e c t e d number o f r e n e w a l s ( t r a n s i t i o n s ) I n t o a n y p a r t i c u l a r s t a t e ( i ) up t o t i m e T . |f t h e f i r s t t r a n s i t i o n o c c u r s a t t i m e t , t h e n t h e e x p e c t e d n u m b e r o f t r a n s i t i o n s In t h e r e m a i n i n g t i m e up t o T i s n ( T - t ) , a n d s u m m i n g o v e r a l l p o s s i b l e v a l u e s f o r t , we o b t a i n r ©a N . ( T ) = / [ l • n f ( T - t ) ] d h . ( t ) + o f n | ( t ) The t e r m [ l + N j ( T - t ) J Is t h e e x p e c t e d number o f t r a n s i t - i o n s i n t h e t i m e T i f t h e f i r s t t r a n s i t i o n o c c u r s a t time t (0<_t<T)/ the p r o b a b i l i t y of t h i s event being d h j j j . The second sum is the p r o b a b i l i t y that the f i r s t t r a n s i t i o n w i l l exceed T time u n i t s . If we denote the expected number of t r a n s i t i o n s 5 In the s,.y s t e m by N(T) ( = ̂ j of expected number <»1 of t r a n s i t i o n s In each s t a t e ( i ) up to time T ) , we d e f i n e { N ( T ) , T > U } = <£ n j ( T ) . It may be of i n t e r e s t to know the s t a t e of the process at each time po i n t ; t h i s i s d e s c r i b e d by a semi-Markov process. We say: S(o) > is the i n i t i a l s t a t e of the process. A f t e r the n-th t r a n s i t i o n / the process is in the s t a t e S ( n ) . The process with the the t r a n s i t i o n s t a t e s S(n), (n=l/2,...5) Is a Markov Chain with t r a n s i t i o n probab1111 i es P j j . Z(T) > ts the s t a t e of the process at time T. If we know the I n i t i a l s t a t e S(o) of the process and the expected number of v i s i t s o c c u r r i n g in each s t a t e (I) up to ttme T which Is d e s c r i b e d by the Markov renewal process/ then we can a l s o determine the semi- Markov process £ z ( T ) , T >_ o|/ or , £ s ( o ) / N ( t ) / N ( t ) / . . . N ( t ) / t>0^ = J Z ( T ) / T 2 u j ^ where S(o) is the i n i t i a l s t a t e , and the N . ( t ) ' s , (i = l , 2 , . . . 5 ) i n d i c a t e which s t a t e ( i ) i s occupied at the N-th t r a n s i t i o n . 3. R e s t r i c t i o n s of the Markov Assumptions tn the Model In our example, each s i n g l e s e r v i c e c e n t e r is Interconnected to a s e r v i c e network. In s t u d y i n g net- works, the departure processes from the s e r v i c e c enters play an Important r o l e . In turn, they are components of a r r i v a l processes to other s e r v i c e f a c i l i t i e s . For instance, one of the d i f f i c u l t i e s encountered Is s t a t i s t - i c a l dependence tn the departure processes from the s e r v i c e s t a t i o n s . A second c o m p l i c a t i o n Is the presence of time dependent queue lengths at the s e r v i c e s t a t i o n s . The w a i t i n g times encountered by a job at the d i f f e r e n t s e r v i c e s t a t i o n s on i t s routings are, In g e n e r a l , not Independent. The s t e a d y - s t a t e departure process from a poIsson-exponentI a 1 s e r v i c e stage has been s t u d i e d by Burke. 3^ Burke proved that the departure process from a Polsson-exponential s e r v i c e s t a t e is i t s e l f Poisson. The s t e a d y - s t a t e mean departure 'hate i s the same as the mean a r r i v a l rate so that the departure and a r r i v a l 3) P.J. Burke, The Output of a Queueing System,' Operations Research,4, 699-704, Dec. 1956 p r o c e s s e s a r e I d e n t i c a l . B u r k e ' s r e s u l t s a p p l y t o n - c h a n n e l s e r v i c e s t a t e s w i t h t h e q u e u e d i s c i p l i n e a r b i t r a r y e x c e p t t h a t a l l c u s t o m e r s r e m a i n i n t h e s y s t e m u n t i l t h e y h a v e b e e n s e r v i c e d . F r o m t h i s f o l l o w s , t h e f u n d a m e n t a l a s s u m p t i o n s o f o r d i n a r y q u e u i n g t h e o r y a r e v i o l a t e d i n q u e u i n g n e t w o r k s , e x c e p t when t h e n e t w o r k d e f i n i t e l y s h o w s P o I s s o n - e x p o n e n t I a 1 p r o p e r t i e s . C e r t a i n l y , w h e t h e r t h e d e p e n d e n c e p h e n o m e n a w i l l h a v e a n e f f e c t on t h e s y s t e m f l o w s t a t i s t i c s d e p e n d s u p o n t h e n e t w o r k c h a r a c t e r i s t i c s a n d p a r a m e t e r s . I n t u i t i v e l y , o n e w o u l d e x p e c t t h a t t h e " p a f a ^ e t e r s ; . o f t h e n e t w o r k , s u c h a s t h e number o f s e r v i c e s t a t ! o n s > t h e d e g r e e s o f u t i l i z a t i o n , a s w e l l a s t h e f l o w s t r u c t u r e may be d e t e r m i n a n t s o f i m p o r t a n c e f o r t h e d e g r e e o f d e p e n d e n c e o f t h e n e t w o r k c h a r a c t e r i s t i c s . . - D o u b t l e s s , o u r a s s u m p t i o n s i n r e s p e c t o f t h e v a l i d i t y o f t h e M a r k o v t a n p r o p e r t i e s i n c o n t i n u o u s t i m e f o r t h e s e r v i c e n e t w o r k h a v e t o be r e g a r d e d c r i t i c - a l l y . C e r t a i n l y , t h e y a r e v i o l a t e d u n d e r a p u r e t h e o r e t i c a l p o i n t o f v i e w b e c a u s e o f a t l e a s t two r e a s o n s : a ) The s e r v i c e t i m e d i s t r i b u t i o n c o n c e r n i n g t h e l i s t e n i n g room d o e s n o t f i t an e x p o n e n t i a l f u n c t i o n . R a t h e r , I t s e e m s t h a t t h e d i s t r i b u t - i o n o f t h e l i s t e n i n g t i m e s Is i n f l u e n c e d essentially by the duration of listening for one, two, or more sides of a LP-record. b) The queue formation which may occur at the information desk contradicts the assumption of Independency of the input process. However, If we are conscious\of those restrictions in our Markov assumptions, under approving circumstances we may accept such an approach as a kind of "practical solution". For instance, as it is shown in the results of the later simulation, the distribution of the service time considering the total service system may s t i l l be accepted as exponentially distributed (table 15, computer output). This fact might be considered as a kind of proof that the Markov properties are dominant in terms of the flow characteristics within the service network. S I M U L A T I O N OF THE MODEL The f l o w m o d e l / d e v e l o p e d , I n I t s b a s i c p r o p e r t i e s by o b s e r v a t i o n s , was s i m u l a t e d on a c o m p u t e r In t h r e e v a r i a t i o n s i n o r d e r t o o b t a i n m o r e a p p l i c a b l e r e s u l t s f o r e v a l u a t i o n . The f l o w m o d i f i c a t i o n s w e r e p e r f o r m e d by t h e " G e n e r a l P u r p o s e S i m u l a t i o n S y s t e m / 3 6 0 / ( G P S S / 3 6 0 ) " . T h e y c o m p r i s e d m o d i f i e d s y s t e m ' s a r r i v a l s t r e a m s and o n e o r two s e r v e r s a t t h e i n f o r m a t i o n d e s k , s u c h a s In p a r t i c u l a r : a ) an i n t e r a r r i v a l t i m e o f 3 m i n u t e s a n d o n e s e r v e r e q u i v a l e n t t o a l o w / m o d e r a t e t r a f f i c f l o w In t h e m o r n i n g b e t w e e n 8 : 3 0 a n d 1 0 : 0 0 a n d t n t h e a f t e r n o o n a f t e r h o ' c l o c k ( w i n t e r t e r m ) , b) an i n t e r a r r i v a l t i m e o f 2 m i n u t e s a n d 1 s e r v e r d e s c r i b i n g a f o r c e d t r a f f i c f l o w a p p r o x i m a t e l y b e t w e e n 1 0 : 0 0 a n d 1 2 : 0 0 a n d 2 : 0 0 a n d 4 : 0 0 o ' c l o c k / r e s p e c t i v e l y / a n d c ) an I n t e r a r r i v a l t i m e o f 1 m i n u t e a n d two s e r v e r s r e p r e s e n t i n g an e x t r e m e r u s h t r a f f i c s i t u a t i o n w h i c h may a p p e a r , d u r i n g t h e n o o n h o u r s b e t w e e n 1 2 : 0 0 a n d 2 : 0 0 . The arrivals of customers were generated in state (1) of the flow model. The job routing to the different service stations were determined in a probabilistic sequence as it has been shown in the flow model. A flow chart of the simulation model is out- lined on the following page. R A W D O M G E N E R A T I O W OF" A R R I v A l - 5 a) 3 min./l server b) 2 min./l server c) 1 m?n./2 servers S.TG •STORAGE. •SHELVES1; A U U M 6 O C A P A C I T Y O P 100 UWnlfS STORAGE ' c i S T E N f t J © R O O M " L i H , C A P A C I T Y O F 2 3 L t M | T 5 Z3 U M M S Figure 10: The simulation model The s i m u l a t e d s p r e a d o f t h e j o b f l o w s a n d t h e a s s o c i a t e d d a t a was s a v e d i n t a b l e s a n d p r e s e n t e d i n a s t a t i s t i c a l o r d e r . The t a b u l a t i o n g a t h e r e d t h e n u m b e r o f o c c u r e n c e s i n d e f i n e d f r e q u e n c y c l a s s e s . G e n e r a l s t a t i s t i c s , f o r I n s t a n c e , t h e m e a n , t h e s t a n d a r d d e v i a t i o n , t h e p e r c e n t a g e o f o c c u r e n c e s i n e a c h f r e q u e n c y c l a s s h a v e b e e n c a l c u l a t e d . The i n f o r m a t i o n c o n t e n t o f t h o s e t a b l e s i n c l u d e d t h e f r e q u e n c y d i s t r i b u t i o n s o f t h e i n t e r a r r i v a l t i m e s , t h e number o f a r r i v a l s d u r i n g a n i n t e r v a l o f 10 m i n u t e s , t h e t r a n s i t t i m e s , t h e number o f j o b s w a i t i n g f o r s e r v i c e , a n d t h e number o f j o b s o c c u p y i n g s i m u l t a n e o u s l y a c e r t a i n f a c i l i t y . T a b l e s w e r e m a i n t a i n e d f o r e a c h s i n g l e f a c i l i t y s u c h a s t h e I n f o r m a t i o n d e s k , t h e s h e l v e s , t h e l i s t e n i n g r o o m , b u t a l s o , t h e ' r e c o r d i n g s c o l l e c t i o n ' , a n d t h e ' s y s t e m ' . The ' r e c o r d i n g s c o l l e c t i o n ' i s u n d e r s t o o d a s t h e c o m b i n - a t i o n o f t h e I n f o r m a t i o n d e s k p l u s t h e s h e l v e s ; t h e ' s y s t e m ' c o m p r i s e d a l l t h r e e f a c i l i t i e s . The f o l l o w i n g s k e t c h may d i s p l a y some i n t e r r e l a t i o n s h i p s d e s c r i b e d a b o v e : Arr i v a l s Fac i 1 i ty / / -" I nformat ? on 7/7 7 / Storage "Shelves" / / / / ' S t o r a g e / / / " L i s t e n i n g / Room" / . Departures "Recordings j! C o l l e c t i o n " 1 " S e r v l c e 7 System" Simulated s t a t i s t i c s a v a i l a b l e of V77m J each s i n g l e s e r v i c e center ( i n f o r m a t i o n desk, s h e l v e s , l i s t e n i n g room) the recordings c o l l e c t i o n ( Information desk plus s h e l v e s ) the s e r v i c e systern ( i n f o r m a t i o n desk plus shelves plus 1 i stenIng room) In a d d i t i o n , the s i m u l a t o r maintained general i n f o r m a t i o n which pe r t a i n e d to f a c i l i t i e s , s t o r ages, and queues. The Information contents of the t a b l e s have been d i s p l a y e d g r a p h i c a l l y to achieve a f a s t e r and more con- venient understanding. MEASUREMENT AND EFFECTS OF STATISTICAL PROPERTIES ON THE SERVICE NETWORK UNDER VARIOUS SIMULATION CONDITIONS The objective Is to gather the analytic results of the simulation for arguments; they will be formulated In graphs as an approach of measurement and evaluation. 1. The Information Desk Jobs requiring service from the Information desk may be concerned with a l l kind of questions In respect to the recordings collection or the listening room. They include the treatment of new applications, the registrations of loaned record.^ the acceptance and the reshelvlng of returned records. All jobs are handled in a f i r s t - i n first-service order except those dealing with reshelvlng that can be saved for periods of lower employment. However, in the simulation, ajgenera 1 i zed f i r s t - l n first-service pattern was assumed without any exception for a l l kind of desk jobs. By this proposition, the simulation could be simplified. This approach involved that returned records were available Immediately for the new use, but also. 2̂0 t h a t t h e w a i t i n g t i m e s i n q u e u e t u r n o u t t o be s l i g h t l y l a r g e r . C o n s e q u e n t l y , t h e a s s u m p t i o n made e m p h a s i z e s c o n g e s t i o n o f j o b s w a i t i n g f o r d e s k s e r v i c e . In V K H a g r a m 1 1 , t h e a v e r a g e number o f j o b a r r i v a l s p e r 10 m i n u t e s t o t h e i n f o r m a t i o n d e s k and l i k e w i s e , t h e a v e r a g e t r a n s i t t i m e o f t h e j o b s ( w a i t i n g t i m e i n q u e u e p l u s s e r v i c e t i m e ) i s shown i n r e l a t i o n t o t h e a v e r a g e number o f c u s t o m e r s e n t e r i n g t h e s e r v i c e s y s t e m d u r i n g t h e same i n t e r v a l . A r r i v a l s t o t h e I n f o r m a t i o n d e s k a r e o r i g i n a t e d by t h e a r r i v a l s f r o m o u t s i d e a n d by t h e i n t e r n a l a r r i v a l s f l o w i n g f r o m t h e s h e l v e s a n d f r o m t h e l i s t e n i n g r o o m t o t h e d e s k . The i n t e r n a l s h a r e o f t h e t o t a l number o f d e s k j o b s i s a m u l t i p l e o f t h e e x t e r n a l j o b c o n t r i b u t i o n a n d c a u s e s a n o n - l i n e a r b e h a v i o r o f t h e d e s k a r r i v a l -f, f u n c t i o n . ' : The w a i t i n g t i m e i n c r e a s e s c o n s i d e r a b l y w i t h a h i g h e r s y s t e m ' s a r r i v a l r a t e , w h i l e t h e a v e r a g e d e s k s e r v i c e t i m e i s c o n s t a n t . I f t h e r e i s o n l y o n e s e r v e r In a c t i o n , t h e w a i t i n g t i m e may amount 3 - 4 0 0 % o f t h e a c t u a l s e r v i c e t i m e ; t h i s i s v a l i d In t h e c a s e o f t h e h i g h e s t s y s t e m ' s a r r i v a l r a t e o f 1 a r r i v a l / m i n u t e . Under same c o n d i t i o n s , 2 s e r v e r s on duty would reduce the w a i t i n g time to approximately 100% of the pure s e r v i c e time. There w i l l be no w a i t i n g time %n queue unless the system's a r r i v a l rate i s l a r g e r than 5 a r r i v a l s / 1 0 minutes. The extent of desk congestion i s represented by the area of time delay d e p i c t e d in diagram 11 . 2. The Shelves In the s i m u l a t i o n , the shelves have been con- s i d e r e d as a storage with the a b i l i t y to s e r v i c e a l i m i t ed number of job requests s i m u l t a n e o u s l y at each time. Job requests may be the s e l e c t i o n of recordings f o r l i s t e n i n g , or general i n t e r e s t of info r m a t i o n f o r the recordings a v a i l a b l e . Even under c o n d i t i o n s of rush t r a f f i c , there n e i t h e r appears congestion in terms of jobs crowding the s h e l v e s , nor can there be observed a s e r v i c e time delay.  3 . The L i s t e n i n g Room J o b s a r r i v e t o t h e l i s t e n i n g f a c i l i t y w i t h t h e i n t e n t i o n o f l i s t e n i n g t o r e c o r d i n g s p r e v i o u s l y p i c k e d up f r o m t h e s h e l v e s . T h e r e Is a l i m i t e d number o f 23 l i s t e n i n g u n i t s a v a i l a b l e . C u s t o m e r s f i n d i n g no v a c a n c y / u s u a l l y l e a v e t h e s e r v i c e s y s t e m , o r t h e y may s p e n d some more t i m e a t t h e s h e l v e s w a i t i n g f o r t h e n e x t v a c a n c y . The l i s t e n i n g room i s t o be c o n s i d e r e d a s a s t o r a g e w i t h l i m i t e d c a p a c i t y . In t h e s i m u l a t i o n / c u s t o m e r s who f i n d no v a c a n c y a r e d e s c r i b e d a s d i s s a t i s - f i e d c u s t o m e r s . H o w e v e r , I n s t e a d o f l e a v i n g , t h e y w i l l e n t e r an I m a g i n e d r e s e r v e l i s t e n i n g room e q u i v a l e n t t o t h e r e a l l i s t e n i n g room w i t h t h e same a s s u m e d s e r v i c e f e a t u r e s . T h u s , u n d e r v a r i e d s y s t e m ' s a r r i v a l r a t e s , t h e t r a f f i c f l o w t o t h e r e s e r v e l i s t e n i n g room r e - p r e s e n t s d i s s a t i s f i e d c u s t o m e r s . In e s s e n c e , t h e r e a p p e a r s a n I n t e r e s t c o n f l i c t b e t w e e n a h i g h u t i l i z a t i o n o f t h e p r o v i d e d f a c i l i t i e s a n d t h e r a t e o f "sa.t'lS;€%e*dUcurstomers u n d e r c h a n g i n g t r a f f i c d e n s i t i e s . I f e v e r y c u s t o m e r I n t e r e s t e d i n l i s t e n i n g s h a l l be a b l e t o f i n d a v a c a n c y e v e n d u r i n g p e a k t r a f f i c p e r i o d s , r e l a t i v e l y many l i s t e n i n g u n i t s w i l l be u n u s e d d u r i n g l o w t r a f f i c . F l u c t u a t i o n s o f t h e t r a f f i c d e - p e n d In p a r t i c u l a r u p o n t h e c o n s i d e r e d t i m e i n t e r - v a l o f a d a y , on t h e s p e c i f i c d a y o f a w e e k , a n d on t h e s e a s o n , a n d t h e y a r e u n a v o i d a b l e . In d e c i d i n g w h a t a n a d e q u a t e c a p a c i t y o f t h e e q u i p m e n t t o be p r o v i d e d w i l l b e , t h e I n t e r r e l a t i o n s h i p , b e t w e e n t h e f a c i l i t y ' s u t i l i z a t i o n r a t e a n d t h e s a t i s f a c t i o n o f t h e c u s t o m e r s h a s t o be c o n s i d e r e d u n d e r v a r i e d t r a f f i c c i r c u m s t a n c e s . In d i a g r a m 1 3 , t h e c u r v e o f a v e r a g e u t i l i z a t i o n a n d t h e p r o b a b i l i t y c u r v e t h a t t h e c a p a c i t y o f 23 l i s t e n i n g u n i t s w i l l be s u f f i c i e n t f o r e v e r y a r r i v i n g c u s t o m e r Is p l o t t e d a s a f u n c t i o n o f t h e a v e r a g e number o f t h e s y s t e m ' s a r r i v a l s d u r i n g an I n t e r v a l o f 10 m i n u t e s . In o t h e r w o r d s , I f t h e r e a r r i v e 5 c u s t o m e r s on t h e a v e r a g e d u r i n g an I n t e r v a l o f 10 m i n u t e s , t h e u t i l i z a t i o n w i l l be 6 9 % , a n d t h e p r o b a b i l i t y t o f i n d a v a c a n c y w i l l be 9 5 . 7 % . I f t h e c o u n t e d number o f s y s t e m ' s a r r i v a l s d r o p s down t o 3 . 3 / 1 0 m i n u t e s , t h e a s s o c i a t e d u t i l i z a t i o n a n d p r o b a b i l i t y r a t e s w i l l be 3 3 . 7 % a n d 1 0 0 % , r e s p e c t i v e l y , e t c . The u t i l i z a t i o n c u r v e a n d p r o b a b i l i t y c u r v e I n t e r s e c t a t 8 5 . 5 % a n d 7 . 6 a r r 1 v a 1 s / 1 0 m i n u t e s . The utilization curve and the probability curve are derived from values obtained by the simulation. The uti l i z a t i o n curve represents the average number of occupted listening units at different system's arrival rates relative to the total number of listening units available (23 units). The probability curve of finding a vacancy is derived from observations related to customers entering the reserve listening room. If no customer will enter the reserve listening room, the provided capacity of 23 turntables will be sufficient by 100%. Overflowing customers to the reserve listening room represent the possibility to find no vacancy in the listening room. The relative share of number of entries Into the reserve listening room to the total number of entries that intend to use the listening f a c i l i t y represents a measurement of the probability not to find a vacancy in the listening room. The utilization rate curve and the curve of the probability of satisfied customers are displayed jn dependency of the system's arrivals c a n t e d per 10 minutes in a range from 0 to 10 arrivals. This scale represents the actually observed t r a f f i c extent of the U.B.C. Recordings Collection. MOre detailed data Is shown In the table of dally arrival rates observed In the winter term: S Y S T E M L I S T E N I N G R O O M PERIOD AVGV ARRIV". RATES/10 MIN. PERIOD AVG. ARRIV. RATES/10 MIN. 8:30-10:00 4.4 8:30-10:30 4.0 10:30-12:00 7.0 10:30-11:45 4.4 12:00- 2:00 9.7 ll's 45-12: 30 2.4 2:00- 4:00 5 : 8 12:30- 1:30 6:0 4:00- 5:00 4.7 1:30- 5:00 2.9 5:00-:i;6:00 1.3 5: 00-06:$.3- 1.1 6:00- 8:00 2.9 6:45- 7:30 1.5 day 5.5- day 2.9 Table III: The average arrival 'fates of the system and of the listening room on an average day in the winter term (see also diagram 2) The s imudtjtt i on related to the listening room has been performed under the assumption of a constant number of 23 turntables installed in the listening room. From those simulation results, we have formulated two arguments: the probability that the arriving customer will find a vacancy In the listening room versus the utilization rate of the equipment provided. Both functions, as des- ) c r l b e d above In more d e t a i l , show the c h a r a c t e r i s t i c s such as : F i g u r e 12: The average u t i l i z a t i o n r a t e v s . the p r o b a b i l i t y t h a t e v e r y cus tomer w i l l f i n d a vacancy }n the l i s t e n i n g room However, In our d e c i s i o n what an adequate number of t u r n t a b l e s wou ld be, we may want t o o b t a i n more i n f o r m a t - ion about the r e l a t i o n s h i p " p r o b a b i l i t y v e r s u s u t i l i z a t - i o n " under the c o n d i t i o n s o f v a r i e d numbers o f l i s t e n i n g u n i t s i n s t a l l e d . T h i s r equ i r emen t l ead s t o more s i m u l a t - ion i n o b t a i n i n g o f r e l i a b l e d a t a . Because, we a re r e s t r i c t e d by the scope o f our pe r fo rmed s i m u l a t i o n , we want t o o u t l i n e an ex tended decision model with anticipated data but on the basis of our results obtained so far. For instance, we may anticipate a simulation map which comprises a number of turntables ranging from 22 to 27 units; simulated values, anticipated values s t i l l to s imu1 ate Figure 13: Anticipated simulation map In a decision process, such a model might be used in the following ways: a) The manager wants to have an average utilization of his equipment of at least 30% on the average. He observes a mean stream of 8 custom- ers per 10 minutes. In accordance to the assumed decision model, there should be installed no more than 2k turntables. Then, an arriving customer would find a vacancy In the listening room with a probability of approximately 85%. b) On the average, there arrive 11 customers during an interval of 10 minutes. A satisfaction of the patrons Is required with a probability of at least 90%. The manager should decide for 27 listening units. However, under this condition, the average utilization rate will be ca. 5k% at the most. Similarly, other arising questions may be answered. It might be of interest, what combination of a certain number of turntables available related to a given t r a f f i c density causes always a. utilization rate of, for instance, 80%, or also the same probability rate of 80% of finding a vacancy. From the previously described decision model,the equa1-uti1 Ization curves and the equal-probab11ity curves can be derived and dis- played in a possibly morê c'ohM"e'nif.en̂ tcre.onfe!;ĝ â-tilb.î '%s:-vs-hown below: 11111111H 111 1111111'l [tr i p i i i \m :::Jff[ +: trrB ICJ nrrral ::±EEES»j i t 1: t ttltlllffll 1111 HfltH"" s 11 H|-I-HIM-U 111444 -)4[444444 TBI tuttn Wlili ]j| jfjjl11 [[[njjjjljj: probability of satisfied cus tomers uti1ization rate equal probability rate and uti1ization rate Figure lk: Map of Indifference curves In the new map of "indifference curves", for instance, the 80%-probab11 Ity curve and the 80%-ut ?1I zat- fon curve intersect at the equilibrium Ej, Correspond- ing, the 70%-curves intersect at the equilibrium E 2 , etc. The line connecting all those points of equilibrium give the "equilibrium curve". That means,all combinations of both variables (number of turntables, number of arrivals/time interval) which l i e along of this curve lead to the same percentage level of the equipment utilization and the probability of customer satisfaction. For instance, a[j?60% utilization rate corresponds to a 0.6 probability rate. We may determine the decision fi e l d of our model by the coordinates represented by the range of the number of turntables installed in the listening room, and on the other hand, by the range of the average number of system arrivals per 10 minutes. The equilibrium curve divides this dec I s I on. jf I el d in two parts. Decisions which may f a l l in the upper f i e l d emphasize the satis- faction of the customer but lower the utilization of the equipment. The lower decision f i e l d favours the equipment utilization at the expense of the customer satisfaction. The equilibrium curve represents the "neutral dectsions" without any emphasis of one or the other argument. These relationships are outlined in the graph below: -#1+ tt •if s 5 I E . -IIP Tfff: If Hi 111" i t 'A 11 I'm if S+ Figure 15: Decision f i e l d of the model BIBLIOGRAPHY i BOOKS: Adams, Douglas: Nomdgraphv, Theory and Applicatfon,Arcon Books 1964, Hamden, Connecticut. ...Alven, Willfam: Reliability Engineering, ARINC Research Corporation, PrentIce-Ha11, Inc. 1964, Englewood C l i f f s , N. J. Buffa, El wood: Readings in Production and Operations Management, Part I, John Wiley & Sons, Inc., New York 1966 Churchmann, West; Ackoff, Russel; Arnoff, Leonhard: Introduction to Operations Research, Part I, II, III, VI, John Wiley + Sons, Inc., New York 195 7 Cox, Edwin; Boot, John: Statistical Analysis for Managerial Deci s ? ons, McGraw-Hill Book Company 1970 Cruon,R.: Queuing Theory, Recent Developments and Applications, Chapman .•; Hall, Ltd., London 195 2 Feller, W.; An Introduction to Probability Theory and its A D D ! 1 cat ? ons, Holden-Day, San Francisco 1970 Hald, A.: Statistical Theory with Engineering Applications, Chapman & Hall, Ltd., London 1952 H i l l i e r , F.; Lieberman: Introduction to Operations Research, Hoi den-Day,Inc., San Francisco Hoelscher, Randolph: Graphic Aids tn Engineering Computation, Bait Publishers, West Lafayette, Indiana '64 Karlin, Samuel: A First Course in Stochastic Processes, Academic Press, New York 1968 Kaufmann, Arnold: Methods and Models of Operations Research, Prentice-Hall, Inc., Englewood C l i f f s , N.J. 1963 Kemeny, John; Snell, Laurie: Finite Markov Chains, Van Nostrand Co., Inc., New York 1963 Morse, Philip: Queues, Inventories and Maintenance, The Analysis of Operational Systems with Variable Demand and Supply, John Wiley & Sons, Inc., New York 1958 BOOKS: Parzen,E.: Stochastic Processes, Holden-Day, San Francisco 1962 Rlgby, Paul: Models in Business Analysis, Charles E. Merrill Publishing Company, Columbus, Ohio, 1969 Roberts, Edward: The Dynamics of Research and Development, Harper & Row, Publishers, 1964 di Roccaferrera, Gulseppe: Operations Research Models for p u g f n p s s and Industry, South-Western Publishing Company, 1964 Ross, Sheldon: Applied Probability Models with Optimization Applications, Holden-Day, San Francisco 1970 Shook, Robert; Highland, Joseph: Probability Models with  Rusiness Applications, Richard Irwin, Inc. Homewood, Il l i n o i s , 1969 Wagner, Harvey: Principles of Operations Research, Prentice-Hall, Inc., Englewood C l i f f s 1969 ARTICLES, MANUALS: Burke, P. J.: The Output of a Queuing System, Operations Research, 4, 699-704, Dec. 1956 Disney, Ralph: Analytic Studies of Stochastic Networks Using Methods of Network Decomposition, The Journal of Industrial Engineering, Volume XVIII No, 1, 140-145, Jan. 1967 Farley, John; Ring, Winston: A Stochastic Model of Super- market Traffic Flow, Operations Research, July /August 1966, page 555 f f . Gue, Ronald: Signal Flow Graphs and Analog Computation in ARTICLES^MANUALS: the Analysis of Finite-Queues, Operations Research, page 3U2 f f . IBM - Manual GH20-0304-4, General Purpose Simulation System /360, Introductory User's Manual IBM - Manual H20-0326, General Purpose Simulation System /360, User's Manual Moettle, John: Information Concepts in Network Planning, The Journal of Industrial Engineering, July '67, pg. 428 f f . A P P E N D I X T a b l e IV : C u m u l a t 1 v e n u m b e r o f c u s t o m e r s e n t e r i n g o r 1 e a v I n g , r e s p e c t f v e l y , t h e s y s t e r n a t c e r t a I n t i m e s d u r i n g t h e summer t e rm: hou r s m i n . 9 . 1 0 . 1 1 - 1 2 . 1 . 2 . 3 . 4. 5 . . 0 0 ( e n t e r . ) 0 11 27 40 66 97 114 129 145 ( 1 e a v . ) 0 8 20 34 56 8k 102 119 145 . 1 5 ( e n t e r . ) 3 18 30 kl 77 100 116 136 • ( 1 e a v . ) 0 12 22 36 65 90 106 123 . 3 0 ( e n t e r . ) 6 22 33. 50 83 105 1 2 1 140 ( 1 e a v . ) 2 18 25 kl 70 96 109 128 .'+5 ( e n t e r . ) 8 25 36 60 91 106 125 142 ( 1 e a v . ) 4 20 30 49 78 97 114 134 . 5 6 ( e n t e r . ) 145 oo Table V: Cumulative number of customers e n t e r i n g or l e a v i n g , r e s p e c t i v e l y , the l i s t e n i n g r o o m at c e r t a i n times (summer term): hou rs min. 9. 10. 11. 12 . 1. 2. 3. k. .00 (e n t e r . ) o 5 11 16 2k 3k k2 k7 ( 1eav.) 0 1 6 11 18 27 3k 39 .15 (e n t e r . ) 1 6 12 17 26 35 k3 50 ( 1eav.) 0 3 6 13 20 30 35 l+l .30 (e n t e r . ) 2 8 13 19 29 38 kk 51 ( 1eav.) 0 5 8 lk 22 31 36 k2 .kS ( e n t e r . ) 3 10 15 22 31 39 k5 52 ( 1eav.) 0 5 9 16 25 33 38 k7 Table VI: Cumulative number of customers e n t e r i n g or l e a v i n g , the s y s t e m at c e r t a i n times (winter term): respect i v e l y , hou rs min. 8. 9. 10. 11. 12 . 1. 2. 3. 4. 5. 6. 7. 8. .00 ( e n t e r . ) 0 9 40 81 124 177 241 281 311 339 347 369 380 (1eav.) 0 2 29 60 104 154 220 266 301 322 343 361 380 .15 ( e n t e r . ) 0 13 k7 87 132 190 251 283 319 341 355 371 (1eav.) 0 6 35 68 113 166 231 272 307 327 346 365 .30 ( e n t e r . ) 0 26 69 10 5 150 221 263 297 325 343 357 374 (1eav.) 0 23 50 83 137 197 249 287 314 335 349 369 ,45 ( e n t e r , ) 3 34 76 117 166 232 274 306 333 346 363 378 (1eav.) 0 26 57 93 144 207 257 285 318 339 354 371 Table VII: Cumulative number of customers e n t e r i n g or l e a v i n g , r e s p e c t i v e l y , the l i s t e n i n g r o o m at c e r t a i n times (winter term): hou rs min. .00 ( e n t e r . ) (1eav.) .15 ( e n t e r . ) (1eav.) .30 ( e n t e r . ) (1eav.) .^5 ( e n t e r . ) (1eav.) 8. 9. 10. 11 0 5 17 kO 0 0 7 20 0 6 18 43 0 2 9 2k 0 12 39 56 0 7 15 38 3 14 37 63 0 7 17 k2 12. 1. 2. 3. 67 92 120 140 48 72 103 125 68 97 123 143 55 79 108 131 74 110 127 146 64 90 117 137 85 116 136 152 65 94 121 141 4. 5. 6. 7. 153 170 176 187 143 153 170 177 157 173 179 187 147 158 172 181 161 174 182 189 149 165 174 182 167 176 182 189 151 169 175 182 189 189 oo Table V I M : D i s t r i b u t i o n of elapsed time between a r r i v a l s to the recordings c o l l e c t i o n (see diagram 3 and 4) time i n t e r v a l a c t u a l frequency t h e o r e t . frequency t <jx<t? prob.(%) cumulat. prob.(%) cumu-lat. 1 p r o b . ( l ) p r o b . U ) 0 < X < 1 35.2 35.2 42.3 42.3 1 < X < 2 28.9 64.1 24.4 66.7 2 1 X < 3 15.3 79 .4 14.1 80.8 3 1 X < h 7.2 86.6 8.1 88.9 4 1 X < 5 5.9 92 .5 4.7 93.6 5 < X < 6 1.0 93 .5 2.7 96,3 6 1 X < 7 1.3 94.8 1.6 97.9 7 < X < 8 1.3 96.1 0.9 98.8 8 1 X < 9 0.3 96.4 0.4 99.0 9 < X < 10 0.8 97.2 • • 101 X < 11 0.5 97.7 x < 0.2 • H< X < 12 0.5 98.2 » • 12< X < 13 0.5 98.7 131 X < 14 0.8 99.5 141 X < 15 0.5 100 • 100 - 0,55 cust./min. Table IX: D i s t r i b u t i o n of s e r v i c e time In the recordings c o l l e c t i o n (diagram 5 and 6): time i n t e r v a l a c t u a l frequency t h e o r e t . frequency of expon. d i s t r . tj_ <_ x < t? prob.% cumulat. prob.(%) cumulat. prob.(%) prob.(|) 0 < X < 1 18.8 18 .8 15.4 15.4 1 < X < 2 13.2 32.0 12.7 28.1 2 < X < 3 10.0 42.0 10 .9 39 .0 3 < X < 4 P.8 51.8 9.3 48 .3 4 < X < 5 8.7 60.5 7.9 56.2 5 < X < 6 6.6 67.1 6.7 62 .9 6 X < 7 6.1 73.2 5.6 68.5 7 < X < 8 3.2 76.4 4.8 73.3 8 < X < 9 3.2 79.6 4.1 77.4 9 < X < 10 3.2 82. 8 3.4 80.8 10 < X < 11 2.9 85.7 2.9 83. 7 11 < X < 12 3.2 88.9 2.5 86.2 12 < X < 13 2.4 91.3 2.1 88.3 13 < X < 14 1.6 92 .9 1.7 90.0 14 < X < 15 1.3 94.2 1.6 91.6 15 < X < 16 .8 95.0 1.1 92.7 16 < X < 17 .3 95.3 1.0 93.7 17 < X < 18 .5 95.8 .9 94. 6 18 < X < 19 .5 96.3 .7 95.3 19 < X < 20 .5 96.8 .6 95.9 20 £ X < 21 .3 97.1 .5 96.4 21 < X < 22 .3 97.4 • • 22 < X < 23 .3 97.7 • • 23 < X < 24 .3 98.5 • • 31 • X < 32 • .2 100* • 100 mean = 2279 cus t . min./378 c u s t . = 6.§4 min./cust.=.165 c/mln. Table X: Distribution of elapsed time between arrivals to the listening room (diagram 7 and 8) time interval actual frequency theor. frequency of expon. distr. t-, <_ x <_ t prob. % cum. prob. (%) cumulat. 1 1 prob. (%) prob. (|) 0 < X < 1 26.7 26.7 24.9 24.9 1 <. X < 2 18 .7 k5.k 18. 7 43.6 2 < X < 3 18 .5 53.9 lk .0 57.6 3 < X < k 10 .6 6k .5 10.6 68.2 ^ < X < 5 9.7 7k.2 7.9 76.1 5 1 X < 6 8.5 82,7 5.9 82.0 6 <_ X < 7 k.8 87.5 k.5 86.5 7 < X < 8 2.7 90.2 3.3 89.8 8 < X < 9 1.6 91.8 2.6 92'.4 9 < X < 10 * 1.6 93.k 1.9 94.3 10<_ X < 11 1.0 9k.k l.k 95.7 111.' <x < 12 1.6 96.0 1.1 96.8 12< X < 13 .5 96.5 .8 97.6 30< • X < 31 • .5 • 100 • 100 avg. = 0.286 cust./min. Table XI: D i s t r i b u t i o n of s e r v i c e time concerning the l i s t e n i n g room (diagram 9 and 10) time i n t e r v a l < X < t 1 - 2 o <;. X < .-5 5 < X < io 10 < X < 15 15 < X < 20 20 < X < 25 25 < X < 30 3o < X < 35 35 < X 40 40 < X < 45 45 < X < 50 50 < X < 55 55 < X < 60 60 < X < 65 65 < X < 70 70 < X < 75 75 < X < 80 80 < X < 85 85 < X < 90 90 < X < 95 95 < X < 100 100 <. X •< 105 105 < X < 110 n o < X < 115 115 < X < 120 120 < X < 125 125. < X < 130 130' X < 135 13 5 X < 140 140 < X < 14 5 145 < X < 150 150 < X < 155 155 < X < 160 160, < X < 165 165 < X < 170 170 X < 175 175 < X < 180 180 < X < 185 185 < X < 190 190 < X < 195 a c t u a l frequency prob. (!) cumulative probabi1i ty {%) 2.4 2.4 4.7 7.1 6.0 13.1 7.4 20.5 4.8 28.9 7. 7 36.6 7.0 43.6 6.2 49.8 5.8 55.6 6.7 62.3 7.6 69.9 5.5 75.4 3.2 78.6 2.8 81.4 2.2 83.6 1.9. 85.5 1.7 87.2 1.6 88.8 1.5 90.3 1.4 91. 7 1.0 92. 7 .9 9 3.6 .8 94.4 .7 9 5v.l .6 95. 7 .5 96.2 .4 96.6 .4 97.0 .4 97.4 .3 97.7 .3 98.0 .3 98.3 .3 98.6 .3 98.9 .3 99.2 .2 99.4 .2 99.6 .2 99.8 .2 100.0 RFS NO. 771D90 UNIVERSITY DF 3 : COMPUTING CENTRE MTS(AN120) 00:23:13 12-30-70 ******************** THIS JOB SUBMITTED THROUGH FR3NT DESK READER ******************** $SIGM3M WULI T=150 P=400 PRIO=V C0PIES=4 »»l A S T S l f t N i r i M WAS: 0Q:l?i49 I 7-30-7Q : s USER "WULI" SIGNED ON AT 00:23:20 ON 12-30-70 $*UN *3PSS P&R=SIZE=B -6X-g-GU-T-I-0N-B.E-G-Î .S . BLOCK NUMBER *LOC OPERATION A , B , C , D , E, F ,G CD^MEMTS SIMULATE SIMULATION! OF UBC RECORDINGS COLLECTION BV JOHANNES KRAMAR CARD NUMBER 1 2 * FUNCTION DEFINITIONS __ ; * SYSTEM ARRIVAL TIME EXPONENTIALLY DISTRIBUTED ARRIV FUNCTION RN1,C16 NE3. E X ? . 01STR. ,ME AN=3MIN. 0 . 0 , 0 . 0 / . 1 B ? , . l / . 2 B 3 , . 2 6 7 / . 4 B 6 , . 5 / . 6 3 2 , .B3/ . 7 3 5 , 1 . 1 7 / . 8 1 . 1 . 5 / . 8 6 5 . 1 . 8 3 3 4 _5_ 6 7 8 . 9 0 3 , 2 . 1 6 / . 9 3 Or 2 . 5 / . 9 5 , 2 . 8 4 / . 9 6 4 , 3 . 1 6 / . 9 7 5 , 3 . 5 / . 9 3 2 , 3 . 8 4 / . 9 8 7 , 4 . 1 5 . 9 9 , 4 . 5 _ „ ___ , * DESK SERVICE TIME EXPONENTIALLY DISTRIBUTED DPSK FUNCTION R N l . f . 2 4 NHS, EX?. OISTR, 9 ID 11. 12 13 14 0 . 0 , 0 . 0 / . I , . 1 0 4 / . 2 , . 2 2 2 / . 3 , . 3 5 5 / . 4 , . 5 0 9 / . 5 , . 6 9 / . S , . 9 1 5 / . 7 , 1 . 2 / . 7 5 , 1 . 3 8 / . 8 , 1 . 6 / . 8 4 , 1 . 8 3 / . 8 8 , 2 . 1 2 / . 9 , 2 . 3 / . 9 2 , 2 . 5 2 / . 9 4 , 2 . 8 1 / . 9 5 , 2 . 9 9 _K_ A . . 3 „ 2 X ^ i , 3 - . 5 X . S - 8 . . 0 L ^ ^ ^ * . ' * SHELF SERVICE TIME EXPONENTIALLY DISTRIBUTED SHELF FUNCTI3N RN1.C23 . NES. EXP. DI STR. ._ 15 16 - I X 18 19 20 0 . 3 , 3 . 3 / . 1 5 4 , . 8 4 D / . 2 3 1 , . 2 5 0 / . 3 9 0 , . 4 2 0 / . 4 8 3 , . 5 8 0 / . 5 6 2 , . 7 5 0 / . 6 2 9 , . 92/ . 5 8 5 , 1 . 0 8 / . 7 3 3 , 1 . 2 5 / . 7 7 4 , 1 . 4 2 / . 8 3 8 , 1 . 5 9 / . 8 3 7 , 1 . 7 5 / . 3 6 2 , 1 . 9 2 ^.8a,X._0.8./_.-9-,-2...2.5.>L_ - — . 9 1 6 , 2 . 4 2 / . 9 2 7 , 2 . 5 8 / . 9 3 7 , 2 . 7 5 / . 9 4 6 , 2 . 9 2 / . 9 5 3 , 3 . 0 8 / . 9 5 9 , 3 . 2 5 . 9 6 4 , 3 . 4 2 / 1 . 0 , 5 . 2 7 * 21 22 X3- 24 25 _2__ * LISTENING ROOM SERVICE TIME GENERALLY DISTRIBUTED LIST FUNCTION RN1,C25 GEM. DISTRIBUTION D.-Q-,O.D/:. 024. , - . -053Z. .07X, - .L8Z . 4 3 6 , . 8 2 0 / . 4 9 8 , . 9 4 0 / . 5 5 6 , 1 . 0 6 / . 6 2 3 , 1 . 1 8 / . 6 9 9 , 1 . 3 1 / . 7 5 4 , 1 . 4 4 / . 7 8 6 , 1 . 5 5 / . 8 1 4 , 1 . 6 9 / . 8 3 6 , 1 . 8 1 / . 8 5 5 , 1 . 9 4 / . 8 7 2 , 2 . 0 6 / . 8 8 8 , 2 . 1 8 / . 9 0 3 , 2 . 3 1 / . 9 1 7 , 2 . 44/ . 9 2 7 . 2 . 5 5 / . 9 6 2 , 3 . 1 9 / . 98 9 , 4 . 2 0 / 1 . 0 0 , 4 . 820 27 28 -2SL 30 31 32 * STORAGE DEFINITIONS —IX) SXO.RAG.E_ 200- 11 STORAGE 150 30 STORAGE 100 40 STORAGE 23__ J).E F.LN E_S.IXE^O F__SXSXEM,S-SX3&AG .E_ DEFINE SIZE OF REC. COLL. DEFINE S H E OF STOR. 30 DEFINE SIZE 3F STOR. 40 33 34 35.... 36 37 38 41 STORAGE 23 * TABLE DEFINITIONS TJLai_J .AaL .E_ _ I A , L , L X O - TA82 TABLE R T , 0 , 1 , 3 0 , 1 0 ^TA83 TA3LE M l , 1 , 1 , 3 0 TAB4 QTABLE 2 . 3 . 1 . 3 0 DEFINE SIZE OF STOR. 41 J _ U = R A R R IMJLL__II M £ _ ARRIVAL RATE TRANSIT TIME TABLE LIMITS IM 3U5. . 39 40 4,1... 42 43 44 TA35 TA36 —T.ABX TA38 TAB9 TABIC TABLE TA3LE XA.BLE- TA3LE TABLE TABLE I A , RT, M l , S30 M l , S l l 1 , 1 , 0 , 1 , 1 ,1 . , , 0 , 1 1 . 1 , » o « i 30 ' 2 0 , 1 0 6Q_ , 4 0 60 «60 INJTERARRI/AL TIME SHELVES ARRIVAL RATE TRAM S I X - I I VIE STDR. 3D OCCUPANCY TRAMS. TIME SERVI STORAGE 11 Of. CUP AMC Y 45 46 _4X 48 49 _50_ T A B U TAB12 TAB 13 TAB 14 TA315 T A Rl 6 TABLE TABLE TABLE TABLE TABLE TARI F I A , RT, . . M X , . S40 M l , U l , 0 , 1 , 0 , -5 , - , 0 , 1 0 , 5 , - a « ? 30 1 5 , 1 0 6X)_ _ , 2 6 60 • 6 " INTERARR. TIME FAC. 43 IARRIVALS FAC. 40 J _ t J L > i S - _ U J l £ - _ L A _ ^ _ _ 0 _ _ STORE 4D OCCUPANCY TRANS. TIME IN SYSTEM S Y < ; T . nr.r.iiPV.Mr.Y 51 52 -53^ 54 55 ___ > * GPSS PROGRAM GENERATE FMTFR 3,FN$ARRIV J L Q ARRIVALS TO SYSTEM CUM. STDR. SYSTEM TRANSFER STG2 MARK E-N-T-E-R QUEUE LINK . 36 » S TG3,STG2 - L l - 2 2 , F I F O , D E S K GD TO 3 0* 2 SET TRAMS. TIME = 0 -C.UM._SXORE_.RC. JDIM QUE. 2 LINK USER CHAIN 2 57 58 59 60 61 62 63 64 -6.5_ 66 67 r 6 P S S / 3 6 0 / M T S VERSION (4/8/13) A ^ 8 DESK SEIZE 2 OCC. DESK 68 9 DEPART 2 LEAVE QUE. 2 69 ID ADVANCE 1»FNSDESK DESK SERVICE 70 > 1 1 RFI FASF 2 RELEASE DESK 71 ( 12 UNLINK 2 , D E S K , 1 UNLINK USER CHAIN 2 72 • < 13 TABULATE TAB1 TAB. INTERARR. TIME 73 L 4 T A BU LAT E T AR? TAR, ARRIVALS 74 15 TABULATE TAB3 TAB. TRANS. TIME 75 16 LEAVE 11 76 17 TARUlAFF TAR9 77 18 , TABULATE TAB10 78 19 ASSIGN 2 , K 1 SET PI TO 1 79 2D T.E.S-T LE Cl , K 3 (S!JO , F T N F T=ST TTMF an 21 TEST E P3,K1 ,GEH2 81 22 TEST E P4,K1»GEH3 82 2 3 TRANSFFR • EXIT 83 24 GEH2 TEST E P 4 , K 1 , G E H 4 84 25 TRANSFER . 7 5 , S T G 3 , E X I T 85 2.6 GFH3 TRANSFER . 9ft f ST£4, F X I T Aft 27 GEH4 TRANSFER . 7 3 , G E H 5 , E X I T 87 28 SEH5 TRANSFER . 1 1 ,STG3,STG4 88 _ 2 9 STG3 MARK 89 30 ENTER 11 CUM. STORE RC. 90 31 ENTER 30 EMTER STOR. 30 91 3? ADVANCE ft,FN$ SHF IF SHFI F SFRV ICF T I M F q? 33 LEAVE 30 LEAVE STOR. 30 93 34 TABULATE TAB5 IMTERARRIVAL TIME 94 35 TABULATE TAB6 ARRIVAL RATE 95 36 TABULATE TAB 7 TRANSIT TIME 96 37 TABULATE TAB8 STDlE . SHELVES OCCUPANCY 97 3.8 | FAVF 1 1 1 FA*/F STRRF 1 1 9R 39 TABULATE TAB9 99 43 TABULATE TAB 10 STORE RECORD. COLLECT. 100 41 ASSIGN 3 . K 1 SET P2 TO 1 101 42 TEST LE C 1 , K 3 6 0 0 , F I N E TEST TIME 102 43 TEST E P 2 f K 1 . 5 E H 7 103 44 TEST E P 4 , K 1 , G E H 8 1 04 45 TRANSFER ,EXIT 105 46 GEH7 TEST E P 4 , K 1 , G E H 9 106 47 TRANSFER . 2 B . S T G 2 . F X I T 107 48 GEH8 TRANSFER . 2 2 , S T G 4 , E X I T 108 49 3EH9 TRANSFER . 1 4 , G E H 1 0 , E X I T 109 5.0 QFHIQ TRANSFFR , ^ f l , S T f ; ? t ST^4 1 1 n 51 STG4 MARK 111 52 GATE SNF 40,OFLOW 112 53 ENTER 40 ENTER STOR. 40 113 54 ADVANCE 40 ,FN$L IST L IST . ROOM SERVICE TIME 114 55 LEAVE 40 LEA\/E STORAGE 40 115 5.6. T.AB.ULA-TE TAR 1 1 INTFR ARRIVAL T I M F FAT. 4 11 57 TABULATE TAB12 ARRIVAL RATE FAC. 4 117 58 TABULATE TAB13 TRANSIT TIME FAC. 4 113 59 TABULATE TAR14 STORE. 40 OCCUPANCY 119 60 TRANSFER , BE IDE 120 51 OFLOW ENTER 41 121 G P S S / 3 6 0 / M T S VERSION ( 4 / 8 / 1 3 ) A 62 63 64 ADVANCE LEAVE TABULATE TR ANSFFi* 40 ,FN$-LI5T L I S T . ROOM SERVICE TIME 41 TAB 17 ODCUP. OF RESERV. L I S T . ROOM T R F T DF 122 123 124 125 J f 66 67 5 8 BEIDE ASSIGN TEST E TRANSFER 4 , K 1 SET P4 TO 1 P 3 , K 1 , S E H 1 1 . 0 9 * S T G 2 i E X I T 126 127 12B \ S9 70 71 GEH11 TEST LE T E S T E TRANSFFR C l , K 3 6 0 0 , F I N E TEST TIME P 2 , K 1 , G E H 1 3 . ™ t STr,-} tFXT T 129 130 1 31 72 73 7-4 GEH13 GEH14 E X I T TRANSFER TRANSFER LEAVE , 0 8 , G E H 1 4 , E X I T , 1 4 , S T G 2 , S T G 3 10 1FAVF SYST - S T O R „ 132 133 1 34 75 76 77 T A B U L A T E TABULATE TFRMTMATF TAB 15 TVAMS. TIME IN SYSTEM | TAB16 SYSTEM OCCUPANCY j 135 136 137 78 79 8 0 F I N E L E A V E T A B U L A T E T.A.RU.L AXF 10 L E A V E S Y S T . STOR. TAB15 U M S . TIME IM SYSTEM TAB16 S / S T F M OCCUPANCY 138 139 140 31 TERMINATE * CONTROL CARD START 1 1 141 142 1 43 * REPORT E J E C T 144 145 146 FAC 01JF T I T L E SPACE T I Tl. F 2 , S T A T I S T I C S CONCERNING THE INFORMATION DESK 3 ? . S T A T I S T I C S CONIC E RNl NS THE DESK QUEUE 147 148 149 CHA SPACE T I T L E E J E C T 3 2 , S T A T I S T I C S CONCERNING THE DESK USER CHAIN 150 151 152 i FAB * T I T L E E J E C T 1 ,DESK INTERARRIVAL TIMES ( M I N . ) : 153 154 1 «S«5 * GRAPH GRAPH ORIGIN T P , T A B 1 5 0 , 1 0 156 157 158 7 X Y STATFMFNT , 2 , 1 3 , 1 , 1 , 8 0 , 4 , 2 0 , 2 4 t l , 2 159 160 1 M 100 10 STATEMENT STATEMENT ENDGRAPH 52 , 2 4 , I NTERARRIVAL TIME ( M I N . ) 5 5 , 4 6 , F I G U R E 1: R E L . FREQUENCY OF INTERARRIVAL TIMES 162 163 164 * TAB T I T L E F.IFf.T 2,NUMBER OF ARRIVALS TO D E S K / 1 0 MIN. 165 166 167 * * GRAPH GRAPH TD,TAD? 168 169 1 70 i ORIGIN X Y f-f̂ -~w * Mt# -—- •• ••• • •• •' '• —,.—•„. i i i i 5 0 , 1 0 , 2 , 2 , 0 , 1 , 3 0 n t i t ? i r ? 171 172 l 7^ 7 100 STATEMENT STATEMENT *tlt3B 5 2 , 2 0 , A R R I V A L R A T E / 1 0 M I N . 174 175 J t i f i i / J O U / M I 5 V t K i l J N XtfVfli) A 10 STATEMENT 5 5 , 6 4 . F I G U R E 2 : REL. FREQUENCY OF ARRIVALS TO I N F . DEI 176 SK DURING 10 MIN. 177 ENDGRAPH 178 * : . , : : L7_ T A3 TITLE 3,DESK TRANSIT TIMES ( MI N. ) (=W Al T. & SERVICE TIME) 180 EJECT 181 J* _ . ___1.8.2 * GRAPH 183 GRAPH TP ,TA33 184 ORTf i lN 5 0 . 1 0 ; L8_5 X , , 1 4 , 1 , 1 , 8 186 Y 0 , 3 , 2 0 , 2 187 —7- SXAT.EMENT k.,-U-% '. 1.8.3 100 STATEMENT 52 ,19 ,TRANS IT TIME (MIN.) 189 10 STATEMENT 5 5 , 6 0 , F I G U R E 3 : REL. FREQUENCY OF TRANST TIMES AT INF1 190 OR MAT ION DFSK ; . L9_J ENDGRAPH 192 * 193 —T.A.B -T.I-.T-LE 4-,^.UMBE.R_0F_J.0B.S-_W.A.IJ_I.NG_.E0R_S.£RV-I.C.E_A.T_D-ESK 1.9J4 EJECT 195 * 196 * GRAPH : 197 GRAPH TP,TAB4 198 ORIGIN 5 0 , 1 0 199 X ,.2.,-1.3,.0.vl.,-8 2-0.0 Y 0 , 3 , 2 0 , 2 201 7 STATEMENT 4 , 1 , ? 202 IQQ STATEMENT 5 2 . 1 3 . JOBS IN QUEUE ; ^203 10 STATEMENT 5 5 , 7 2 , F I G U R E 4 : REL . FRE3UENCY OF JOBS WAITING FOR SEI 204 RVICE AT INFORMATION DESK 205 . . ENDGRAP-H _ , . 2 . 0 . 6 _ . . * 207 STO TITLE 30,THE SHELVES AS STORAGE 208 SPACE 3 ; . , 209 ; TAB TITLE 5,SHELF INTERARRIVAL TIMES (MIN.) 210 EJECT 211 -* ^ . . : . . _ _ : . : : 2-1-2- — • — * GRAPH 213 GRAPH TP,TAB5 214 ORIGIN 5Q, IQ : : Z15 X , 2 , 1 8 , 1 , 1 , 6 216 Y 0 , 4 , 2 0 , 2 217 _ J Z SXAXEM-E-NJ. <M_L.»-S '. : : 2.1.8 : 100 STATEMENT 52 ,24 , INTERARRIVAL TIME (MIN. ) 219 10 STATEMENT 5 5 , 4 6 , F I G U R E 5 : REL . FREQUENCY OF INTERARRIVAL TIMES 220 ENDGRAPH ; 2_2J * 222 TAB TITLE 6,NUMBER OF ARRIVALS TQ SHELVES/10 MIN. 223 E.J.E-C-T : , -—22& : . — * GRAPH 22 5 GRAPH TP,T AB6 226 ORIGIN S O . ! n ! : 221 X , 2 , 4 , 0 , 1 , 2 0 228 Y 0 , 1 , 2 0 , 2 229 7 STATEMENT 4 , 1 , £ IOO STATEMENT 52 , 2 0 , A R R I V A L RATE/10 MIM. 10 STATEMENT 5 5 , 6 2 , F I G U R E 6 : REL. FREQUENCY OF ARRIVALS TO SHELVES1 niiRTNir, in M T M . 230 231 232 233 -T-A8- ENDGRAPH X I X L E - EJECT _7-,-SHE-L F—T.R A N S IX_TXME.S-XMLM- 234 235 _23.6_ 237 238 2 39 7 1 00 GRAPH ORIGIN _X Y STATEMENT ST AT FMFNT TP,TAB7 5 0 , 1 0 _,_,5- , - l - , - l - , - l -5- __ 0 , 1 , 2 4 , 2 4 , 1 , * x 5 2 , 1 9 , T R A N S IT TIME ( MIM.) 240 241 .2-42- 243 244 245 10 ELVES STATEMENT 5 5 , 5 2 , F I G U R E 7 : REL . FREQUENCY OF TRANSIT TIMES AT SHI -ENDGRAP-H . TAB TITLE FJFr.T 8,OCCUPANCY OF SHELVES 246 247 -2-48- 249 250 251 * * GRAPH - G R A P H - ORIGIN X Y ju_ fxA.aa 5 0 , 1 0 , 2 , 6 , 0 , 1 , 1 5 0 , 1 , 2 4 , ? 252 253 -25-4- 255 256 ?5 7 STATEMENT 4 , l , i g STATEMENT 52 ,9,OCCUPANCY -ST-AT-EME.M-T 55-,X9-,F-LG URE-8-: PYING SIMULTANEOUSLY THE SHELVES ENOGRAPH 7 100 _L0— -RE-I F-REQUENC Y_„0 F—NUMBER.-OF—JOB S—0 C C U.L 258 259 -260- 261 262 ? 6 3 STO RAGE TAB SHELVES TITLE -SP-ACE- TI TLE ) F.IFf . T 11,THE RECORDINGS COLLECTION (=OESK £ SHELVES) AS ST01 9,TRANSIT TIMES THROUGH REC. COLL. (MIN. ) , (=DESK £ 1 264 265 -266- 267 268 269 * GRAPH -GRAP-H- ORIGIN X ¥ XP_,XAB3 5 0 , 1 0 , , 7 , 1 , 1 , 1 5 Q , l , 4 5 , 1 270 271 -2-7-2- 273 274 275 7 STATEMENT 4 . 1 , * 100 STATEMENT 5 2 ,19 ,TRANS IT TIME (MIN. ) LO- .ST-A-T-EMENT 55-,X5-,FXGURE_-9-: .~-AE.L.^F^ GH THE RECORDINGS COLLECTION ENDGRAPH 276 277 -2X8- 279 280 281 TAB TI TLE EJECT 10,OCCUPANCY OF RECORD. COLLECT. (=DESK & SHELVES) 282 283 GRAPH GRAPH ORIGIN TP,TAB10 5Q,1Q 284 285 286 287 -< 100 10 X Y .S-T-AT_E ME NT- STATEMENT STATEMENT , 2 , 4 , 0 , 1 , 2 0 0 , 1 , 1 5 , 3 Jt- .-L,-* 52 ,9,OCCUPANCY 5 5 , 8 5 , F I G U R E 1 0 : REL . FREQUENCY OF NUMBER OF JOBS 0CC1 IJPYTNfi SIMU1 TANFmiSI V DF.SK AMD SHF IVFS 288 289 -29.0- 291 292 293 - S X O - ENDGRAPH -T-I-T-LE- T A B SPACE TI TLE FJFCT _4.0-,-T.HE_LI-SXENI-NG_R0OM_AS_SXORAG.E 3 11 ,L ISTENING ROOM INTERARRIVAL TIMES (MIN. ) 294 295 -29.6_ 297 298 299 * GRAPH -GRAR.H ORIGIN X Y X.P_,XABL1 5 0 , 1 0 , , 7 , 1 , 1 , 1 5 0 . 4 . 1 5 . 3 300 301 .3.0.2- 303 304 30 5 7 S T A T E M E N T 100 S T A T E M E N T a.o___ S X A X E J M . E . N X - 4 , 1 , ? 52 ,25 , INTERARRIVAL TIME (MIN. ) _5.5.,.6iM-EXG U R . E - 1 U - R E X *_AR E.QU.E NC-Y_OF_I.NXE.RAR RLVA L-TJ.MESl- TO LISTENING ROOM ENDGRAPH 306 307 .30.8- 309 310 TAB TITLE 12,NUMBER OF ARRIVALS TO L I S T . ROOM/10 MIN 312 EJECT 313 * 314 * GRAPH 315 GRAPH TP,TAB12 316 OR I GIN 5 0 . 10 317 X , 2 , 6 , 0 , 1 , 1 5 318 Y 0 , 1 , 2 4 , 2 319 7 ST-AXE-ME-NX 4 , 1 , ? 3?n 100 STATEMENT 5 2 , 2 0 , A R R I V A L RATE/10 MIM. 321 10 STATEMENT 5 5 , 7 0 , F I G U R E 1 2 : REL . FREQUENCY OF ARRIVALS TO LISTEN1 322 IMG R01M OUR IMG 10 MIN. 323 ENDGRAPH 324 325 TAR TI T IF l ^ t I T S T T RnnM SFRS/ICP TTMFS (MTis|.» 326 EJECT 327 323 * GRAPH 329 GRAPH TP,TAB13 330 ORIGIN 5 0 , 1 0 331 x , , 3 , 5 , 1 , 3 0 332 Y 0 , 1 , 2 1 , 2 333 7 STATEMENT 4 , 1 , ? 334 1 00 STATFMENT 5 2 . 1 9 t T R A N S IT TIMF (M T M.) 335 10 STATEMENT 5 5 , 5 8 , F I G U R E 1 3 : REL . FREQUENCY OF TRANSIT TIME OF L U 336 STENINS ROOM 337 TAB ENDGRAPH TITLE F.IFCT 14,OCCUPANCY OF L I S T . ROOM 338 339 340 341 * GRAPH -GRAPH— ORIGIN X _Y _XP_,X-ABl-4- 5 0 , 1 0 , 2 , 4 , 6 , 1 , 1 8 0 , 1 , 1 6 , 3 342 343 3ik_4_ 345 346 347 7 STATEMENT 4 , 1 , 2 100 STATEMENT 52,9,OCCUPANCY 1.0 SXAXEMEN-T 5.5-,-87-,-U-S.UR.E-_l-4-:_REL.._J_REm UPYING SIMULTANEOUSLY THE LISTENING ROOM ENDGRAPH 348 349 _35D_ 351 352 353 STO -TAB- TITLE SPACE -XIX LE- EJECT 41,THE RESERV. LISTENING ROOM AS STORAGE 3 -1X,.0C.CUP_ANC.Y— OE„RES.ERV-E_L-ISX._RO0M_ * GRAPH 354 355 -35.6_ 357 358 359 7 1QQ GRAPH ORIGIN _X Y STATEMENT STATFMFMT TP,TAB17 5 0 , 1 0 -,-2-,-6-,-0,-l- , - l -5 0 , 1 , 3 5 , 1 4 , 1 ,% 57.9.nCCUPANCY 360 361 -362- 363 364 365 10 STATEMENT 5 5 , 9 6 , F I G U R E 14A: REL . FREQUENCY OF NUMBER OF JOBS 0C1 COPYING SIMULTANEOUSLY THE LISTENING ROOM E-ND-G.RA.P-H STO T ITLE SPACE 10,THE SYSTEM AS STORAGE _ : 366 367 -368- 369 370 371 TAB TITLE -EJECX- 15,SYSTEM TRANSIT TIMES (MIN. ) ( = S E R V I C E S WAIT. TIME1 * GRAPH APH TP.TAFU5 372 373 -37-4- 375 376 377 ORIGIN X _Y 5 0 , 1 0 , , 3 , 5 , 1 , 3 0 -0-,.5.,.2.0-,.2 4 , 1 , 3 7 STATEMENT 100 STATEMENT 52 ,19 ,TRANSIT TIME (MIM.) 10 STATEMENT 55.49.FIG1JRE 1 5 : REL. FREQUENCY DF SYSTEM TRANSIT TIM1 378 379 -380- 381 382 383 ES _* ENDGRAPH TAB TITLE EJECT 16,OCCUPANCY OF SYSTEM (=DESK,SHELVES,L IST . ROOM) 384 385 -386- 387 388 389 * GRAPH GRAPH TP,TAB16 390 391 ORIGIN X Y STATFMFMT 5 0 , 1 0 , 2 , 4 , 2 , 2 , 2 0 0 , 2 , 2 0 , 2 4 .1 .X 392 393 394 39 5 100 STATEMENT 52,9,OCCUPANCY 10 STATEMENT 5 5 , 7 9 , F I G U R E 16: REL, -URVJJ^G--SI-MULXANEOU.SLY--XHE_Sy-SXEM ENDGRAPH END FREQUENCY OF NUMBER OF J03S QCC1 396 397 3-9.8„ 399 400 401 BLOCK NUMBER SYMBOL REFERENCES BY CARD NUMBER 66 BE IDE 120 125 8 DESK 67 72 -7-4— -EXIT -83 85 8i> 87- UL5 1-07 L08- 109 128 131 132 78 FINE 80 102 129 -5-0- GFH1 D LDJ9 69 GEH11 127 72 GEH13 130 _7_3 G EH 1-4 13 2- 24 GEH2 81 26 GEH3 82 77 P,PH4 BA. 28 GEH5 87 46 GEH7 103 _48 G.E-H-8 1-0.4 49 GEH9 106 61 OFLOW 112 4 STC? 63 UU LLQ L2_8 1_3_ 29 STG3 63 85 88 131 133 51 STG4 86 .88 108 110 J ABLE SYMBOLS AND CORRESPONDING NUMBERS 1 TAB1 10 TAB10 _1_1 XAB-1-1- 12 TAB12 13 TAB13 JJt TAB14 15 T4B15 16 TABIS -1-7 -TJYB17- 2 TAB2 3 TA33 __t T AB4 5 TAB5 6 TAB6 - X - TJVB-7- 8 TAB8 9 TAB9 F U N C T I O N S Y M B O L S AND CORRESPONDING NUMBERS 1 ARRI V 2 DESK -4 L-IS-T— * 1 * FUNCTION DEFINITIONS * SYSTFM ARRIVAL TTMF FXPDNFNT TAI 1 Y DISTRIBUTED J 1 FUNCTION RN1 C16 O.p 0 . 0 . 1 8 2 . 1 . 283 . 2 6 7 . 4 8 6 . 5 . 6 3 2 .-83 . 736 1 . 1 7 . 8 1 1 . 5 . 8 6 5 1 .83 . 9 0 3 2 . 16 ' . 9 3 0 2 . 5 . 9 5 2 . 8 4 . 9 6 4 3 . 1 5 . 9 7 5 3 . 5 . 9 8 ? 3 . 84 . 9 8 7 4 . 1 6 . 9 9 4 . 5 __*_-0-E-S.K- ^ F a U I r F TIMF FKPnMFMTI A l 1 V n I C.TR T Rl IT FH 2 FUNCTION RN1 C24 0 . 0 0 . 0 . 1 . 1 0 4 . 2 . 2 2 2 - 3 . 355 - 4 . 509 . 5 . 6 9 . 6 . 9 1 5 .7 1 . 2 . 7 5 1 . 38 . 8 1 . 6 . 8 4 1 . 8 3 . 8 8 2 . 12 „..X-_ . - 2—3 . 9? 2 . 52 . 94 2 . « 1 . 9 5 2 . 99 . 9 6 3 . 2 . 9 7 3 . 5 E . 9 8 3 . 9 .99 4 . 6 . 9 9 5 5 . 3 . 9 9 8 6 . 2 . 9 9 9 7 . 0 . 9 9 9 7 8 . 0 * * SHELF SERVICE TIME EXPONENT I ALLY DISTRIBUTED 3.- — -.FU.NCXI.Ofcl RN1 C2 3 0 . 0 0 . 0 . 1 5 4 . 8 4 0 . 2 8 1 . 2 5 0 ' . 3 9 0 . 4 2 0 . 4 8 3 . 5 8 0 . 5 6 2 . 7 5 0 . 6 ? 9 . 9? . 6 8 5 1 .08 . 7 33 1 . 25 . 7 7 4 1 . 42 . 8 0 8 1 . 5 9 . 8 3 7 1 . 7 5 . 8 6 2 r 1.92 . 883 2 . 0 8 . 9 2 . 2 5 , .-9X6 2 . 4? . 9 ? 7 2 . 5 8 . 937 2 . 7 5 . 9 4 6 2 . 92 . 9 5 3 3 . 0 8 . 9 5 9 3 . 2 5 . 9 6 4 3 . 42 1 . 0 5 . 2 7 • * * LISTENING ROOM SERVICE TIME GENERALLY DISTRIBUTED FUNCTION 0-1 0...0- 131 . 3 1 2 366 . 6 9 0 5_s 1 . 0 5 RN1 C25 02A-.- . 2 0 5 . 436 . 6 2 3 .0.63- . 4 3 7 . 8 2 0 1 .18 -.-07-1- . 2 8 ? . 498 . 6 9 9 -.-1-87- . 5 6 3 . 940 1 .31 4 . 820 * STORAGE DEFINITIONS 10 : STORAGE 200 _ _ 1 1 — - S - T - 0 R A GE 1-5.0- 30 STORAGE 100 40 STORAGE 23 _A1 STnRAfcF 7% * TABLE DEFINITIONS 1 2 3 4 TABLE XA .3LE— T ABL E QTA8LE TAftl F I A - R X Ml 2 JUL 1 1 20 -0 1 30 1 1 30 0 1 30 1 1 - 30 6 7 8 9 10 _LL_ TABLE TABLE TABLE TABLE TABLE TABI F 12 13 -14- 15 16 _ L _ T ABLE TABLE -T-AB-LE- TABLE TA8LE TABI F * * iPSS PROGRAM 1 2 _3_ 4 5 6 7 8 9 la) i : i I- _L l l 17 18- 19 23 -2_L_ 22 23 24- 25 26 _2L7_ 28 29 -30 - 31 32 __3_ 34 35 -36- 37 38 _3__ 40 4L 42- 43 44 _ _ GENERATE ENTER TRANSFER MARK ENTER -QUEUE— LI NK SEIZE DEPART ADVANCE RELEASE JJ&lL-IJiK TABULATE TABULATE TAftUI A TF LEAVE TABULATE TABULATE. ASSIGN TEST LE TFST F TEST E TRANSFER - T E S T E TRANSFER TRANSFER TRAMSFFS TRANSFER MARK -ENTER ENTER ADVANCE 1 FA V F TABULATE TABULATE -TABULATE- TABULATE LEAVE TAfttll A TP TABULATE ASSIGN -TEST- L E TEST E TEST E T f t A N S F F P RT Ml S30 Ml S l l IA RT Ml _S4-0- Ml S10 S4I 3 10 . 3 6 0 11 . 2 _ 2 2 7 1 2 2- 1 2 _3_ 11 9 -10 . 2 C l J_3_ P4 P4 . 7 5 0 . 9 6 0 . 7 3 3 5 6 8 11 10 3 X I - P2 P4 0 1 0 1 0 JL 3 0 -0- D 0 1 5 - 1 - 5 2 _1_ FNl 79 FIFO 8 FN2 -8 . 1. K l K3600 78 K l 74 X I - 29 51 _2_8_ 26 -2-7- 74 74 74 . 1 1 0 29 11- 30 6 _3__ 51 FN3 K l -K3600—7-8- K l 46 K l 48 JJt 20 60 40 60 60 _Q_ 15 60 .2-6- 60 60 -2__ 10 46 TEST E P4 K l 49 \ 47 TRANSFER . 280 4 74 48 TRANSFER . 2 2 3 51 74 49 TRANSFER . 1 4 0 50 74 50 TRANSFER . 5 8 0 4 51 , 51 MARK J 52 GATE SNF 40 61 \ 53 ENTER 40 54 ADVAMCE 40 FN4 55 LEAVE 40 56 TABULATE 11 57 TAftlll ATF l ? 58 TABULATE 13 59 TABULATE 14 . — 6 0 - TRANSFER 66 61 ENTER 41 62 ADVANCE 40 FN4 63 1 F AV F 41 64 TABULATE 17 65 TRANSFER 66 65 ASSIGN 4 K l 67 TEST E P3 K l 69 68 TRANSFER . 0 9 0 4 74 69 T FS T L F C l K3600 78 70 TEST E P2 K l 72 71 TRANSFER . 3 8 0 29 74 72 T-R.A~M.SF E~R -0-8.0 . 73 74 73 TRANSFER . 1 4 3 4 29 74 LEAVE 10 75 TABUI ATF 1 5 75 TABULATE 16 77 TERMINATE 78 - LEA-VE 10 79 TABULATE 15 83 TABULATE 16 Rl TERMINATE 1 * CONTROL CARD START 1 STATISTICS CONCERNING H E INFORMATION DESK FACILITY AVERAGE UTILIZATION < ! 2 _ 3 _ NUMBER ENTRIES 1 531 AVERAGE T I ME/TRAM . 5 6 4 SEIZING TRANS. NO. PREEMPT ING TRANS. NO. STATISTICS CONCERNING THE DESK QUEUE M A X I M U M A V F R A C F T OT A1 ZERO p F R r. F M r A l / F R A C F ^AVERAGE T A 3 L F I HR R F NIT CONTENTS CONTENTS ENTRIES ENTRIES ZEROS 2 7 . 1 5 4 1532 1245 8 1 . 2 MVER-AGE—T-I-MEV-T-R A NS = AV-ERAGE—XIME/-T-RANS—EXXLUDXMG—ZERQ—E-MXRXES- TI ME/TRANS . 362 T IME/TRANS 1 . 9 3 7 N U M B E R CONTENTS 1 STATISTICS CONCERNING THE DESK USER CHAIN U-SE-R-XHA-I-N- 2 — X Q X A I ENTRIES 447 AV-ERA.G.E— TIME/TRANS 1. 243 _CU.R.REJy|J_ CONTENTS A - V . E J R A G . E _ C O N T E N T S . 1 5 4 MAXXMUM- COMTENTS 7 DESK INTERARRIVAL TIMES (MIN. ) TABLE TAB1 ENTRIES IN TABLE MEAN ARGUMENT STANDARD DEVIATION SUM OF ARGUMENTS 1530 2. 350 2.57'+ 3597.OOP NON-WE I G A TE D UPPER OBSERVED PER CENT CUMULATIVE CUMULATIVE MULTIPLE DEVIATION I IMIT FREQUENCY OF THTAI PFRTFNTAGF RFMATMDFR OF MF AM F R H M MFAM 1 720 4 7 . 0 5 4 7 . 0 5 2 . 9 . 4 2 5 - . 5 2 4 | 2 255 1 6 . 6 6 6 3 . 7 3 5 . 2 . 8 5 0 - . 1 3 6 3 ?H9 1 ^ . 6 6 7 7 . 3 7 7 . 6 1 . 2 7 6 . 2 5 2 j 4 108 7 . 0 5 8 4 . 4 1 5 . 5 1 .701 . 6 4 0 5 77 5 . 0 3 8 9 . 4 1 0 . 5 2 . 1 2 6 1 .029 6 42 2 . 7 4 9 2 . 2 7 . 7 2 . 55? 1 , 4 1 7 7 41 2 . 6 7 9 4 . 9 5 . 0 2 . 9 7 7 1 . 8 0 5 8 27 1 . 7 6 9 6 . 5 3 . 3 3 . 4 0 2 2 . 1 9 4 9 19 1 .74 9 7 . 9 2 . 0 3 . 8 7 8 2 . 5 8 2 10 13 . 8 4 9 3 . 7 1 .2 4 . 2 5 3 2 . 9 7 1 11 3 . 1 9 9 8 . 9 I.D 4 . 6 7 8 3 . 3 5 9 ! 17 4 . 7 6 9 9 . 7 . 7 5 . 1 0 4 3.74R i 13 4 . 2 6 9 9 . 4 . 5 5 . 529 4 . 1 3 6 14 3 . 1 9 9 9 . 6 . 3 5 . 9 5 4 4 . 5 2 5 15 2 . 1 3 9 9 . 8 . 1 5 . 3 8 0 4 . 9 1 3 16 0 . 0 0 9 9 . 8 . 1 5 . 8 0 5 5 . 3 0 2 17 0 .OD 9 9 . 8 . 1 7 . 2 3 1 5 . 6 9 0 18 3 . 1 9 1 0 0 . 0 . 3 7 . 6 5 6 6 . 0 7 9 Ri; MAINING FREQUENCIES ARE ALL ZERO - % * * * * •V* 80 * * 76 * """•"~™~™~™—1 vJ» * •—• • • 1 • — 1 1 ~™~ * 72 * 68 * * 64 * * 60 * * 56 * I * 1 5 2 * ! * 48 * * ** 44 * ** 1 * ** 40 * ** * ** i 36 * ** ! * ** 32 * ** * ** 28 * ** * ** 24 * ** * ** 20 * ** * ** I A A ft ft ftft * * * * * 12 * ** ** ** * ** ** ** 8 * ** ** ** *- ** ** ** ** 4 * ** ** ** ** ** * ** ** ** ** ** ** ** 0 ********************************************************************>>>*************>************************************* 1 ? 3 4 <5 h 7 R INTERARRIVAL TIME (MIN. ) FIGURE l : R E L . FREQUENCY OF INTERARRIVAL TIMES J TABLE EM.TRTFS TAB2 IN TABLE MEAN ARGUMENT STANDARD DEVIATION SUM OF ARGUMENTS 360 4. 250 2.2 57 1530.000 MON-WEIGHTED UPPER OBSERVED PFR f. FMT r.UMtll A TI VF ~ tIMUl ATT \/F Mil TT PI F DFV T A T TnM LIMIT FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAM F * DM MEAN 0 10 2.77 2.7 97.2 -.000 -1.882 1 74 6. 66 9.4 90.5 .235 -1.439 2 49 13.61 23. 0 76.9 .470 -. 996 3 63 17.49 43.5 59.4 .705 -. 553 4 61 16. Q4 57. 4 4? -5 .94] - T11 n 5 52 14.44 71.9 28. 0 1.176 .332 6 45 12.50 84.4 15. 5 1.411 . 775 7 34 9.44 93.8 6.1 1 .647 1.217 8 7 1.94 95.8 4.1 1.882 1 .660 9 7 1.94 97.7 2.2 2 . 117 2.103 10 3 .83 93.6 1 .3 ?. 352 ?. 546 11 2 . 55 99.1 .8 2.588 2.989 12 3 .83 100.0 .0 2.823 3.432 R = MAIMING FRFQliF NT. I F 5> ARF A l l 7 FR D •NIW 0 I / 3 1 V , 1VAI__V 62 82 Lc 92 _2 _Z ZZ IZ QZ 61 til LI 91 _ I M £1 _ l 11 C l 6 ti _ 9 _ £ _ I 0 ***********************************:M **$*************4****$*^ $ * * * * * * * * * * * * * * * * jj.************* 0 ** * * * * * * * * * * 4 * * * * * ** * • ' • • , , . 3 f * ** 4* * * * * * * * * * * * 1 * * * * * * * * * * * * * * ** * * * * * * * * * 4 4 #* ** * z * * * * * * * * 4 * 4 4 * * * ** 4* * * ** ** * * * £ - * * * * * * * * 4 * 4 4 * * * • * * * * ** * * * * * 4 * * * * * * * * * * * 4 * * * * * * ** ** ** * * * * 4 4 * * * S * * * * * * 4 4 4 4 4 4 * * * * * * * #* * * * * 4 4 * * * 9 * * * * .** * * * * * * * * * #* 4 * 4 * *# *-* # L * * * * * * * * 4 4 *."*• * * * * * * * * * 4 * 4 4 * 8 * * * * * * * * #4 4 * * * * * * 4 4 4 * 4 4 4 4 * 6 * * * * * * * * 4 4 * *# * 4 ** * * 4 4 * 0 1 * * * * * * 4 * * * * * * 4 4 4* * * * * * 11 * * * * * * * * 4 4 * * * ** 4 * * * 4 4 * 21 * * * * * * ** * 4 4 44 4~* 4~4 * CT' 4 * * * 4 4 * * * * * * * * *?\ 4 * * * * * * * * * ST 4 * 4* * * * * * 4 4 4 * * * * 91 LI 4 * 8 T * Tjf— 6- T- * 4 02 * * IZ * ~4 * * % DESK TRANSIT TIMES {MIN.) (=WAIT. & SERVICE TIME) TA8LE TAB3 ENTRIFS 1M T A B L E MEAM ARGUMENT STANDARD DEVIATION SUM OF ARGUMENTS 1531 -U&RER- LIMI T 1 2_ —OBSERV-ED- FREQUENCV 1160 707 . 9 2 6 _P_ER-X.EN.L 1 .265 1 4 1 9 . 0 3 0 NON-WEIGHTED OF TOTAL 7 5 . 7 6 1 3 , 5 2 _C UM ULA.T_LV.E_ PERCENTAGE 7 5 . 7 8 9 . 2 ..CUMUL ALIVE. REMAINDER 2 4 . 2 1 0 . 7 _MULXLP_LE_ DF MEAN 1.07 3 2 - 1 5 7 .D.E.VLAXI.ON- FROM MEAN . 0 5 7 . 3 4 7 3 4 _5- 6 7 _8_ 94 38 -1-7- 8 4 _____ 13 48 X_L 52 25 _JL2_ 9 5 . 4 9 7 . 9 —9-9.-0- 9 9 . 5 9 9 . 8 1 0 0 - 0 4 . 5 2 . 0 —.J9_ . 4 . 1 . 0 3 . 236 4 . 3 1 5 -5..-3-9L4- 6 . 4 7 3 7 . 5 5 2 8 . 6 3 1 1. 638 2 . 4 2 8 _3...2.1.3_ 4 . 008 4 . 798 5 . 5 8 3 REMAINING FREQUENCIES ARE ALL ZERO _*_ 57 * * 54 * *_ 60 0 * 51 * 45 * * # 42 * _3-9-~*- 36 * * * ft * 33 * _3-0-*- 27 * * 0 *********************************************************************************** ! TRANSIT TIME (MIN. ) 1 FIGURE 3 : REL . FREQUENCY OF TRANST TIMES AT INFORMATION DESK i T A B L E T A B 4 F N T R T F s TNI TABt F MFAM ARGUMFNT STANDARD DEVIATION SUM OF ARGUMENTS ] 1531 . 3 6 2 . 9 3 2 5 5 5 . 0 3 0 NON-WEIGHTED UP-P-E-R 03 SERVED P_E.R_CE.NT_ CUMJ.L.A.T-L„E C J.MJ.L.A.T_I.V-E_ M.J.LXLP-L.E DE-V-I-AXI.O.N. LIMIT FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 1245 8 1 . 3 1 8 1 . 3 1 8 . 6 - . 0 0 3 - . 3 8 8 ] L_2 9 . 7 7 9 0 . 5 9__4 ?• 758 . 6 3 3 2 78 5 . 0 9 9 5 . 6 4 . 3 5 . 517 1 . 755 3 . 34 2 . 2 2 9 7 . 9 2 . 3 8 . 2 7 5 2 . 8 2 7 4 13 .-84- 98.-7 1___2 : 1_._D3A 3...8J9X 5 12 . 7 8 9 9 . 5 . 4 1 3 . 7 9 2 4 . 9 7 1 6 6 . 3 9 9 9 . 9 . 3 1 6 . 5 5 1 6 . 0 4 3 1 J __£ 1QQ.Q _3 1 9 . 3 0 9 7 . 1 1 5 REMAINING FREQUENCIES ARE ALL ZERO * * _*_ * * 60 * 00 * ** 57 * ** * ** 54 * ** * ** 51 * ** * ** 4B * ** * ** 45 * ** ** 1 42 * «* ' * ** ** 1 * ** ! 36 * ** * ** 33 * ** * ** i 30 * ** * ** 27 * ** * ** , 24 * ** * ** 21 * ** * ** 18 * ** * ** 15 '* ** * ** JL2 * ** * ** 9 * ** ** * ** ** 6 * ** ** * ** ** ** ...3...„.,* ____ *_* *_*. *_*_ * ** ** ** ** 0 ************************************************************************************************************************** J O B S IM QUEUE i F I G U R E 4: R E L . FREQUENCY OF JOBS W A I T I N G FOR S E R V I C E AT INFORMATION DES< i i J STORAGE CAPACITY AVERAGE AVERAGE ENTRIES AVERAGE CURRENT MAXIMUM 30 100 1 . 8 7 6 IJ 1 I L 1 /-HI 1 UIM . 018 1195 i i n c / i A H !«• 5 . 6 5 6 L. U ;M 1 _ SM 1 O u Ji» 1 L 1 1 J 9 < ¥SHE.LF INTERARRIVAL i _ _ . TIMES (MIN. ) ENTRIES IN TABLE . I U S A - MEAN ARGUMENT 3..J1L1- STANOARD DEVIATION 3...0J7-8- SUM OF ARGUMENTS 3 5 9 6 . 0 0 0 - -N.ON-W.E.LGJJ.E.D_ UPPER OBSERVED PER CENT CUMULATIVE CUMULATIVE MULTIPLE DEVIATION • 1 IMIT FREQUENCY DF TDTAl PERCENTAGE REMAINDER OF MEAN FROM MEAN 1 499 4 1 . 7 9 4 1 . 7 5 8 . 2 . 3 3 2 - . 65 3 2 196 1 6 . 4 1 5 3 . 2 U . 7 . 6 6 4 - . 3 2 8 110 9 . 2 1 6 7 . 4 1 ? . 5 . 996 - . 0 0 3 ! * 104 8 . 7 1 7 6 . 1 2 3 . 8 1 . 3 2 8 . 321 i - 5 88 7 . 3 7 3 3 . 5 1 6 . 4 1 . 6 6 0 . 6 4 5 6 39 3 . 2 6 8 6 . 7 1 3 . 2 1 . 9 9 2 . 9 7 0 • ', 7 42 3 . 5 1 9 0 . 2 9 . 7 2 . 3 2 4 1 . 2 9 5 8 30 2 . 5 1 9 2 . 7 7 . 2 2 . 6 5 6 1 . 6 2 0 9 27 2 . 2 6 9 5 . 0 4 . 9 ? . 9 8 8 1 . 945 10 17 1 .42 9 6 . 4 3 . 5 3 . 3 2 3 2 . 2 7 0 11 13 1 .03 9 7 . 5 2 . 4 3 . 6 5 2 2 . 5 9 5 < 12 14 1 .17 9 8 . 7 1 .2 3 . 9 8 4 2 . 9 2 0 13 5 . 4 1 9 9 . 1 . 8 4 . 3 1 6 3 . 2 4 4 14 4 . 3 3 9 9 . 4 . 5 4 . 6 4 8 3 . 5 6 9 1 5 . 2 5 9 9 . 7 , ? 4 . 980 3 . 894 16 1 . 0 8 9 9 . 8 . 1 5 . 3 1 2 4 . 2 1 9 17 0 . 0 0 9 9 . 8 . 1 5 . 644 4 . 5 4 4 - 18 0 . 0 3 9 9 . 8 .1 5 . 9 7 6 4. 869 19 0 . 0 0 9 9 . 8 . 1 5 . 3 0 8 5 . 194 20 2 . 16 1 0 0 . 0 . 0 6 . 6 4 0 5 . 5 1 9 -RE-M AI-N LN G-ER EQ U E.N C J -ES-A RE-A L-L-_ZE-R 0- * * * * k * 1 8 0 * * 76 * * 7 2 * * 6 8 * * ft4 * i * 6 0 * * 5 6 * * - 52 * •< * 4 8 * * 4 4 * * . , . 4 0 * ** * ** 3 6 * * * * ** »- 3 2 * ** * ** 28 * ** * ** 2 4 * ** * * * > Ih 20 * ** * ** u * ** ** ft ft* ** 12 * ** ** _ * ** ** 8 * ** ** ** ** * ! * ** ** ** ** ** 4 * ** ft* ** ft* ft* * ** ** ** ** ** ** 0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * _.. i 1 • ? 3 , S 6 Ir c. , — — i I N T E R A R R I V A L TIME ( M I N . ) i F I G U R E 5: R E L . FREQUENCY OF I N T E R A R R I V A L T I M E S - i . DUMBER OF ARRIVALS TO SHELVES/10 MIN. TABLE TAB6 > FMTRTFS TN TARI F M FAM ARGllMFNT STANDARD DEVIATION SUM OF ARGUMENTS / 360 3 . 3 1 6 2 .074 1 1 9 4 . 0 0 0 NON-WEIGHTED \ UPPER OBSERVED PER CFNT CUMIM ATI VF ri iMiir AT I VE Ml| T I P| E DFtf I ATT ("INI LIMIT FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 8 2 . 2 2 2 . 2 9 7 . 7 - . 0 0 0 - 1 . 598 1 1 f>. 3R 1 8 . 6 qi .3 .331 - 1 . 1 1 6 2 78 2 1 . 6 6 4 0 . 2 5 9 . 7 . 6 0 3 - . 6 3 4 3 82 2 2 . 7 7 6 3 . 0 3 6 . 9 . 9 0 4 - . 1 5 2 4 48 1 3 . 33 7S . 3 ?3 . 6 1 .206 . 329 5 30 8 . 33 8 4 . 7 1 5 . 2 1 . 5 0 7 . 8 1 1 6 21 5 . 8 3 9 0 . 5 9 . 4 1 . 8 0 9 1 . 2 9 3 * 7 ?Ci 5 . 55 96.1 3 . 8 2 - 1 1 0 1 . 775 8 7 1 . 9 4 9 8 . 0 1 .9 2 . 4 1 2 2 . 2 5 7 9 5 1 .38 9 9 . 4 . 5 2 . 7 1 3 2 . 7 3 9 10 0 ,rv3 9 9 , 4 T S 0] «5 ^, ?2? 11 1 . 2 7 9 9 . 7 .2 3 . 3 1 6 3 . 7 0 4 12 0 . 0 0 9 9 . 7 . 2 3 . 6 1 8 4 . 1 8 6 1 3 1 - 2 7 1 0 3 . 0 . 0 3 . 9 1 9 4 . 6 6 8 REMAINING FREQUENCIES ARE ALL ZERO _*_ * r 2 0 * o n 0 0 * ** *<« 19 * ** ** I * ** ** 1 18 * ** ** * ** ** 1 17 * ** ** * ** ** l 1 6 * ** ** ** 1 ** ** ** 15 **  ** * ** ** ** 14 * ** ** ** - y ** ** ** 13 * ** ** ** ** * ** ** ** ** 12 * ** #* ** ** ** ** ** ** 1 1 * ** ** ** ** * ** ** ** ** 10 ** ** ** ** * ** ** ** ** 9 * ** ** ** ** * ** ** ** ** 8 * ** #* ** ** ** * ** ** ** ** ** 7 * ** ** ** ** ** * ** ** ** ** ** 6 # ** ** ** ** ** ** ** ** ** ** 5 ** ** ** ** ** ** ** * ** ** ** ** ** * * * * * ** ** ** ** ** ** ** * ** ** ** ** ** ** ** 3 * ** ** ** ** ** ** ** * ** ** ** ** ** ** ** 2 * ** ** ** ** ** ** ** ** * ** ** ** ** ** * * ' * * - 1 ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** 0 ***** ***** ***************************************** £ *** ************^ * * *********** **** * ********* ** ********* 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 9 A R R I V A L R A T E / 1 0 MINI. 'SHELF TRANSIT TIMES (MIN) TABLE TAB7 FMT3 I F S IM TAR I F MFAM ARGtlMFNT STANDARD PF V I AT I (IN SUM P F ARGUMENTS ; 1195 5.656 5.457 6759.ODD NON-WEIGHTED UPPER OBSERVED PER CENT f~UMUI AT IV E CUMULATIVE MUL TIPL F DEVIATION LIMIT FREQUENCY OF TOTAL PERCENTAGE REMAINDER 3F MEAN FROM MEAN 1 157 13.13 13. 1 86. 8 .176 -.853 ? 1 7.43 30.6 69.3 . 353 669 3 182 15.23 45.8 54.1 .530 -.486 4 178 14.89 60.7 39.2 . 707 -.303 5 60 .̂02 65.7 ^4. 2 . 8R4 -.120 6 67 5.60 71.3 23.6 1.060 .063 7 50 4. 18 75.5 24.4 1.237 .246 R 50 4. 1 R 79.7 20.? 1.414 .429 9 37 3.03 32.8 17.1 1.591 . 612 10 39 3.26 86.1 13.8 1.768 . 796 U 20 1.̂ 7 R7. 7 12.2 1 . 944 . 979 12 25 2.03 89.8 10. 1 2. 121 1.162 13 20 1. 67 91.5 3.4 2.298 1.345 1 4 1 4 1.17 92.7 7.2 2.475 1.529 15 16 1.33 94.0 5.9 2.652 1.712 16 10 .83 94.8 5.1 2.828 1.895 17 6 . 50 -9-5.-3 4.5 3.005 2.078 18 5 .41 95.8 4.1 3. 182 2.262 19 5 .41 96.2 3.7 3.359 2.445 20 3 .25 96.4 3.5 3.536 7.628 21 4 .33 96.8 3. 1 3.712 2.311 22 6 .50 97.3 2.6 3. 889 2.995 ?3 6 .50 97.8 2.1 4,066 3.178 24 5 .41 98.2 1.7 4.243 3.361 25 2 .16 98.4 1.5 4.420 3.544 76 3 .25 98.6 1.3 4. 596 3.72 8 27 3 .25 98.9 1.0 4.773 3.911 28 4 .33 99.2 ' .7 4.950 4.094 29 . 33 Q3 . 5 . 4 5,127 4. 277 30 4 .33 99.9 .0 5.3D4 4.461 31 1 .08 100.0 .0 5.480 4.644 R F MAT N I NG F RFQ1IF NT. I F s ARF At L 7ERD GR APH 24 * * % * * _2-2—*. * 21 * *. 20 * * _1_9—*. * 18 * * 1 7 * .-46—*- — * : — — — - - ., . . . * * 15 * * * * * * '. 14 * * * * * 4 ft ft __1_3 * * *. * .* . . . . , . . . . ft ft * * * 12 * * * * * * * * * * 11 * * * * ft ft * * * * _1.0—* * * *—_—__* ft * * * * g * ft * ft ft * * ft *_ * : : 8 * * * * * ft ft ft ft ft _ 7 * * *. *. *. : : , ft ft ft ft ft 6 * * * * ft ft ft * ft ft : 5 * * * * * * * • * * ft ft ft * * 4 ft ft. *. * *. * *. * * * * * * * * * * * 3 * * * * * * * * * * * * * * * * * *_ * * * * 2 * * * * * * * * * * * * * * * * * * * * * * * * _.-!.-*- * *. * * .* * * .» *- * * * * * *. * * * * * * * * * * * * * * * * 0 ********************************************************************************************** 1 2. 3 k S ft 1 8 3. LO 1_] 1.2 13 lit _L5 TRANSIT TIME ( M I N . ) OCCUPANCY OF SHELVES TABLE TAB8 FNTRTFS TN TAR I F MFAM ARGUMFNT STANDARD DEVIATION SUM OF ARGUMENTS 1195 1 . 9 1 1 1 .476 2 2 8 4 . 0 0 0 NON-WEIGHTED I I P P F B flRSFRVFn PFR PFMT C. 11 M 11 AT T <J F r.! I M ! II AT T V F MIIITTPIF DFWTATinN LIMIT FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 195 1 6 . 3 1 1 6 . 3 8 3 . 6 - . 0 0 0 - 1 . 2 9 4 1 347 7 9 . 0 3 4«S.3 5 4 . 6 . 5 2 3 - . fS17 2 298 2 4 . 9 3 7 0 . 2 2 9 . 7 1 . 0 4 6 . 0 6 0 3 189 1 5 . 8 1 8 6 . 1 1 3 . 8 1 . 5 6 9 . 7 3 7 4 91 7 . 6 1 9 3 . 7 6 . 7 2 . 0 9 ? 1 .414 j 5 47 3 . 9 3 9 7 . 6 2 . 3 2 . 6 1 6 2 . 0 9 1 6 22 1 .84 9 9 . 4 . 5 3 . 1 3 9 2 . 7 6 9 7 S .41 9 9 . 9 . 0 3.fcfc? 3 . 4 4 6 ! 8 1 . 0 3 1 0 0 . 0 . 0 4 . 185 4. 123 REMAINING FREQUENCIES ARE ALL ZERO i j . f i 1 • 1 24 * 00 * * 2S * ** ** ** ** 22 * ** ** * ** ** 21 * ** ** ** ** 20 * ** ** * ** ** 19 * ** ** ** ** 18 * ** ** ** ** 17 * ** ** *** ** ** 1.6- ** ** ** -* ** ** ** 15 * ** ** ** ** * ** ** ** ** 1 4 * ** ** ** ** ** ** ** ** 13 * ** ** ** JL. ^ *r» ** ** ** ** 12 * ** ** ** ** ** ** ** ** 11 * ** ** ** ** * ** ** ** ** 10 * ** ** ** ** * ** ** ** ** 9 * ** ** ** ** * ** ** ** ** 8 ** ** ** ** * ** ** ** ** 7 * ** ** ** ** ** 1 * ** ** ** ** ** 6 * ** ** ** ** ** # ** ** ** ** ** 5 * ** ** ** ** *fc i * ** ** ** ** ** 4 * ** ** ** ** ** * ** ** ** #* ** 3 * ** ** ** ** ** ** * ** ** ** ** ** ** i ' 2 ** ** ** ** ** ** 1 1 * ** ** ** ** ** ** * ** ** ** ** *<C * * * * * ** ** ** ** ** ** ** i 0 ************************************************************************************^^ j 0 1 7 4 5 6 7 8 9 1 0 11 12 13 14 OCCUPANCY j F I G U R E 8: R E L . FREQUENCY OF NUMBER OF JOBS OCCUPYING S I M U L T A N E O U S L Y THE S H E L V E S STORAGE C A P A C I T Y AVERAGE r.riNTFNTS AVERAGE E N T R I E S U T I l I 7 A T i n N AVERAGE TTMF/TR AM- CURRENT CONT-NTS MAXIMUM CONTENTS 1 11 150 2. 271 .015 2727 2.999 1 10 r Tr*J ,NSI T T I M E S THROUGH REC. C O L L . ( MIN . ) t {=DESK £ S H E L V E S ) Ti Ef VBLE TAB9 ^ T R I E S I N T A B L E 2726 MEAN ARGUMENT i . n n n STANDARD D E V I A T I O N 4 . 41 fj SUM OF ARGUMENTS 8 1 7 8 .000 NON-WEIGHTFD UPPER LIMIT OBSERVED FREQUENCY PER OF CENT TDTAI C U M U L A T I V E C U M U L A T I V E P E R C F N T A G F RFMAINDER M U L T I P L E OF MEAN D E V I A T I O N FROM MEAN 1 2 1317 416 27-6 48.31 15.26 10-12 48.3 63.5 7^. 6 51.6 35.4 76. 3 . 3 33 .666 i . nnn - . 453 - . 2 2 6 - .003 4 5 6 216 77 75 7.92 2.82 7.75 81.6 34.4 87.1 18.3 15.5 12.8 1. 333 1 .666 2.003 . 226- .453 .680 7 8 Q 54 53 37 1.93 1.94 1.35 89.1 91.1 92.4 10.8 8.8 7 .5 2. 333 2.666 ^ .003 . 906 1.133 1.360 10 11 12 39 20 25 1.43 .73 . 91 93.9 94.6 95.5 6.0 5.3 4 .4 3.333 3.666 4.000 1.587 1.813 2.040 13 14 1 5 20 14 1 * .73 .51 . 58 96.2 96.8 97.3 3.7 3.1 7 T 6 4.333 4. 666 5 . non 2.267 2.494 7. 7?n 16 17 18 10 6 5 .36 .22 .13 97.7 97.9 98.1 2.2 2.0 1.8 5.333 5. 666 6.000 2.947 3. 174 3. 401 19 20 21 5. 3 . 18 .11 .14 98.3 98.4 93.6 1.5 1.5 1.3 5.333 6.666 7. 000 3.627 3.854 4. 081 22 23 74 6 6 5 . 22 .22 .13 98.8 99.0 99 .7 1.1 .9 .7 7.333 7.666 8.000 4. 308 4. 534 4. 761 25 26 77 2 3 3 .07 .11 .11 99.3 99. 4 99 . 5 .6 . 5 , 4 8 .333 8.666 9. 000 4.988 5.215 5.441 28 29 3 0 4 4 4 . 14 . 14 .14 99.6 99.8 99.9 .3 .1 .0 9.333 9.666 10.000 5.668 5.895 6.122 R£ 31 r M A I N I N G F R E Q U E N C I E S ARE 1 ALL ZERO .03 100.0 .0 10.333 6. 348 i — • • \ ! 5 g * 45 * 0 44 * * 43 * * 42 * * 41 * ft 40 * * 39 * * 38 * * 37 * * 36 * * 35 * * 34 ft * 33 * * 32 * * 31 * * 30 * * ?9 * * 1 28 * * 27 * * O A * * 1 1 1 — " V I » * •-«..-—"...u mi. .. .. ~ -. . . 25 * * 24 * * i ?3 * * 22 * * 21 * * 20 * * 19 * * 18 * * 1 7 * * _ 16 * * 15 * * * 14 * * * 13 * * * 12 * * * i i ft * * 10 * * * * 9 * * * * 8 ft * * * 7 * * * * * 6 * * * * * 5 * * * * * 4 * * * * * 3 * ft ft ft ft 2 * * f t * * f t * I * * * * * * * * * * * 0 A * * * * * * * * * * * * * * * * * * * * * * * * * 1 ? 3 4 5 h 7 ft q v n 11 1? 13 14 IS TRANSIT TIME ( MIN. ) FIGURE 9 : R E L . FREQUENCY OF TRANSIT TIMES THROUGH THE RECORDINGS COLLECTION J O C C U P A N C Y OF RECORD. C O L L E C T . (=DESK £. S H E L V E S ) T A B L E TAB 10 MFAN ARGUMFNT STANDAR 0 OFVI ATT QN SUM PF ARGUMENTS 2 7 2 6 2 . 3 7 2 1.753 6 4 6 8 . 0 0 0 NON-WEIGHTED UPPER 08 SERVED PER CENT CWMULATIVF CU M U L A T I V E M'JLT I P L E D F V I AT ION L I M I T FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 3 3 0 1 2 . I D 1 2 . 1 8 7 . 8 - . 0 0 0 - 1 . 3 5 2 1 6 3 3 7 3 - 7 ? 3 5 - 3 6 4 . 6 .471 - . 7 8 ? 2 6 7 9 2 4 . 9 0 6 0 . 2 3 9 . 7 . 842 - . 2 1 2 3 4 6 6 1 7 . 0 9 7 7 . 3 2 2 . 6 1. 2 6 4 . 3 5 7 4 2 9 7 1 0 . 89 R P , T ? 1 1 . 7 1 . 6 8 5 . 9 2 7 5 1 4 7 5. 39 9 3 . 6 6.3 2.10 7 1.497 6 8 6 3. 15 9 6 . 7 3.2 2. 5 2 8 2 . 0 6 8 7 6 5 7 . 3 3 99.1 .8 7 . 9 5 0 2 . 6 3 8 8 22 .80 9 9 . 9 .0 3 . 3 7 1 3 . 2 0 8 9 1 . 0 3 1 0 0 . 0 .0 3 . 7 9 3 3.778 -R EM A I N I-NG-ERE-Q UE.NCI-E-S-A R E - A L L - Z E R 0- i o * * # ft o • * » • o •* ft ft « o •«• ft » -ft O ft ft ft -ft 0 ft ft -ft ft ft -if ft ft ft in OL < fi-ts ft ft ft •ft * ft ft * ft ft ft ft ft ft ft ft ft ft * ft ft ft ft tt ft -ft ft •ft ft -ft ft ft. ft •ft ft ft ft ft ft ft -ft ft ft ft -ft ft PO ft -ft -ft CM ft ft ft ft ft -ft ft ft ft -ft f  ft ft ft ft ft ft -ft ft- ft * ft ft ft » ft ft -ft •ft ft ft ft -ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft**-*** ft ft # # ft ft ft ft ft -ft ft ft ft # ft- ft ft ft ft ft. ft ft * ft ft ft ft ft ft * ft ft ft ft ft ft * # * # • » * ft ft ft * ft- ft ft ft .ft ft ft ft •ft ft ft- ft ft ft ft ft ft «• ft «• •ft ft ft ft ft ft 0> 00 ft ft ft -ft ft ft # ft ft ft ft -ft ft * * ft- • f t ft • f t ft ft ft -ft •ft ft ft ft • f t ft ft ft -ft ft ft •ft •» ft -ft •ft ft • f t ft ft ft •ft ft ft -ft ft # ft ft ft ft tt ft ft ft ft ft ft ft- • f t ft ft ft ft ft- • f t ft ft ft •ft ft ft -ft ft ft •ft ft ft ft • f t ft • f t ft ft ft * ft ft -ft ft ft- ft -ft ft ft ft ft ft «• ft ft * i n ft - f t •» «• ft « * ft -ft •ft ft •ft ft •ft -ft •ft -ft ft -ft ft ft ft -ft ft -ft * ft ft ft ft » ft ft # ft •» CO ft ft ft -ft ft ft ft ft ft ft ft ft * ft ft ft ft. ft ft -ft ft -ft ft ft -Si- ft tt ft ft # ft ft ft * ft ft ft ft ft ft ft ft -ft •ft tt ft ft -ft ft CM ft -ft •ft -ft •ft -ft ft ft ft ft tt ft- ft ft •ft -ft ft * tt ft ft ft ft ft ft ft ft ft ft # ft ft ft ft -ft ft ft ft ft ft ft ft «. ft AS- ft •ft ft * •ft « ft ft ft ft cr cc in C J < O. _3 C J O Q cc -c pr 00 ill > 00 Q v: OO LU o 00 n UL) 5» oo 05 Z > o. O C J o 00 00 O u_ o c_ Ol CO X r> 2 a >-o _r UJ =5 a UJ u. LU rvr UJ CD STORAGE CAPACITY AVERAGE AVERAGE ENTRIES AVERAGE CURRENT MAXIMUM CONTENTS UTILIZATION : TIME/TRAN CONTENTS CONTENTS 40 23 7.751 .337 660 42.290 9 23 LISTENING ROOM INTERARRIVAL TIMES (MIN. ) TABLE T A B U ENTRIES IN TABLE MEAN ARGUMENT STANDARD DEVIATION SUM OF ARGUMENTS 650 5. 496 5 . 4 0 ? 3573,000 NfiN-WFI G.HTFD UPPER OBSERVED PER CENT CUMULATIVE CUMULATIVE MULTIPLE DEVIATION LIMIT FRFOUENCY OF TDTA1 PFRCFNTAGF REMAINDER OF MEAM F*DM MEAN 1 140 21.53 21.5 78.4 .181 -.832 2 80 12. 30 33.8 66.1 .363 -.647 3 80 12.30 46.1 5 ^ T f t . 5 4 5 -.46? 4 53 8. 15 54.3 45.6 .727 -. 277 5 54 8. 30 62.6 37.3 .909 -.091 6 41 6.30 68.9 31.0 1 .091 .093 7 44 6.75 75.6 24.3 1.273 .278 8 29 4.46 80.1 19.8 1.455 .463 Q 28 4. 30 84. 4 I 5 . 5 1,63 7 . 648 10 15 2.30 86.7 13.2 1. 819 . 833 11 14 2. 15 88.9 11.0 2.001 1.018 1 7 9 1. 38 90.3 9.6 2.18 3 1.203 13 9 1.38 91.6 8.3 2.364 1.388 14 11 1.69 93.3 6.6 2. 546 1. 573 1 5 4 . 61 93. 9 6,0 7.728 1.759 16 8 1.23 95.2 4.7 2.910 1.944 17 4 .61 95.8 4.1 3.092 2. 129 1 8 4 .61 96.4 3.5 3.274 2.314 19 3 .46 96.9 3.0 3.456 2.499 20 2 .30 97.2 2.7 3. 638 2. 684 21 3 . 46 97.6 2 .3 3.820 7. 869 22 3 .46 98. 1 1.8 4.00 2 3.054 23 1 .15 98.3 1.6 4.184 3. 239 74 1 - 1 5 98.4 1 m 5 4.366 3. 475 25 2 .30 98.7 1.2 4.547 3.610 26 I . 15 98.9 1.0 4.729 3.795 77 1 . 1 * 99.0 .9 4.911 3. 980 28 1 .15 99.2 .7 5.093 4.165 29 2 .30 99. 5 .4 5.275 4.350 OVERFLOW 3 .45 100.0 .0 AVERAGE VALUE OF OVERFLOW 32.00 A GR APH * J % 60 * * * 56 * * * 52 * * 48 * * * 44 * * 40 * * • j 36 * * 32 * * * ' 28 * * 24 * * * 20 * * * 16 * * * * 12 * * * * * * * * * 8 * * * * * * * * * * * * * * * * 4 * * * * * * * * * * * * * * * * * * * * * * * * * * * * 0 * * * * * * * * * * * * ************************************************************************************************************************** 1 7 * 4 5 A 7 f t Q 10 11 1? I"* 14 15 INTERARRIVAL TIME (MIN. ) FIGURE 1 1 : REL. FREQUENCY OF INTERARRIVAL TIMES TO LISTENING ROOM TABLE TAB 12 FMTPTFs- r N T ARI F MFAM ARGUMENT STANDARD DEVIATION SUM OF ARGUMENTS 360 1 . 8 0 5 1 .351 6 5 0 . 0 0 0 NON-WEI3HTED ; UP-P-ER 03SERVED P_ER—CENT CUMU.LAXI.V.E CUMJ.LA.T-I-V-E MJLT IPLE DEV-LAX.I.ON LIMIT FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 61 1 6 . 9 4 1 6 . 9 8 3 . 0 - . 0 0 0 - 1 . 3 3 5 1 1_Q_6 ? 9 . 44 4 6 . 3 5 3 . 6 .553 - . 5 9 6 2 95 2 6 . 3 8 7 2 . 7 2 7 . 2 1 . 1 0 7 . 1 4 3 3 56 1 5 . 5 5 8 8 . 3 1 1 . 6 1 .661 . 8 8 3 L__ 4 27 X.4,9 — 9 5 . 3 - . . 4...1 2..-215 l.._623 - 5 12 3 . 3 3 9 9 . 1 .3 2 . 7 6 9 2 . 3 6 3 6 3 . 8 3 1 0 0 . 0 . 0 3 . 3 2 3 3 . 1 0 3 REMAINING FRFOUFNCIFS ARF A M 7FRD 00 «* 00 * * % * ** ** 22 * * ** ft* ** ** * ** ft* 21 * * ** ** ** ** • 20 19 * * ** ** ** ** ** ** * ** ** 18 * * ** ** ** ** 1 i 17 * * ** ** ** ** , 1* * ft* ** ** I * ** ** ** l 15 ft ft ** ** ** ** ** ** ** ** ' 14 ft ** ** ** ** * ** ** ** ** 1 3 ft ft* ** *ft ft* * ** ** ** ** 12 * * ** ** ** ** ** ** ** ** 11 * ft ** ** ** ** ** ** ** ** V 10 ft ** ft* ** ft* * ** ** ** ** 9 * * ** ** ** ** ** ** ** ** 8 ft * ** ** ** ** ** ** ** ** 7 ft ** ** ft* ** ** 1— * ** ** ** ** ft* 6 * ** ** ** ft* ** * ** ** ** ** ** 5 * ** ** ** ** ** * ** ** ** ** ** 4. * ** ** ** ** ** * ** ** ** ** ** 3 * ** ** ** . ** ** ** * ** ** ** ** ** ** 2 ft ** ** ** ** *> ** ft ** ** ** ** ** ** 1 ft ** ** ** ** ** ** i *• ft ** ** ** ** ** ** ************************************************************************************************************************** Q ] 7 3 4_ 5 6. 1 3 9 LQ_ L l 12 13. L _ _ ARRIVAL RATE/10 MIN. FIGURE 1 2 : REL. FREQUENCY OF ARRIVALS TO LISTENING ROOM DURING 10 MIN. TABLE TAB 13 J—lTfUFS MF AM AR CVilM FMT STAMDAR 0 3FVIATIOM SUM OF ARGUMENTS 651 4 2 . 1 8 1 3 1 . 4 3 7 2 7 4 6 0 . 0 0 0 NON-WEIGHTED ' 1 UPPER OBSERVED PER CENT CUMULATIVE CUMULATIVE MJLT IPLF nF.* TATTONI LIMIT FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 4 ,6V . 6 9 9 . 3 - . 0 0 0 - 1 . 3 4 1 5 38 5- 83 6 . 4 9 3 . 5 . 1 1 8 - 1 . 1 8 2 10 34 5 . 22 1 1 . 6 8 8 . 3 . 2 3 7 - 1 . 0 2 3 15 49 7 . 5 2 1 9 . 2 8 0 . 7 . 355 - . 8 6 4 20 49 7. 52 2 6 . 7 7 3 . 2 . 474 - . 7 0 5 25 49 7 . 52 3 4 . 2 6 5 . 7 . 5 9 2 - . 5 4 6 30 46 7 . 0 6 4 1 . 3 5 8 . 6 . 7 1 1 - . 3 8 7 35 4? 6 . 4 5 4 7 . 7 5 7 . 7 . 879 228 40 32 4 . 91 5 2 . 6 4 7 . 3 . 9 4 8 - . 0 6 9 45 47 7 . 2 1 5 9 . 9 4 0 . 0 1 . 066 . 0 8 9 — < ^0 52 7 . 9 3 67 .8 3 7 . 1 1 . 1 8 5 . 248 55 48 7 . 37 7 5 . 2 2 4 . 7 1 .30 3 . 4 0 7 60 32 4 . 9 1 8 0 . 1 1 9 . 3 1 .422 . 5 6 6 fi5 25 3 . 8 4 8 4 . 0 1 5 . 9 1 . 540 . 7 2 5 ! 70 20 3 . 0 7 8 7 . 0 1 2 . 9 1 .659 . 884 - ! 75 10 1 . 53 8 8 . 6 1 1 . 3 1 . 7 7 8 1 . 0 4 3 BO 10 1 . 53 90 . 1 9 . 8 1 . 3 9 6 1 .202 85 11 1 .63 9 1 . 8 8 . 1 2 . 0 1 5 1 .362 90 6 . 9 2 9 2 . 7 7 .2 2 . 1 3 3 1 .521 95 6 . 9 7 9 3 . 7 6 . 2 2 . 2 5 2 1 . 6 8 3 100 5 . 7 5 9 4 . 4 5 . 5 2 . 370 1 . 839 105 6 . 92 9 5 . 3 4 . 6 2 . 4 8 9 1 . 9 9 8 110 2 . 30 9 5 . 6 4 . 3 7 . 607 7 . 1 5 7 115 4 . 6 1 9 6 . 3 3 . 6 2 . 7 2 6 2 . 3 1 6 120 4 . 6 1 9 6 . 9 3 . 3 2 . 8 4 4 2. 475 175 1 . 1 5 9 7 . 0 7 . 9 7 . 9 6 3 2 . 6 3 4 130 2 . 3 0 9 7 . 3 2 . 6 3 . 081 2 . 7 9 3 135 2 . 3 3 9 7 . 6 2 . 3 3 . 2 0 0 2 . 952 140 2 . 30 9 8 . 0 1 . 9 3 . 3 1 9 3 . 1 1 1 145 3 . 4 6 9 8 . 4 1 . 5 3 . 437 3 . 2 70 150 2 . 3 0 9 8 . 7 1 . 2 3 . 5 5 6 3 . 429 155 1 . 1 5 9R .9 1 .3 3 . 6 7 4 3 . 5 8 8 160 1 . 15 9 9 . 0 . 9 3 . 793 3 . 7 4 7 165 2 . 3 0 9 9 . 3 . 6 3 . 911 3 . 9 0 6 1 70 1 . I 5 9 9 . 5 . 4 4 . 0 3 0 4. 065 175 1 . 15 9 9 . 6 . 3 4 . 1 4 8 4 . 2 2 4 130 1 . 15 9 9 . 8 . 1 4 . 2 6 7 4 . 3 8 3 185 1 . 1 5 100 .0 . 0 4 . 3 8 5 4. 542 REMAINING FREQUENCIES ARE ALL ZERO % ft * ! *. * 21 * *_ 20 * * _l-9—*- * 18 * _ 17 * * _ l -6 -* - * 15 * *_ 14 * * -1-3—*. 12 * * 11 * * * 9 * *_ 8 * 7 4c * * * * * * * —• 1" • |— * * * * * * * 6 * * * * * * ft * * ' * * * * * 4c 5 * * ft * * * * * * * * * * * * * * * * * * * * * * * * ft * * * * * ft * * * * * * * * ft 3 * * * * * * * * * * * * ft ft * * * * * * * * * * * * * ft ft 2 * * * * * * * * ft * * ft ft ft * * * * * * * * * * * * ft * 1 * * * * ft ft * * ic * ft * ft ft ft ft ft ft . x.— * * * * ft * * * * ft * ft ft * ft * 0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 5 i n l 5 20 25 30 35 40 45 Sfi 55 _0_ 63 7_Q 15 8_Q_ 85 9_Q 95 100 1 Q5 110 115 120 125 1 30 1 35 143 145 150 T R A N S I T . TIME ( M I N . ) FIGURE 1 3 : REL . FREQUENCY OF TRANSIT TIME OF LISTENING ROOM \ OCCUPANCY OF L I S T . ROOM TABLE TAB14 F N T R T F s f Nl TAR I F MEAN ARGIJMFNT STANDARD DEVIATION! SUM OF ARGUMENTS 651 7 . 7 7 4 3 . 3 8 5 5 0 6 1 . 0 3 3 NON-WEIGHTED U.&P-ER OBS-ERV-ED P_ER_.CENT C.UiM.U.LAJ.LVE C.UM.U.LJLI.I-V.E MUJ-XLP_L£ DEV.I.A.LLON. LIMIT FREQUENCY OF TOTAL PERCENTAGE REMAINDER 3F MEAN FROM MEAN 0 0 . 0 0 . 0 1 0 0 . 0 - . 0 0 0 - 2 . 5 1 9 1 J _JL5 __1 9 9 , 8 , 1 2 3 - 2 . 1 9 5 2 4 . 6 1 . 7 9 9 . 2 . 2 5 7 - 1 . 8 7 1 3 17 2 . 6 1 3 . 3 9 6 . 6 . 3 8 5 - 1 . 5 4 7 4- 47- . . 7 . -21-___ L0..-5— 8-9_. A .-5.1-4. - - 1 — 2 2 3 - 5 87 1 3 . 3 6 2 3 . 9 7 6 . 0 . 6 4 3 - . 8 9 8 6 89 1 3 . 6 7 3 7 . 6 5 2 . 3 . 7 7 1 - . 5 7 4 Z LOJ 1 5 . 5 1 53.1 46 . f l . 9 0 3 - . 2 5 0 8 79 1 2 . 13 6 5 . 2 3 4 . 7 1 .029 . 0 7 3 9 63 9 . 6 7 7 4 . 9 2 5 . 0 1 . 1 5 7 . 3 9 7 1.0 55 8.-4.4 8 3 . 4 1-6.5 1-2-8.6 : . .721. U 50 7 . 6 8 9 1 . 0 8 . 9 1 . 4 1 4 1 . 0 4 5 12 22 3 . 3 7 9 4 . 4 5 . 5 1 . 5 4 3 1 . 3 6 9 13 9 1 . 3 3 9 5 . 8 4_-_l 1 . 6 7 ? 1 . 6 9 3 14 7 1.07 9 6 . 9 3 . 0 1 . 8 0 0 2 . 0 1 7 15 2 . 3 0 9 7 . 2 2 . 7 1 . 9 2 9 2 . 3 4 1 1-6 4 . 6 1 97—8 2 -4 2.-058 2.-665- 17 2 . 3 0 9 8 . 1 1 .8 2 . 1 8 6 2 . 9 8 9 18 5 . 7 6 9 8 . 9 1 .0 2 . 3 1 5 3 . 3 1 3 l 9 2 . 3 3 9 9 . 2 __2 7 . 4 4 3 : 3 . 637 20 3 . 4 5 9 9 . 6 . 3 2 . 5 7 2 3 . 9 6 1 21 1 . 1 5 9 9 . 8 . 1 2 . 7 0 1 4 . 2 8 5 -2.2 : 1 .-1-5 1-0-0-0 .-0 2.-82-9. 4.-60-9- R E M A l N I N G F R E Q U E N C I E S ARE A L L ZERO % * 15 * ** * ** 14 * * ** ** * ** 13 * * ** ** ** ** * ** ** 12 * * ** ** ** ** ** ** ** ** ** 11 * * ** ** ** ** ** ** * ** ** ** 1.0 * * ** ** ** ** ** ** * ft* ** ** 9 * * ** ft* ** ** ** ft* ** ft* * ** ** ** ** 8 * * ** ** ft* ** ** ** ** ** ** ** * ** ** ** ** ** 7 * ft* ** ** ** ** ** * ** ** ** ** ** ft* * ** ** ** ** ** ** 6 * ** ** ** ** ** ** * ** ** ** ** ** ** * ** ** ** ** ** ** 5 * ** ** ** ** ** ** * ** ** ** ** ** ft* * ** ** ** ** ** ** 4 * ** ** *# ** ** ** * ** ** ** ** ** ** * ** ** ** ** ** ** 3 * ** ** ** ** ** ** ** * ** ** ** ** * * ** ** I * ** ** ** ** ** ** ** 2 * ** ** ** ** ** ** ** * ft* ** ** ** ** ** ** 1 * *ft ** ** ** ** ** ** 1 * ** ** ** ** ** ** ** ** ** * ** ** ft* ** ** ** ** ** ** * ** ** ** ** ** ** ft* ** ** g ***************************************************************************************************************** 6 7 fl 9 10 I t L2 L3 Lit L5_ L6 LZ LS L2 21 11 23 •_ O C C U P A N C Y FIGURE 1 4 : REL . FREQUENCY OF NUMBER OF JOBS OCCUPYING SIMULTANEOUSLY THE LISTENING ROOM '. * *_ : : * 33 * __32—* : : 31 * 30 * ?Q * : : 28 * 27 * __2-6—* : = 25 * 24 * ?3 • — — 22, * 21 * _2-0- * : : '• : — 19 * 18 * 1 7 * : — 16 * 15 * . _ l - 4 - * • '• • • — — — 13 * 12 * 1 1 * : : : 10 * 9 * —_8____ . . . 7 * 6 * : 4 * 3 * _ 2 — * — - — • _ _ _ _ _ _ _ _ 1 * 0 * * * * * * * * * * * * * * * * * * * * U i / - 1 . 4 •> *> / n v i n i i id i i i t OCCUPAMCY FIGURE 1 4 A : R E L . FREQUENCY OF NUMBER OF JOBS OCCUPYING SIMULTANEOUSLY THE L I S T E N I N G ROOM STORAGE C A P A C I T Y AVERAGE AVERAGE E N T R I E S AVERAGE CURRENT MAXIMUM CONTENTS I IT 11 I 7 AT I ON T IM E/ TR AN CONTENTS CONTENTS ) 10 2 0 0 1 0 . 0 2 2 . 0 5 0 1 6 1 3 2 2 . 3 7 5 10 2 6 ' SYS TEM T R A N S I T T I M E S ( M I N . ) ( - S E R V I C E £ WAIT. TIME I TA 3LE T A B 1 5 E N T R I E S I N T A B L E J _ - 1 6 0 3 - MEAN ARGUMENT 3. 085- STANDARD D E V I A T I O N — . L I U 2 X 0 - SUM OF ARGUMENTS 4-9A6..-G0-Q- -NON=.WLELGJXE.D- U P P E R • T MIT OBSERVED FREQUENCY PER -OIL- CENT TOTAL C U M U L A T I V E PERCENTAGE C U M U L A T I V E REMAINDER M U L T I P L E OF MEAN D E V I A T I O N FROM MEAN 0 5 -10- 1 5 2 0 _2_5_ 6 9 5 7 7 1 —5.4 2 3 9 7_ 4 3 . 3 5 4 8 . 0 9 ._3.36- 1.43 . 5 6 __43_ 4 3 . 3 9 1 . 4 .94.-8. 9 5 . 2 9 6 . 8 9 7 . 2 5 6 . 6 8.5 - . 5 . X 3.7 3.1 2.7 - . 0 0 0 1 .620 4. 8 6 1 6 . 4 8 2 8 . 1 0 2 -. 3 0 2 . 187 ___*.6.7_7_ 1 . 1 6 6 1 . 6 5 6 2 . 1 4 6 3 0 3 5 40 4 5 5 0 _5_5_ 6 3 3 5 6 JL .37 .13 .18- . 3 1 .37 .43 9 7 . 6 9 7 . 3 -£8-0- 9 8 . 3 9 8 . 6 9 9 . 1 2.3 2.1 - L . X 1.6 1.3 . 8 9 . 7 2 3 1 1 . 3 4 3 -1-2..J964- 1 4 . 5 8 4 1 6 . 2 0 5 1 7 . 8 2 5 2 . 6 3 5 3. 1 2 5 3.-615- 4 . 1 0 4 4. 5 9 4 5 . 0 8 4 50 6 5 .7-0- 75 8 0 _a__ 2 2 _1_ 2 2 _D_ . 12 .12 . 06. . 12 . 12 .00 9 9 . 2 9 9 . 3 -9-9—4- 9 9 . 5 9 9 . 6 9 9 . 6 .7 .6 -.5- .4 .3 _ 3 _ 1 9 . 4 4 6 2 1 . 0 6 6 -22.6B7- 2 4 . 3 0 7 2 5 . 9 2 8 ? 7 . 5 4 8 5 . 5 7 3 6. 0 6 3 -6.-553- 7.042 7 . 5 3 2 8. n?? 9 0 9 5 -100- 1 0 5 110 11 5 0 1 -0- 1 0 _1_ .00 .06 -.-0-3- . 0 6 .00 .06 9 9 . 6 9 9 . 7 9 9 . 7 9 9 . 8 9 9 . 8 9 9 . 8 .3 .2 -.2- .1 .1 2 9 . 1 6 9 3 0 . 7 8 9 3 2 . 4 1 0 3 4 . 0 3 3 3 5 . 6 5 1 3 7 . 2 7 1 8 . 5 1 1 9.001 9. 491 9.980 1 0 . 4 7 3 1 0 . 9 6 0 120 1 2 5 13 0 1 3 5 1 4 0 •1 45 1 0 JL 0 0 _D_ . 0 6 .00 - 0 3 - . 0 3 .00 .00 9 9 . 9 9 9 . 9 J9S..S- 9 9 . 9 9 9 . 9 9 9 . 9 .3 .0 ...0. .3 .3 ___0_ 3 8 . 8 9 2 4 3 . 5 1 2 -42.-133- 1 1 . 4 4 9 1 1 . 9 3 9 .1.2.-42-9- 4 3 . 7 5 3 4 5 . 3 7 4 4 6 . 9 9 4 12. 9 1 8 1 3 . 4 0 8 1 3 . 3 9 3 150 1 R E M A I N I N G F R E Q U E N C I E S . ARE A L L ZERO ,06 1 0 0 . 0 4 8 . 6 1 5 1 4 . 3 8 7 *_ * * 1 0 0 * * 9 5 * * 90 * * 85 * * - * 7 5 * * 7 0 * * " 6 5 * * 6 0 * * 5 5 * * 50 ' * * * 45 * * * * 4 0 * * * * 3 5 * * * * 30 * * * * 25 * * * * 2 n * * * * 15 * * * * 1 0 * * * * 5 * * * * * o * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ^ 5 1 0 1 5 70 75 30 35 40 45 50 55 60 65 70 75 ft 0 R5 91 95 100 1 05 110 115 17_ 1 25 130 135 140 145 150 TRANSIT TIME (MIN.) FIGURE 1 5 : REL. FREQUENCY QF SYSTEM TRANSIT TIMES T A B L E T A 8 1 6 F M T R t F S TN T A R l F MF AM ARGUMFMT STANQAR 3 OE VI ATI ON SUM OF ARGUMENTS 1 6 0 3 1 0 . 2 1 2 3 . 4 2 9 1 6 3 7 1 . 0 0 0 NON-WEIGHTED UPPE-R- - OBSERVED BER CENT C U.MU LAX L V J E — XUJMUL AT LVE MJLT I P L E D E V I A T I O N L I M I T FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 0 .03 .0 1 0 0 . 0 - . 0 0 0 - 2 . 9 7 7 ? 4 .24 .? 9 9 . 7 . 1 9 5 - 2 . 3 9 4 4 30 1.87 2.1 9 7 . 3 .391 - 1 . 3 1 1 6 158 9.85 1 1 . 9 8 8 . 0 . 5 8 7 - 1 . 2 2 8 8 ...... 3 4 7 2 1 . 6 4 3 3 . 6 ...  6 6 . 3 . 7-83 - . 6 4 5 10 3 9 1 2 4 . 39 5 8 . 0 41 .9 .979 - . 0 6 2 12 3 1 9 1 9 . 9 0 7 7 . 9 2 2 . 0 1 . 1 7 5 . 5 2 1 1 4 1 8 9 1 1 .79 3 9 . 7 1 0 . 2 1 . 3 7 0 1 . 1 0 4 16 9 4 5.86 9 5 . 5 4.4 1 .566 1.687 18 36 2.24 97.8 2.1 1.762 2 . 2 7 0 2 0 16 - .99 98 .8 1.1 L.-9.5.8 - . 2. R53 22 11 . 68 9 9 . 5 .4 2. 1 5 4 3 . 4 3 6 24 6 . 37 9 9 . 8 .1 2 . 3 5 3 4 . 0 1 9 ? 6 ? .12 1 0 0 . 0 .0 2 . 5 4 5 4 . 6 0 3 R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO — - — — — ^ GRAPH _ : ^ % ft ' ft ft * * * 4 0 3fi ft ft * 00 ** ** .36 ft * ** ** ** 3 4 3 ? * * * ** ** ** r — — • — • — - — 30 ft * ** ** ** ft* ** ** 28 26 ft * ft ** ** ** ** ** ** i 2 4 * * ft ** ** ** ** ** ** 22 70 ft * ft ** ** ** ** ** ** 18 * * * ** ** ** ** ** ** 16 1 4 * * ** ** ** ** ** ** 12 * * ** ** ** ** ** ** ft* 10 8 * ft * ** ** ** ** ft* ** ** ** ** * * . . . . . . L 6 * ft ft ** ** ** ** ** ** ** ** ** ** 4 2 ft * * ** ** ** ** ft* ft* ** ** ** ** ** ** _ _—, _ — 0 ft *ft *ft *ft ft* ** ****************************************************************************************^ 7 h 1 n 14 1ft 77 7ft 30 34 3R 4? 46 5 0 54 53 6? 66 70 74 7R OCCUPANCY FIGURE 16 : REL. FREQUENCY OF NUMBER OF JOBS OCCUPYING SIMULTANEOUSLY THE SYSTEM END CPU TIME USED: -ASSEMBL-Y-: 3.-1-45—S E-C ON D S- * EXECUTION: 3 5 . 8 5 0 SECONDS --EX-EC U-T-IO N-T-E^M LN A-T-E D- ,SSIGNOFF 4 V RFS NO. 771390 UNIVERSITY OF B.C COMPUTING CENTRE MTS<AN123) 00:23:19 12-30-70 USER: WULI DEPARTMENT: COMM #*** 2H AT 00:28:20 **** OFF AT 03:29:19 _*JL*_*_.ELARSED_T-LME 5-8-.--Jh.5_ **** -PU TIME USED 42.207 **** STORAGE USED 2578.686 CARDS R FAD 4J_7_ -S.EC- SEC. PAGE- •SEC, **** LINES PRINTED 9100 **** PAGES PRINTED 280 _*_*_*_*__-CARDS_P-UNCHED 0 — — **** DRUM READS 39 **** RATE FACTOR 0. 6 »»»» APPROX. COST OF THIS RUN f.-10.86 **** FILE STORAGE 3 PG-HR. .00 **LAST SI3N3N WAS: 00:12:49 12-30-70 MMMMM MMMMMM -MMMMMMM- MMMMMMMM MMMMMMMMM MMMMMMMMMM MMMMM MMMMMM MMMMMMM- MMMMMMMM MMMMMMMMM MMMMMMMMMM TTTTTTTTTTTTTTTTTTTTTTTTT TTTTTTTTTTTTTTTTTTTTTTTTT _T_T-T_T_T_TXT_T_TJ_TXT̂ ^̂ ^ TTTTT TTTTT TTTTT SS -SS.SS SSSSS SSSSS SSSSS SSSSSSSSS SSSSSSSSSSS SSSSSSSSSSSSS - S SSSSSSS SSSSS MMMMM MMMMM MMMMf MMMMM MMMMM MMMMM -MM MM M- M MMMM MMMM M— MMMMM MMMMMMMMMMM MMMMM , MMMMMMMMM MMMMM MMMMMMM MMMMM MMMMM -MMMMM- MMMMM MMMMM MMMMM TTTTT TTTTT _T_TXT-T- TTTTT TTTTT TTTTT SSSSS SSSS SS SSSSSSSSS SSSSSSSSSSS SSSSSSSSSSSSS SSSSSSS SSSSS MMMMM MMMMM -MMMMM- MMMMM MMMMM MMMMM MMMMM MMM MMMMM MMMMM -MM-1 MM- MMMMM MMMMM MMMMM TTTTT TTTTT _T-T-T_T-T_ TTTTT TTTTT T T T T T SSSSS SSSSS SSSSS -SSSSSSS S SSSSS S- SSSSSSSSSSSSSSSSS SSSSSSSSSSSSS R F S NO. 7 7 1 0 8 3 U N I V E R S I T Y OF B C COMPUTING C E N T R E M T S . A N 1 2 0 ) 0 0 : 1 2 : 4 8 12-30-70 * * * * * * * * * * * * * * * * * * * * T H I S JOB SUBMITTED THROUGH FRONT DESK READER * * * * * * * * * * * * * * * * * * * * $ S I G N O N UULI T = 1 5 0 P=400 PRIO^V C 0 P l E S = 4 * * L A S T SIGNON WAS: 1 0 : 5 4 : 1 3 1 2 - 2 9 - 7 0 , USER " W U L I " S I G N E D CN AT 0 0 : 1 2 : 4 9 ON 1 2 - 3 0 - 7 0 " ^ $RUN * G P S S P A R = S I Z E = B E X E C U T I O N B E G I N S BLOCK NUMBER <LGC O P E R A T I O N A, B, C, D, E, F, G COMMENTS S I M U L A T E S I M U L A T I O N OF UBC RECORDINGS C O L L E C T I O N BY JOHANNES' KRAMAR CARD NUMBER 1' 2 T 4 * F U N C T I O N D E F I N I T I O N S 5 * SYSTEM A R R I V A L T I M E EXPONENT I ALL Y D I S T R I B U T E D A R R I V F U N C T I O N R N 1 . C U N EG. E X P . D I S T R . 0 . 0 , 0 . 0 / . 4 2 3 , . 2 5 / . 6 6 7,. 7 5 / . 8 08 , 1. 25/-. 8 8 9 , 1 . 7 5 / . 9 3 6 ,2 .25 / . 9 6 3 , 2 . 7 5 / 6 7 8 .979 ,3 "V - . 2 5 / . 9 8 8 , 3 . 7 5 / . 9 9 0 , 4 . 2 i > / 1 . 0 , 7.25 9 10 11 * D E S K D E S K 0.0, 0. S E R V I C E T I M E E X P O N E N T I A L L Y D I S T R I B U T E D F U N C T I O N R N 1 , C 2 4 N EG, E X P . D I S T R . 0 / . 1 , . 1 0 4 / . 2 , . 2 2 2 / . 3 , . 3 5 5 / . 4 , . 5 0 9 / . 5 , . 6 9 / . 6 , . 9 1 5 / . 7 , 1 . 2 / 12 13 14 . 7 5 , 1 . . 9 6 , 3. 3 8 / . 8 , 1 . 6 / . 8 4 , 1 . 8 3 / . 8 8 , 2 . 1 2 / .9, 2 .3/.9 2, 2 . 5 2 / . 9 4 , 2 . 8 1 / . 9 5 , 2 . 9 9 2 / . 9 7 , 3 . 5 / . 9 8 , 3 . 9 / . 9 9 , 4 . 6 / . 9 9 5 ,5 . 3 / . 9 9 8 , 6 . 2 / . 9 9 9 , 7 . 0 / . 9 9 9 7 , 8 .0 15 • 16 17 * S H E L F S E R V I C E T I M E EXPONENT I A L L Y D I S T R I B U T E D SHELF F U N C T I O N R N 1 , C 2 3 NEG• E X P . D I S T R . 0 . 0 , 0 . 0 / . 1 5 4 , . 8 4 0 / . 2 8 1 , . 2 5 0 / . 3 9 0 , . 4 2 0 / . 4 8 3 , . 5 8 0 / . 5 6 2 . . 7 5 0 / . 6 2 9 , . 9 2 / 18 19 20 .6 8 5 ,1 . 8 8 3 , 2 . 9 1 6 , 2 . 0 8 T . 7 3 3 , . 0 8 / . 9 , 2 . . 4 2 / . 9 2 7 , 1.2 5./. 7 74,1 . 4 2 / .808 ,1 .59/ .8 3 7 , 1 • / 5 / . 8 6 2 , 1.92 2 5 / 2 . 5 8 / . 9 3 7,2.7 5 / . 9 4 6 , 2 . 9 2 / . 9 5 3 , 3 . 0 8 / . 9 5 9 , 3 . 2 5 21 22 23 . 9 6 4 , 3 . 4 2 / 1 . 0 , 5 . 2 7 •j. * L I S T E N I N G ROOM S E R V I C E T I M E G E N E R A L L Y D I S T R I B U T E D 2 4 2 5 2 6 L I S T 0.0,0 . .4 3 6 , . F U N C T I U N K N 1 , C 2 5 GEN, D I S T R I B U T I O N 0 / . 0 2 4 , . 0 6 3 / . 0 7 1 , . 1 8 7 / . 1 3 1 , . 3 1 2 / . 2 0 5 , . 4 3 7 / . 2 8 9 , . 5 6 3 / . 3 6 6 , . 6 9 0 / 8 2 0 / . 4 9 8 , . 9 4 0 / . 5 5 6 ,1 . 0 6 / . 6 2 3 ,1 . 1 8 / . 6 9 9 , 1 . 3 1 / . 7 5 4 , 1 . 4 4 / . 7 8 6 , 1 . 5 6 / 27 28 29 . 8 1 4 , 1 . 9 2 7 , 2 J , <v . 6 9 / . 8 3 6 , . 5 5 / . 9 6 2 » 1 . 8 1 / . 8 5 5 , 1 . 9 4 / . 8 7 2 , 2 . 0 6 / . 8 8 8 , 2 . 1 8 / . 9 0 3 , 2 . 3 1 / . 9 1 7 , 2 . 4 4 / 3 . 1 9 / . 9 89 , 4 . 2 0 / 1 . 0 0 , 4 . 8 2 0 30 31 3 2 * STORAGE D E F I N I T I O N S 10 STORAGE 2 0 0 D E F I N E S I Z E OF SYSTEM,S STORAGE 11 STORAGE 1 5 0 D E F I N E S I Z E OF R E C . C O L L . 33 . 34 35 30 4 0 • 41 STORAGE STORAGE STORAGE 100 D E F I N E S I Z E OF STOR. 3 0 23 D E F I N E S I Z E OF STOR. 4 0 23 . D E F I N E S I Z E OF STOR. 4 1 36 3 7 38 * T A B L h D E F I N I T I O N S TAB1 T A B L E I A . 1 . 1 , 2 0 I N T E R A R R I v A L T I M E TAB2 T A B L E R T , 0 , 1 , 3 0 , 1 0 . A R R I V A L RATE 39 4 0 41 TAB3 TAB4 TAB5 T A B L E QTABLE T A B L E M l , 1 , 1 , 3 0 T R A N S I T TIME T A B L E 2,0,1 ,30 UNITS IN QUE. I A , 1,1,30 I N T E R A R R I V A L TIME SHELVES 42 4 3 4 4 1 Ab6 T A B 7 TABS 1 A b L b • T A B L E T A B L E k f , 0 , i , _ 0 , 1 0 ARK I V A L k A1 fc M l , l , l , 6 0 T R A N S I T T I M E S 3 0 , 0, 1,40 STOR. 30 OCCUPANCY . 45 46 4 7 TAB9 TAB 10 T A B U T A B L E TABLE T A B L E . M l , 1 , 1 , 6 0 T R A N S . TI M E S E R V I 5 1 1 , 0 , 1 , 6 0 STORAGE 11 OCCUPANCY I A , 1 , 1 , 3 0 . INT E R A R R . TIME F A C . 4 0 48 49 50 1 A B 1 2 T A B 1 3 T A 8 1 4 TABLE T A B L E T A B L E R T , 0 , 1 , 1 5 , 1 0 - A R R I V A L S F A C 4 0 M l , 0 , 5 , 6 0 TRANS. TIME F A C . 4 0 S 4 0 , 0 , 1 , 2 6 STORE 4 0 OCCUPANCY 51 52 53 TAB 15 T AB 16 TAB17 T A B L E T A B L E T A B L E Ml , 0 , 5 , 6 0 TRANS. T I M E IN SYSTEM S 1 0 , 0 , 2 , 6 0 SYST. OCCUPANCY 5 4 1 , 0 , 1 , 2 6 STOR. 41 OCCUPANCY 54 55 56 J * GPSS PROGRAM 58 * 59 1 GENERATE 2 , F N $ A R R I V A R R I V A L S TO SYSTEM 60 2 ENTER 10 CUM. STOR. SYSTEM 61 3 TRANSFER . 3 6 . STG3 , S TG 2 GO TO 3 OR 2 ; ; 62 4 STG2 MARK : SET TRANS. TIME = 0 : 53" 5 ENTER 11 CUM. STORE RC. 64 _6 QUEUE 2 J O I N QUE. 2 6 5 7 L I N K 2» F I F O * DESK L I N K USER C H A I N 2 66 G P S S / 3 6 0 / M T S V E R S I O N ( 4 / 8 / 1 3 ) A •> 8 DESK S E I Z E 2 • OCC. DESK 67 9 DEPART 2 L E A V E QUE. 2 68 10 ADVANCE 1 ,FN$DESK DESK S E R V I C E 69 1.1 R E L E A S E 2 R E L E A S E DESK 7 0 / 12 U N L I N K 2, DESK,1 UNLINK USER C H A I N 2 71 \ 13 T A B U L A T E TAB 1 TAB. I N T E R A R R . T I M E 72 14 T A B U L A T E TAB2 TAB. A R R I V A L S 7 3 15 T A B U L A T E TAB3 T A B . TRANS. T I M E 74 16 L E A V E 11 75 17 T A B U L A T E T A B 9 76 18 T A B U L A T E IAB1.0 / / 19 A S S I G N 2t.Kl SET P I TO 1 78 2 0 TEST L E C 1 , K 3 6 0 0 , F I N E TEST TIME 79 21 TEST E P 3 , K 1 , G E H 2 80 22 TEST E P 4 , K 1 , G E H 3 81 23 TRANS FER , EX IT 82 24. GEH2 TEST E P4 , K l , G E H 4 83 25 TRANSFER .7 5 1 STG.3* E XI T 84 26 GEH3 T R A N S F E R . 9 6 , S T G 4 , E X I T 85 27 GEH4 TRANSFER . 7 3 , G E H 5 , E X I T 86 28 GEH5 T R A N S F E R . 1 1 , S T G 3 , S T G 4 8 7 29 STG3 MARK 88 30 ENTER 11 CUM. STORE RC. 89 31 ENTER 30 ENTER STOR. 3 0 90 32 ADVANCE 6» FN$ S H E L F S H E L F S E R V I C E T I M E 91 1 1 L E A V E 30 LEAVE STOR. 30 92 34 T A B U L A T E TABS I N T E R A R R I V A L TIME 93 35 T A B U L A T E TAB6 A R R I V A L RATE 9 4 36 . T A B U L A l E IAB7 THAN SI i f i MI- V5 37 T A B U L A T E TAB8 S T O R E . S H E L V E S OCCUPANCY 96 38 L E A V E 11 L E A V E STORE 11 9 7 39 T A B U L A T E T A B 9 9 8 40 T A B U L A T E T A B 1 0 STORE RECORD. C O L L E C T . 99 41 A S S I G N 3.K1 SET P2 TO 1 100 42 T t S T L t C l > K 3 6 0 0 , F I N E ' TEST TIME 101 43 TEST E P 2,K1,GEH7 102 44 TEST E P 4 , K1,GEH 8 1 0 3 45 • T R A N S F E R , E X I T 1 0 4 46 GEH7 TEST E P4,K1» GEH9 1 0 5 47 TRANSFER •2 8 , S T G 2 , E X I T 1 0 6 48 . GEH8 T R A N S F E R . 2 2 , S I G 4 , E X IT 107 49 GEH9 T R A N S F E R . 1 4 , G E H l 0 , E X l T 1 0 8 50 GEH10 TRANSFER . 5 8 , S T G 2 , STG4 1 0 9 51 STG4 MARK 1 1 0 52 GATE SNF •40, OFLOW 11 1 53 ENTER 40 ENTER STOR. 4 0 112 54 ADVANCE 4 0 , F N $ L 1 S I L l b 1 . KUUM S t K V l C t 1 1Mb 1 1 3 55 L E A V E 40 L E A V E STORAGE 40 1 1 4 56 T A B U L A T E T A B U INTER A R R I V A L TIME FAC 4 115 57 T A B U L A T E T A B 1 2 A R R I V A L RATE FAC . 4 116 58 TABULATE TAB 1 3 T R A N S I T TIME F A C . 4 1 1 7 59 T A B U L A T E T A B 1 4 STORE. 40 OCCUPANCY 118 60 T R A N S F E R ,«tiut 1 1 9 61 OFLOW ENTER 41 120 6 2 ADVANCE 4 0 , F N $ L I S T L I S T . ROOM S E R V I C E TIME 1 2 1 6 3 L E A V E 4 1 122 6 4 TABULATE T A 8 1 7 OCCUP. OF R E S E R V . L I S T . ROOM 1 2 3 6 5 T R A N S F E R , BE IDE ______ . 1 2 4 "66 BEI DE A S S I G N 47KT bt! P 4 TO 1 ; '~ TZ5 6 7 T E S T E P 3 , K l , G E H l l " 1 2 6 6 8 ] T R A N S F E R . 0 9 , S T G 2 , E X IT • 127 6 9 "GEH 11 TEST LE C l , K 3 6 0 0 , F I N E TEST T I M E 1 28 7 0 T E S T E P 2 , K 1 , G E H 1 3 129 7 1 TRANSFER . 3 8 ,STG3 , Ex IT • . 1 3 0 72 GEH 13 TRANSFER . 0 8, GEH 1 4 , EX I T : : : '. 131 7 3 GEH14 TRANSFER . 1 4 , S T G 2 , S T G 3 132 74_ E X I T L E A V E 10 L E A V E S Y S T . S TOR . 1 3 3 1 5 ' " ~ T A B U L A T E TAB 1 5 TRANS. TIME IN S Y S T E M 1 3 4 7 6 T A B U L A T E T A B 1 6 SYSTEM OCCUPANCY 1 3 5 7 7 T E R M I N A T E . ' 1 3 6 "78 F I N E L k A V b : T O ! : L E A V E S Y S T . SI OR. : — T3T 7 9 T A B U L A T E T A B 1 5 T R A N S . TIME IN SYSTEM 138 8 0 T A B U L A T E T A B 1 6 S Y S T E M OCCUPANCY 13_9 8 1 " ' ' ~ T E R M I N A T E 1 140 * CONTROL CARD ' ' * 141 START 1 • ' • 142_ _ . . . - ; ' T43" REPORT 1 4 4 _ _ ____ _ E J E C T '. L__ FAC T I T L E 2 , S T A T I S T I C S CONCERNING THE INFORMATION DESK 146 SPACE 3 1 4 7 QUE T I T L E 2- , S T A T I S T I C S CONCERNING THE DESK QUEUE " 148 S P A C E 3 ' ' 149" CHA T I T L E 2 , S T A T I S T I C S CONCERNING THE DESK USER CHAIN 150 E J E C T i i • . 15_L " " T A B T I T L E l . D E S K INT ER ARR I VAL • TIME'S '( M I N . J . ~ 152 E J E C T 1 5 3 * " 1J54 * GRAPH 1 5 5 GRAPH TP,TAB 1 1 56 , jORJ GIN 5 0 , 1 0 : . ' _ 1 5 7 X , 2 , 1 . 3 , 1 , 1 , 8 " 1 5 8 Y 0 , 4 , 2 0 , 2 . 1 5 9 7 STATEMENT 4 , 1 , 3 6 1 6 0 TOO STATEMENT 5 2 , 2 4 , I N T E R A R R I V A L TIME ( M I N . ) ; 1 6 T 10 STATEMENT 5 5 , 4 6 , F I G U R E 1 : R E L . FREQUENCY OF I N T E R A R R I V A L TIMES 1 6 2 ^ ENDGRAPH ; 1 6 3 ' * 1 6 4 TAB T I T L E 2 ,NUMBER OF A R R I V A L S TO D E S K / 1 0 MIN. 1 6 5 EJ E C T ; 166_ * GRAPH 168 GRAPH TP ,T AB2 : , 1 6 9 ' ~ O R I G I N 5 0 , 1 0 1 7 0 X , 2 t 2 t O , l , 3 0 171 Y 0 , 1 , 2 1 , 2 : •_ 172_ •7 STATEMENT 4 , 1,X 173 100 STATEMENT 5 2,20» ARR I VAL R A T E / 1 0 MIN. 1 7 4 10 STATEMENT 5 5 , 6 4 , F I G U R E 2: R E L . FREQUENCY OF A R R I V A L S TO I N F . DEI SK DURING 10 M I N . ENDGRAPH 17 5 1 7 6 1 7 7 1 7 8 77AB I 1 I L t E J E C T 3,DESK I R A N S i J I 1 Mb 5 ( M I N * ) ( = W A l i . _ b b R V l L b I 1Mb) TTT 180 181 GRAPH GRAPH O R I G I N T P , T A B 3 5 0 , 1 0 1 8 2 1 8 3 1 8 4 Y STA TE ME N T , , 1 4 , 1, 1,8 0 , 3 , 2 0 , 2 4,1 ,56 T 8 3 ~ 1 8 6 1 8 7 10"0 STATEMENT 10 STATEMENT ORMATION DESK t N U G k A P h 5 2 , 1 9 » T R A N S I T TIME ( M I N . ) 55 , 6 0 , F I G U R E 3: R E L . FREQUENCY OF TR AN ST TIMES AT I N F 1 188 1 89 190 T9T - 192 193 TAB T I T L E 4,NUMBER OF JOBS WAITING FOR S E R V I C E AT DESK E J E C T * GRAPH 194 195 196 GRAPH O R I G I N X TP,.' AB4 5 0 , 1 0 , 2 , 1 3 , 0, 1, 8 198 199 Y 0 , 3 , 2 0 , 2 7 STATEMENT 4,1 ,-g 100 STATEMENT 5 2 , 1 3 , J O B S I N QUEUE 2 00 2 0 1 2 0 2 IT) S I A i f c M t N l !>b,/2,KlCURb 4. RhL . F K t Q U t N L Y U h J U b b WA.1I1NG J-U R . S b l R V I C E AT I N F O R M A T I O N DESK ENDGRAPH 2 0 4 2 0 5 STO T I T L E S P A C E T I T L E E J E C T 30,THE S H E L V E S AS STORAGE 3 5 , S H E L F I N T E R A R R I V A L TIMES (MIN.) 2 06 2 0 7 2 0 8 w 2 1 0 2 1 1 * GRAPH GRAPH O R I G I N T P , T A B 5 5 0 , 10 2 1 2 2 1 3 2 1 4 Y STATEMENT ,2»18,1,1,6 0, 4 , 2 0 , 2 4, 1, « "ZT5" 2 1 6 2 1 7 7 100 STATEMENT 10 STATEMENT ENDGRAPH 52 , 2 4 , I N T E R A R R I V A L TIME ( M I N . ) 5 5 , 4 6 , F I G U R E 5: R E L . FREQUENCY OF I N T E R A R R I V A L TIMES 2 1 8 2 1 9 2 2 0 " Z 2 T 2 2 2 2 23 TAB T I T L E E J E C T 6,NUMBER OF A R R I V A L S TO S H E L V E S / 1 0 MIN. * GRAPH GRAPH O R I G I N Y TP, TAB6 5 0 , 1 0 ,2 , 4 , 0 , 1 ,20 0 , 1 , 2 0 , 2 2 2 4 2 2 5 2 2 6 " 2 2 T 2 2 8 G P S S / 3 6 0 / M T S V E R S I O N ( 4 / 8 / 1 3 ) A s .7 STATEMENT 100 STATEMENT 10 STATEMENT DURING 10 M I N . 4, 1, % 5 2 , 2 0 , A R R I V A L R A T E / 1 0 M I N . 5 5 , 6 2 , F I G U R E 6: R E L . FREQUENCY OF A R R I V A L S TO S H E L V E S 1 2 2 9 2 3 0 2 3 1 2 3 2 / TAB ENDGRAPH T I T L E 7 , S H E L F T R A N S I T T I M E S ( M I N ) 2 3 3 2 3 4 2 3 5 E J E C T * * GRAPH 2 3 6 2 3 7 2 3 8 GRAPH O R I G I N X I P , ! AB7 5 0 , 1 0 , , 5 , 1 , 1 , 1 5 2 3 9 2 4 0 2 4 1 7 100 Y STATEMENT ' STATEMENT 0 , 1 , 2 4 , 2 4, l,% 5 2 . 19? T R A N S I T T I M E ( M I N . ) 2 4 2 2 4 3 2 44 10 E L V E S STA TE ME N T ENDGRAPH 55 , 5 2 , F I G U R E 7: R E L . FREQUENCY OF I R A N S I I TIMES AT S H I 2 4 5 2 4 6 2 4 7 TAB T I T L E E J E C T 8, OCCUPANCY OF S H E L V E S 2 4 8 2 4 9 2 5 0 * GRAPH GRAPH T P , T A B 8 2 5 1 2 5 2 2 5 3 O R I G I N X . . Y 5 0 , 1 0 , 2 , 6 , 0 , 1 , 1 5 0 , 1 , 2 4 , 2 2 54 2 5 5 2 56 7 100 10 STATEMENT STATEMENT STATEMENT 4,1,S 5 2 , 9 , O C C U P A N C Y 5 5 , 7 9 , F I G U R E 8: R E L . FREQUENCY OF NUMBER OF JOBS O C C U l 2 5 7 2 5 8 2 5 9 P Y ING . S I M U L T A N E O U S L Y THE S H E L V E S ENDGRAPH 2 6 0 2 6 1 2 6 2 STU RAGE T I T L E SPACE 11,THE R E C O R D I N G S C O L L E C T I O N (=DESK 6 S H E L V E S ) AS S 1 0 1 3 2 6 3 2 6 4 2 6 5 TAB T I T L E S H E L V E S ) . E J E C T . 9 , T R A N S I T T I M E S THROUGH REC. C O L L . ( M I N . ) , <=DESK _ 1 2 6 6 2 6 7 2 6 8 * * GRAPH GRAPH TP , TAB9 269 2 7 0 2 7 1 O R I G I N X Y 5 0 , 1 0 , , 7 , 1 , 1 , 1 5 0 , 1 , 4 5 , 1 2 7 2 2 73 2 7 4 100 10 S T A I E M EN T STATEMENT STATEMENT 4 , 1 , 3 5 2 , 1 9 » T R A N S IT TIME ( M I N . ) 55 ,75 , F I G U R E 9: REL. FREQUENCY OF T R A N S I T T I M E S T H R O U l 2 75 2 7 6 2 7 7 GH THE *** RECORDINGS ENDGRAPH C O L L E C T I O N 278 2 7 9 2 8 0 TAB T I T L E E J E C T 10,OCCUPANCY OF RECORD. C O L L E C T . {= DESK _ S H E L V E S ) 2 8 1 2 82 * GRAPH GRAPH O R I G I N TP T T A B 1 0 50 ,1 0 2 8 3 2 8 4 2 8 5 2 8 6 , 2 , 4 , 0 , 1 , 2 0 0 , 1 , 1 5 , 3 4,1 ,38 "2BT- 2 8 8 2 8 9 X Y STATEMENT 100 STATEMENT 5 2 t 9 , O C C U P A N C Y 10 STATEMENT 5 5 , 8 5 , F I G U R E 1 0 : R E L . FREQUENCY OF NUMBER OF JOBS 0 C C 1 U P Y I N G S I M U L T A N E O U S L Y DESK AND S H E L V E S 2 9 0 291 292 ENDGRAPH T I T L E S P A C E T I T L E E J E C T 2 94 2 9 5 STO 40,THE L I S T E N I N G ROOM AS STORAGE 3 ' 1 1 , L I S T E N I N G ROOM I N T E R A R R I V A L T I M E S ( M I N . ) TAB 296 2 9 7 298 " 2 W 3 00 3 0 1 * GRAPH GRAPH TP,TAB 11 O R I G I N X Y 5 0 , 10 , , 7 , 1 , 1 , 1 5 0 , 4 , 1 5 , 3 302 3 0 3 3 0 4 "7 S t A l EMtN! 4, 1, % ! : 100 STATEMENT 5 2 » 2 5 t I N T E R A R R I V A L • T I M E ( M I N . ) 10 STATEMENT 5 5 , 6 4 , F I G U R E 1 1 : R E L . FREQUENCY OF I N T E R A R R I V A L T I M E S 1 TO L I S T E N I N G ROOM ENDGRAPH ~3TJ5~ 3 0 6 301_ 3 0 8 3 0 9 310 T7AB~ 1 IT Lb E J E C T 12,NUMBER (JF A R R I V A L S 10 L I S I . kOOM/10 MIN 3 T T 312 3 1 3 * GRAPH GRAPH O R I G I N T P , T A B 1 2 5 0 , 1 0 . 314 315 316 "X" Y . STATEMENT ,2 ,6,0,1 ,1b. 0 , 1 , 2 4 , 2 4 , 1 , * " I T T 3 1 8 3 1 9 100 STATEMENT 5 2 , 2 0 , A R R I V A L RATE/10 MIN. 10 STATEMENT 5 5 , 7 0 , F I G U R E 1 2 : R E L . FREQUENCY OF A R R I V A L S TO L I S T E N 1 I NG ROOM DURING 10 M I N . 3 2 0 321 322 t N D G k A P H T I T L E T 2 T 32 4 3 2 5 TAB 1 3 , L I S T . ROOM S E R V I C E T I M E S ( M I N . ) E J E C T * GRAPH 3 2 6 3 2 7 32 8 I P , I A B 1 _ 5 0 , 10 , , 3 , 5 , 1 , 3 0 330 331 GRAPH O R I G I N X 7 100 STATEMENT STATEMENT ~TTJ S I A l fcrtfcN I S T E N I N G ROOM 0, 1 , 2 1 , 2 4, 1, % 5 2 , 1 9 T T R A N S I T T I M E ( M I N . ) 5 5 , 5 8 , F I G U R E 1 3 : R b L . 1-RbllUbNtY lib I R A N S l ' l |IMb Ub L11 332 333 3 34 "T35" 3 3 6 G P S S / 3 6 0 / M T S V E R S I O N ( 4 / 8 / 1 3 ) A ^ TAB ENDGRAPH T I T L E E J E C T 14,OCCUPANCY OF L I S T . ROOM 3 3 7 338 3 3 9 3 4 0 J f * GRAPH GRAPH T P , T A B 1 4 3 4 1 3 4 2 3 4 3 O R I G I N X Y 5 0 , 1 0 , 2 , 4 , 6 , 1 , 1 8 0 , 1 , 1 6 , 3 3 4 4 3 4 5 3 4 6 7 10 0 10 STATEMENT STATEMENT STATEMENT 4, 1 , 3 5 2 ? 9 f O C C U P A N C Y 55 ,87 , F I G U R E 14: R E L . FREQUENCY OF NUMBER OF JOBS 0 C C 1 3 4 7 3 4 8 3 4 9 U P Y I N G S I M U L T A N E O U S L Y THE L I S T E N I N G ROOM ENDGRAPH 350 3 5 1 3 5 2 STU TAB T I T L E S P A C E TI TLE 41,THE R E S E R V . L I S T E N I N G ROOM AS STURAGE 3 17,OCCUPANCY OF RESERVE L I S T . ROOM 3 5 3 3 5 4 3 5 5 * * GRAPh E J E C T 3 5 6 3 5 7 3 5 8 GRAPH O R I G I N X I P , 1 A B 1 7 5 0 , 1 0 , 2 , 6 , 0 , 1 , 1 5 3 5 y 3 6 0 3 6 1 7 100 Y STATEMENT STATEMENT 0, 1, 3 5 , 1 4,1,5? 5 2 » 9 , O C C U P A N C Y 3 6 2 3 6 3 3 6 4 10 C U P Y I N G STATEMENT 5 5 , 9 6 , F I G U R E 1 4A: R E L . FREQUENCY OF NUMBER OF J U B S 0C1 S I M U L T A N E O U S L Y THE L I S T E N I N G ROOM ENDGRAPH 3 6 5 3 6 6 3 6 7 • STO T I T L E SPACE 10,THE S Y S T E M AS STORAGE 3 • 3 6 8 3 6 9 3 7 0 TAB ) T IT LE E J E C T 1 5 , S Y S T E M T R A N S I T T I M E S ( M I N . ) ( ^ S E R V I C E E WAIT. TIME1 3 7 1 3 7 2 3 7 3 * GRAPH GRAPH T P , T A B 1 5 3 7 4 3 7 5 3 7 6 O R I G I N X Y 5 0 , 10. • , , 3 , 5 , 1 , 3 0 0 , 5 , 2 0 , 2 377 3 7 8 3 7 9 7 100 10 STATEMENT STATEMENT STATEMENT 4 , 1 , * 5 2 , 1 9 , T R A N S I T TIME ( M I N . ) 5 5 , 4 9 , F I G U R E 1 5 : R E L . FREQUENCY OF S Y S T E M TRANSIT TIM1 38 0 3 8 1 3 8 2 fcS ENDGRAPH 3 83 3 84 3 8 5 TAB T T I T L E E J E C T 16,OCCUPANCY OF SYSTEM ( = D E S K , S H E L V E S , L I ST. ROOM) 3 86 3 8 7 3 8 8 * GRAPh GRAPH T P , T A B 1 6 3 8 9 390 O R I G I N 5 0 , 1 0 3 9 1 X , 2 , 4 , 2 , 2 , 2 0 3 92 Y 0 , 2 , 2 0 , 2 3 9 3 7 S T A T E M E N T 4 , 1 , : ? 3 9 4 "TTTO S I A l tML-NT 5 2 , 9 t O C C U P A N C Y : : ~ TW* "  : \ 10 S T A T E M E N T 5 5 , 7 9 , F I G U R E 1 6 : R E L . F R E Q U E N C Y OF NUMBER OF J O B S 0 C C 1 3 9 6 U P Y I N G S I M U L T A N E O U S L Y THE S Y S T E M 3 9 7 . E N D G R A P H 3 9 8 3 9 9 END . 4 0 0 BLOCK NUMBER SYMBOL R E F E R E N C E S BY CARD NUMBER "66 BE I D E ' : FT9 T l 4 8 DESK 66 71 74 E X I T 82 . 84 . 85 86 1 0 4 106 J L 0 7 ~ ~ " 108 "127 130 131 78 F I N E 7 9 101 128 50 GEH 10 1 _ ' • 69 GEH11 . 126 72 GEH13 ' 1 2 9 L3____Jf__! __' __ _ ___ 2 4 ' GEH2~ " ' " 8 0 " ~ ' " . -~' 26 ' GEH3 81 . 27 GEH4 ~ 83 IB bFFT5 WE — ' : : : 46 GEH7 102 , 48 _ GEH 8 _ 103 ___ _ _ _ _ _ _ .__ ' V 49 " G E ' H 9 ~ ~ 1 0 5 ~~ " ~ " " • " ~ - ~ •" " 61 OFLOW 111 4 STG2 62 1 0 6 109 127 1 3 2 29 5TTJ3 : 62" : 54 87 ETC" r__ 51 STG4 85 87 107 109 T A B L E SYMBOLS AND CORRESPONDING NUMBERS ~T TTfTJT : • ' : — < 10 TAB 10 11 T A B U _ _ , , 12 TAB 12 • " ~ 13 TAB 1 3 14 - T A B 1 4 ' T 5 TAB 15 : : 16 TAB 16 17 TAB17. .. • 2 TAB 2 ' 3 T A B 3 4 TAB4 • ~5 rms ' : ! 6 T A B 6 J TAB7 . " ___________; • 8' TAB 8 " . . ~ 9 T A B 9 F U N C T I O N SYMBOLS AND CORRESPONDING NUMBERS 1 A R R I V 2 DESK 4 L I S T 3 S H E L F * FUNCTTCN D E F I N I T I O N S *. SYSTEM A R R I V A L T I M E E X P O N E N T I A L L Y D I S T R I B U T E D / 1 F U N C T I U N KNI C U \ 0 .0 0.0 . 4 2 3 . 25 . 6 6 7 .75 .808 4 . 2 5 .889 1.75 . 9 3 6 2.25 . "3 63 2. 75 . 9 7 9 3 .25 .98 8 3.7 5 . 9 9 0 4.2 5 1.0 7.25 * DESK S E R V I C E T I M E E X P O N E N T I A L L Y D I S T R I B U T E D 2 F U N C T I O N RN1 C24 0.0 0 .0 .1 . 104 .2 .222 .3 . 3 5 5 . 4 . 5 0 9 .5 .69 .6 . 9 1 5 . 7 1.2 . 7 5 1. 38 . 8 1.6 .84 1 .83 .88 2.12 . 9 2.3 . 92 _. 52 .94 2 .81 .95 2 .99 .96 3.2 . 97 3. 5 .98 3 .9 • 99 4.6 .99 5 5.3 . 9 S 8 .A . 6.2 . 9 9 9 7.0 . 9 9 9 7 ' 8.0 * SHELF S E R V I C E TIME E X P C N E N T I A L L Y D I S T R I B U T E D 3 F U N C T I O N K N I C 2 3 o.o 0 .0 . 1 5 4 . 8 4 0 . 2 8 1 . 2 5 0 . 3 9 0 . 4 2 0 . 4 8 3 . 5 8 0 .562 .750 .629 .92 . 6 8 5 1.08 . 7 3 3 1.25 . 7 7 4 1 .42 .808 1 .59 . 8 3 7 1.75 . 8 6 2 1.92 . 8 8 3 2 . 0 8 .9 2.25 . 9 1 6 2.42 .92 1 2 . 5 8 . 93 / 2.75 . 9 4 6 2 .92 .953 3 . 0 8 . 9 5 9 3.25 .964 3 . 4 2 1.0 5. 27 *f * L I S T E N I N G ROOM S E R V I C E T I M E G E N E R A L L Y D I S T R I BUT ED 4 F U N C T I O N RN1 C 2 5 0.0 0 .0 .0^4 .U63 . 0 / 1 . 18 / . 131 . 3 1 2 . 2 0 5 .437 .289 .563 .36 6 . 6 9 0 . 4 3 6 . 8 2 0 . 4 9 8 . 9 4 0 . 556 1.06 .623 1 .18 . 6 9 9 1.31 . 7 5 4 1.44 . 7 8 6 1. 56 .814 1 .69 .836 1 .81 . 8 5 5 1.94 . . 8 7 2 2. 0 6 . 8 8 8 2 .1 8 .903 2.31 .91 / 2 .44 .927 2.55 . 9 6 2 3. 19 . 9 8 9 4.20 .1 .00 4 .820 * * STORAGE D E F I N I T I O N S 10 STORAGE 2 0 0 11 S l O R A G t 1 5 0 30 STORAGE 1 0 0 4 0 STORAGE 23 41 STORAGE 23 * T A B L E D E F I N I T I O N S 1 T A B L E • I A 1 1 20 2 TABLE R T 0 1 30 i u 3 T A B L E M l 1 1 30 4 Q T A B L E .2 0 1 30 " ~ 5 " " TABLE IA 1 1 30 6 T A B L E RT 0 1 20 10 7 T A B L E Ml 1 1 60 J 8 T A B L E S3 0 0 1 40 9 T A B L E Ml 1 1 60 10 T A B L E S l l 0 1 60 11 T A B L E IA . 1 1 3 0 12 T A B L E RT 0 1 15 13 T A B L E M l 0 . 5 60 / 14 T A B L E S 4 0 0 1 26 15 T A B L E Ml 0 5 60 16 T A B L E S1 0 0 2 60 17 •A- T A B L E S 4 1 0 1 26 •v * GPSS PROGRAM „ f 1 G E N ERATE 2 F N l 2 ENTER 10 3 T R A N S F E R .360 29 4 4 MARK 5 ENTER 11 6 QUEUE 2 7 L I N K 2 F I F O 8 8 S E I Z E 2 9 DEPART 2 10 ADVANCE 1 FN2 11 R E L E A S E 2 1_ U N L I N K 2 8 1 13 T A B U L A T E 1 14 T ABUL ATE 2 ~ 1 5 T A B U L A T E 3 16 L E A V E 11 17 T A B U L A T E 9 18 T ABUL A f E 10 19 A S S I G N 2 K l 20 T E S T L E C l K 3 6 0 0 78 - 21 TEST E P3 K l 24 22 TEST E P 4 K l 26 23 T R A N S F E R 74 24 TEST t P4 K l 27 25 TRANSFER .7 50 29 74 26 T R A N S F E R .960 51 74 27 TRANSFER . 7 3 0 28 . 74 28 TRANSFER . 1 10 29 51 2 9 MARK 3 0 ENTER 11 31 ENTER 30 32 ADVANCE 6 FN3 33 L E A V E 30 3 4 T A B U L A T E 5 35 T A B U L A T E 6 36 T A B U L A T E 7 37 T A B U L A T E 8 3 8 L E A V E 11 T A B U L A T E 9 4 0 T A B U L A T E 10 4 1 A S S I G N 3 K l 42 TEST LE C l K 3 6 0 0 78 4 3 T E ST E P2 K l 46 44 TEST E P4 . K l 48 45 TRANSFER 74 4 6 T E S T E P4 K 1 49 47 T R A N S F E R .280 4 74 J 48 T R A N S F E R .220 51 74 49 T R A N S F E R .140 50 74 50 TRANSFER . 5 8 0 4 51 51 MARK 52 GATE SNF 40 61 5 3 ENTER 40 / 54 ADVANCE 40 FN 4 5 5 LEAVE 4 0 56 T A BULATE 11 57 T A B U L A T E 12 58 T A B U L A T E 13 59 T A B U L A T E 14 6 0 T R A N S F E R 66 61 ENTER 41 6 2 ADVANCE 40 F N 4 6 3 L E A V E 41 64 T A B U L A T E 17 6 5 T R A N S F E R 66 6 6 ASSIGN 4 K l 67 T E S T E P3 K l 6 9 68 T R A N S F E R .090 4 74 6 9 TEST LE C l K 3 6 0 0 78 7 0 TEST E P2 K l 72 7 1 T R A N S F E R .380 29 74 72 TRANSFL-R .080 7 3 74 7 3 TRANSFER . 1 4 0 4 29 74 L E A V E 10 7 5 T A B U L A T E 15 7 6 T A B U L A T E 16 77 T E R M I N A T E 7 8 LEAVE 10 7 9 T A B U L A T E 15 8 0 T A B U L A T E 16 _ _ 8 1 - TERMINATE 1 * CONTROL CARD START 1 S T A T I S T I C S CONCERNING THE I N F O R M A T I O N DESK F A C I L I T Y AVERAGE NUMBER AVERAGE S E I Z I N G P R E E M P T I N G U T I L I Z A T I O N E N T R I E S TIME/TRAN TRANS. NO. TRANS. NO. 2 . 5 0 9 3 0 5 5 .600 , S T A T I S T I C S CONCERNING THE DESK QUEUE QUEUE MA XI MUM AVERAGE TOTAL ZERO PERCENT AVERAGE $A VERAGE T A B L E CURRENT CONTENTS CONTENTS E N T R I t S E N T R I E S ZEROS •T IME/TRANS TIME/TRANS NUMBER CONTENTS 2 16 1.034 3 0 5 5 1 6 3 7 5 3 . 5 1.219 2 . 6 2 7 4 . J _ _ _ _ _ E _ T I M E / T R A N S = AVERAGE TIME/TRANS E X C L U D I N G ZERO E N T R I E S S T A T I S T I C S CONCERNING THE D E S K USER C H A I N USER C HA I N TOTAL AVERAGE C URRENT AV E RAGE MAXIMUM E N T R I E S TIME/TRANS CONTENTS CONTENTS CONTENTS 2 1 8 2 6 2 . 0 4 0 1.034 16 T A B L E TAB 1 E N T R I E S IN T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS 3 0 5 4 1 .178 1.527 3.598.000 NON-WEIGHTED UPPER OBSERVED PER CENT CUMULATIVE C U M U L A T I V E M U L T I P L E D E V I A T I O N L I M I T ' FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 1 2 1 3 6 6 9 . 9 4 6 9 . 9 3 0 . 0 .848 - . 1 1 6 2 4 3 9 1 4 . 3 7 8 4 . 3 1 5 . 6 1.697 .538 3 2 3 4 7.66 9 1 . 9 8.0 2 . 5 4 6 1 . 1 9 2 4 135 4.42 9 6 . 3 3.6 3 . 3 9 5 1 . 8 4 / 5 52 1.70 9 8 . 1 1.8 4. 2 4 4 2 . 5 0 2 6 23 .75 9 8 . 8 1.1 5 . 0 9 2 3 . 1 5 7 7 16 • 52 1 9 9 . 3 .6 5 .941 3 . 8 1 1 8 7 .22 9 9 . 6 . 3 6. 7 9 0 4 . 4 6 6 9 7 .22 9 9 . 8 .1 7.63 9 5 . 1 2 1 10 2 . 06 9 9 . y . 0 8.488 5 . 1 ( b 11 1 .03 9 9 . 9 .0 9.336 6.430 12 1 . 0 3 9 9 . 9 .0 1 0 . 1 8 5 7 . 0 8 5 13 1 .03 1 0 0 . 0 .0 1 1 . 0 3 4 7 . 7 4 0 R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO A GRAPH * * J * * * * * 80 76 * * 72 * * 68 * * 64 * ** ** ** * 60 * * ** ** ** 56 * * 52 * ** ** ** 48 * * ** ** ** 44 * * 40 * ** *.* ** 36 * * ** ** ** 32 * * 2 8 * ** * * ** 24 * ** ** ** 20 * 16 * ** ** ** . * 1 2 * * ** ** ** * * 8 * * 4 * ** ** ** ** ** ** ** ** * o ************* ** 1 ** ** 2 3 ** 4 .****************************************** *** 5 6 7 8 I N T E R A R R I V A L T I M E <MIN.) F I G U R E 1: REL . FREQUENCY OF I N T E R A R R I V A L TIMES J T A B L E TAB2 E N T R I E S I N TABLE MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS ) 3 6 0 8 . 4 8 0 3 . 9 5 3 3 0 5 3 . 0 0 0 N U N - W E I G H T E D UPPER OBSERVED PER CENT CUM ULAT I V E CUMULATIVE M U L T I P L E D E V I A T I O N L I M I T 0 1 FREQUENCY 2 2 OF TOTAL .55 .55 PERCENTAGE . 5 1.1 REMAINDER 9 9 . 4 9 8 . 8 OF MEAN - . 0 0 0 . 1 1 7 FROM MEAN - 2 . 1 4 5 - 1 . 8 9 2 2 3 4 5 21 15 1.38 5 . 8 3 4.16 2.4 8.3 12 .4 97 .5 9 1 . 6 8 7 . 5 .235 . 3 5 3 . 4 7 1 - 1 . 6 3 9 - 1 . 3 8 6 - 1 . 1 3 3 5 6 7 3 1 4 4 47 8. 61 1 2 . 2 2 1 3 . 0 5 2 1 . 1 3 3 . 3 46 .3 7 8 . 8 6 6 . 6 5 3 . 6 . 5 8 9 . 7 0 7 .82 5 - . 8 8 0 - . 6 2 7 - . 3 7 4 8 9 10 4 4 2 9 2 4 1 2 . 2 2 8 .05 6. 66 5 8 . 6 6 6 . 6 7 3 . 3 4 1 . 3 3 3 . 3 26 .6 .943 1.061 1.179 - . 1 2 1 . 1 3 1 . 3 8 4 11 12 13 22 19 15 6.11 5.27 4. 16 7 9 . 4 8 4 . 7 8 8 . 8 2 0.5 1 5 . 2 1 1 . 1 1.297 1.415 1 .532 .637 . 8 9 0 1.143 14 15 16 12 7 5 3.33 1.94 1.38 9 2 . 2 9 4 . 1 9 5 . 5 1. 1 5.8 4.4 1.650 1.768 1 . 8 8 6 1 .3 96 1 . 6 4 9 1 . 9 0 2 17 18 19 4 9 1 1.11 2 . 4 9 .27 9 6 . 6 9 9 . 1 9 9 . 4 3.3 .8 . 5 2 . 0 0 4 2 . 1 2 2 2 . 2 4 0 2 . 1 5 5 2 . 4 0 8 2 . 6 6 1 20 21 22 0 0 0 .00 . 0 0 .00 9 9 . 4 9 9 . 4 9 9 . 4 .5 .5 . 5 2 . 3 5 8 2 . 4 7 6 2. 594 2 . 9 1 4 3. 1 6 6 3 . 4 1 9 23 24 25 ; o l 0 .00 . . 27 .00 9 9 .4 9 9 . 7 9 9 . 7 .5 .2 . .2 2 . 7 1 2 2 . 8 3 0 2 . 9 4 7 3. 6 7 2 3 . 9 2 5 4 . 1 7 8 26 R E M A I N I N G F R E Q U E N C I E S 1 .27 ARE A L L ZERO 1 0 0 . 0 .0 3 . 0 6 5 4 . 4 3 1 * * * 19 * 2 1 "20" 18 * 17 * 16 * 15 T4" 13 * ** * 12 * * ** ** ** ** ** ** 11 * * ** ** ** ** ** 10 ** ** ** * ** ** ** 9 * * ** ** ** ** ** ** 8 * ** ** ** * * ** ** ** ** ** ** 7 * ** ** ** ** ** * ** ** ** ** ** 6 * * ** ** ** ** ** ** ** ** ** ** ** ** ** ** 5 * ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** 4 * ** ** ** ** ** ** ** ** ** ** ** . * ** ** ** ** ** ** ** ** ** ** ** 3 * ** ** ** ** ** ** ** ** ** ** ** ** ** *.* ** ** ** ** ** ** *# ** ** 2 * ** ** ** ** ** **: V * ** ** ** ** ** ** * ** ** ** * * ** ** ** ** ** ** ** ** 1 * ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** t * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 ARRIVAL RATE/10 MIN. F I G U R E 2: R E L . FREQUENCY O F A R R I V A L S TO I N F . DESK DURING 10 MIN. DESK T R A N S I T T I M E S { M I N . ) ( = WAIT. £ S E R V I C E TIME) T A B L E T A B 3 E N T R I E S IN T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N 3 0 5 5 1 .820 2.03 b SUM OF ARGUMENTS 3 5 6 1 . 0 0 0 NUN-WEIGH!bU UPPER OBSERVED ' PER CENT C U M U L A T I V E CUMULAT I VE M U L T I P L E D E V I A T I O N L I M I T FREQUENCY OF TOTAL PERCENTAGE R E M A I N DER OF MEAN FROM MEAN 1 1 7 1 5 5 6 . 1 3 5 6 . 1 4 3 . 8 . 5 4 9 - . 4 0 3 2 4 7 3 1 5 . 4 8 7 1 . 6 2 8 . 3 1.098 .088 3 3 2 7 10 .70 8 2. .3 17.6 1. 6 4 8 .5 79 4 218 7.13 8 9 . 4 10.5 2. 197 1.071 5 135 4.41 9 3 . 8 6. 1 2 . 7 4 6 1.562 6 82 2 .68 ' 9 6 . 5 3.4 3. 2 9 6 2 . 0 5 3 7 4 9 1.60 9 8.1 1.8 3 . 8 4 5 2 . 5 4 5 8 19 .62 9 8.7 1.2 4 . 3 9 4 3 . 0 3 6 9 13 .42 9 9.2 . 7 4.944- 3. 5 2 / 10 14 .45 • 9 9 . 6 .3 5 . 49 3 4 . 0 1 9 11 6 .19 9 9 . 8 . 1 6. 0 4 2 4 . 5 1 0 12 2 .06 99 .9 .0 6.592 5. 0 0 1 13 2 .06 1 0 0 . 0 .0 7 . 1 4 1 5 . 4 9 3 R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO % „ *** 6 0 „ 57 1* 54 ' I - •a. f -J.- •**- 5 1 „ -J. v» i v 4 8 WO *Y* •V j. -v 4 5 v», •V vk- - A , -#* 1- * «*> 42 * 3__ 36 „ „ »v _ •A. •V -A- 33 * - "f * 3 0 •J, f- 27 " V j_ ~>- 24 if •A. - 21 18 V -V 15 »», •J* * 12 "T" -4, -<* •A. T 9 •A- - V >*C J - •*»- „ A - *sr • A . 6 o . — x *** A . T * * A. f - A . - A -1x A. 1*-' * 3 A * * A-v -A, 1- -A- * * * 4 * 0 .J, -J* J. -J, „i„ „ " V - V T 'p. *t# J» J , v<, •r r ^ *r i 4 K " ! * „ „ J , - A - A- ~Jr A* _ j * *fjj .̂ ̂  "r-"/* " V -y 1- ->v 'r- -i» •>» T - f „ J*f „ ^ , O, A. A- A. „ J , .4, -A. T V T T f T 1* 1* 1* V1> T */* W - V, J , -jl. A<f'-J> T - T F * T -r- -V" -v -v *r -»v ******************************** 1 2 3 4 5 6 7 8 T R A N S I T T I M E ( M I N . ) F I G U R E 3: R E L . FREQUENCY OF TRANST TIMES AT INFORMATION DESK NUMBER OF JOBS WAITING FOR SERVICE AT DESK TABLE ENTR IES TAB A IN TABLE MEAN ARGUMENT STANDARD DEVIATION SUM OF ARGUMENTS NON-WblGH!ED 3055 1.219 I . 824 i /26.000 UPPER LIMIT 0 1 OBSERVED PER CENT CUMULATIVE CUMULAT IVE MULTIPLE DEVIATION FREQUENCY 1637 49 8 OF TOTAL 53 .58 16.30 PERCENTAGE 53.5 69. 8 REMAINDER 46.4 3 0.1 OF MEAN - .000 .819 19.2 11.4 6.3 FROM MEAN -.668 -.120 2 3 4 5 6 7 333 238 155 10.90 7.79 5. 07 80.7 88.5 93. 6 1. 639 2.459 3 .279 82 45 32 2 .68 1.47 1.04 96.3 97 .8 98. 8 3.6 2.1 1.1 4. 099 4.919 5.739 rr ,4 .0 6.559 7 .379 8. 199 .427 . 975 1 .524 2.072 2.620 3 .168 3. 716 4.265 4.813 9 10 11 12 13 11 9 12 .36 .29 .39 99.2 9 9 . 5 99. 9 2 0 1 .06 . 00 .03 99.9 99. 9 100.0 ,0 .0 ,0 9.019 9 .838 10.65 8 5. 361 5.909 6.457 REMAINING FREQUENCIES ARE ALL ZERO * * J % * * * • 6 0 5 7 * 5 4 * * * * * 5 1 4 8 * * * * * * * 4 5 * * * * * * * * 4 2 3 9 * * * * * * * ' * * 3 6 * * * * * * * * * 3 3 3 0 * * * * * * * * 2 7 * * * * * * * * * 2 4 2 1 * * * * * * * * 1 8 * * * * * * * * 1 5 1 2 * * * * * * * * * * * * * * 9 * * * * * * * * * * * * * * * * * * 6 3 * * * * * , * * * * * * * * * * * * * * ' * * * * * * * * •V* •%- * * 0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 0 1 2 3 * * * * * * * * * * * * * * * * * * * * * 4 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 5 6 7 J O B S I N Q U E U E F I G U R E 4 : R E L . F R E Q U E N C Y O F J O B S W A I T I N G F O R S E R V I C E A T I N F O R M A T I O N D E S K STORAGE CAPACITY AVERAGE CONTENTS AVERAGE UTILIZATION "TO" TTJTJ" 3.8 IV .0 38 ENTRIES 2J66 AVER AGE TI ME/TRAN b. 813 CURRENT CONTENTS : T~ MAXI MUM CONTENTS T 5 - SHELF INTERARRIVAL TIMES (MIN.) TABLE TAB5 ENTRIES IN TABLE 2364 MEAN ARGUMENT 1.521 STANDARD DEVIATION 1.722 SUM OF ARGUMENTS 3597.000 NON-WEIGHTED UPPER L IMIT OBSERVED FREQUENCY PER OF CENT TOTAL CUMUL AT IV E PERCENTAGE CUMULATIVE REMAINDER MULTIPLE OF MEAN DEVIATION FROM MEAN .657 1.314 1.971 -.302 .277 .858 1 2 3 1 5 24 401 190 64 .46 16 .96 8. 03 64.4 81.4 89.4 35.5 18.5 10.5 4 5 6 105 60 35 4.44 2.53 1.48 93. 9 96.4 97.9 6. 0 3.5 2 .0 2.62 8 3.286 3.943 98.7 99.1 9 9. 5 T7_ .8 .4 4.600 5.257 5.914 1 .438 2. 019 2.599 3.180 3.760 4.341 7 8 9 10 11 12 20 9 9 5 1 1 .84 .38 .38 .21 .04 .04 99.7 99.7 99. 8 .2 .2 . 1 6. 572 7.229 7.886 TOT" . 04 .08 99.8 99.9 100. 0 T T .0 .0 8.543 9 .20 1 9.858 4.921 5.502 6 .082 6.663 7.243 7.8 24 13 14 15 REMAINING FREQUENCIES ARE ALL ZERO % * * * • • - • - " — . \ * 80 * * 76 * * 72 * * 68 * * 64 * ** * 60 * ** ** ** 56 * * 52 * ** ** ** * 48 * ** ** ** 44 * * 40 * ** ** ** * 3 6 * * ** ** ** 32 * * 28 * ** ** ** * 24 * * ** ** ** 20 * * 16 * ** ** ** ** * 12 * * *•* ** ** ** ** ** 8 * * 4 * ** ** ** ** ** ** ** ** ** * o ************** ** 1 ** 2 ** ** ** *********************************************************************** 3 4 5 6 INTERARRIVAL TIME (MIN.) FIGURE 5: REL. FREQUENCY OF INTERARRIVAL TIMES TABLE TAB6 E N T R I E S I N T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS / 36 0 6 . 5 6 6 3 . 2 0 7 2 3 6 4 . 0 0 0 NON-WEIGHTED \ UPPER OBSERVED PER CENT C U M U L A T I V E CUMULATIVE M U L T I P L E D E V I A T I O N L I M I T 0 1 FREQUENCY OF TOTAL 3 .83 5 1.38 PERCENTAGE .8 2.2 REMAINDER 9 9 . 1 9 7 . 7 OF MEAN - . 0 0 0 .15 2 FROM MEAN - 2 . 0 4 7 - 1 . 7 3 5 2 3 4 22 6.11 30 8.33 37 1 0 . 2 7 8.3 1 6 . 6 2 6 . 9 9 1 . 6 8 3 . 3 7 3 . 0 . 3 0 4 . 4 5 6 .609 - 1 . 4 2 3 - 1 . 1 1 2 - . 8 0 0 5 6 7 57 1 5 . 8 3 41 1 1 . 3 8 38 1 0 . 5 5 4 2 . 7 5 4 . 1 6 4 . 7 5 7 . 2 4 5 .8 3 5 . 2 . 7 6 1 ' .913 1 .065 - . 4 8 8 - . 1 7 6 . 1 3 5 8 9 10 3 8 1 0 . 5 5 24 6.66 20 5.5 5 7 5 . 2 8 1 . 9 8 7 . 4 2 4 . f 1 8 . 0 1 2 . 5 1.2.18 1.370 1.522 . 4 4 6 . 7 5 8 1 . 0 7 0 11 12 13 21 .5.83 8 2.22 6 1.66 9 3 . 3 9 5 . 5 9 7 . 2 6.6 4.4 2.7 1. 6 7 5 1.827 1. 9 7 9 1.382 1.694 2 . 0 0 6 14 15 16 2 .55 5 1.38 0 .00 9 7 . 7 9 9 . 1 9 9 . 1 2.2 • 8 .8 2 . 1 3 1 2 . 2 8 4 2 . 4 3 6 2 . 3 1 7 2 . 6 2 9 2 . 9 4 1 17 18 R E M A I N I N G F R E Q U E N C I E S 2 . 55 1 .27 ARE A L L ZERO 9 9 . 7 100. 0 .2 . 0 2. 5 8 8 2 . 7 4 1 3 . 2 5 3 3 . 5 6 5 •- * *_ 2 0 * *~ 19 * 18 * 17 * *~ 16 * 15 * ** * ** 14 * ** -—* :—; -^nr 13 * ** * ** "12 * ** * ** 11 * ** ** * : : ww **- 10 * ** ** ** ** ** * ** ** ** ** ** 9 * ** ** ** ** ** ** ** ** ** ** 8 * ** ** ** ** ** ** ** ** ** ** ** ** 7 * - ** ** ** ** ** ** * ** ** ** ** ** ** 6 ** ** ** ** ** ** ** ** * * * * * ** ** ** ** ** ** 5 * ** ** ** ** ** ** ** ** ** ** * ** **. ** ** ** ** ** ** ** ** 4 * ** ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** ** 3 * ** ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** ** 2 * ** ** ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** ** ** 1 * ** ** ** ** ** ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** ** ** ** ** ** 0 ************************** ************************************************************************************************ 0 1 2 3 4 5 6 7 8 g .10 1 1 12 13 14 15 16 1 7 18 19 A R R I V A L R A T E / 1 0 M I N . F I G U R E 6: R E L . FREQUENCY OF A R R I V A L S TO S H E L V E S DURING 10 M I N . T A B L E TAB 7 E N T R I E S IN T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS J 2 3 6 5 b .815 b. b b 4 13 / 5 3 . 0 0 0 NUN-Wfe1GHI ED UPPER OBSERVED PER CENT C U M U L A T I V E C U M U L A T I V E M U L T I P L E D E V I A T I O N L I M I T 1 2 FREQUENCY 3 2 4 4 0 4 OF TOTAL 1 3 . 69 1 7 . 0 8 PERCENTAGE 1 3 . 6 3 0 . 7 REMAINDER 8 6 . 3 6 9 . 2 ' OF MEAN .171 . 3 4 3 . FROM MEAN - . 8 6 6 - . 6 8 6 3 4 5 3 4 3 30 6 1 4 2 14 .50 1 2 . 9 3 6.00 4 5 . 2 5 8 . 2 6 4 . 2 5 4 . 7 4 1 . 7 3 5.7 . 5 1 b .687 . 8 5 9 - . 5 0 6 - . 3 2 6 - . 1 4 6 6 7 8 1 1 6 104 1 0 2 4 . 9 0 ' 4. 3 9 4.3 1 6 9 . 1 7 3 . 5 7 7 . 8 30.8 2 6 . 4 2 2.1 1.031 1.203 1.375 . 0 3 3 . 2 1 3 .393 9 10 11 fl 13 87 3.00 3. 08 3 .67 8 0 . 8 •83. 9 8 7.6 19.1 1 6 . 0 1 2 . 3 1.547 1 . 7 1 9 1. 8 9 1 . 5 73 .7 53 • 9 3 3 12 13 14 4 7 47 3 0 1.98 1.98 1 .26 8 9 . 5 9 1 . 5 9 2 . 8 10 .4 8.4 7.1 2 . 0 6 3 2.23 5 2 . 4 0 7 1 . 1 1 3 1.293 1.473 l b 16 17 18 17 17 . 76 .71 .71 9 3 . 6 9 4 . 3 9 5 . 0 6 .3 5.6 4.9 2 . 5 7 9 2 . 7 5 1 2 . 9 2 3 1.6 53 1 . 8 3 3 2 . 0 1 3 18 19 20 13 12 9 . 54 .50 .38 9 5 . 6 9 6 . 1 9 6 . 4 4.3 3.8 3.5 3 . 0 9 5 . 3.267 3 . 4 3 9 2 . 1 9 3 2 . 3 7 3 2 . 5 5 3 21 22 23 13 14 4 . 54 .59 .16 9 7 . 0 9 7 . 6 97 .8 2 .9 2.3 2.1 3 . 6 1 1 3. 7 8 3 3 . 9 5 5 2 . 7 3 3 2 . 9 1 3 3 . 0 9 3 24 25 26 9 4 6 .38 .16 .25 9 8 . 1 9 8.3 9 8 . 6 1.8 - 1.6 1.3 4 . 1 2 7 . 4 . 2 9 9 4 . 4 7 1 3 .273 3 . 4 5 3 3 . 6 3 3 27 28 29 5 8 7 .21 .33 .29 9 8 . 8 9 9.1 9 9 . 4 1.1 .8 .5 4 . 6 4 2 4 . 8 1 4 4 . 9 8 6 3 . 8 1 3 3 . 9 9 3 4 . 1 7 3 30 31 R E M A I N I N G F R E Q U E N C I E S '8 5 ARE A L L ZERO .33 .21 9 9 . 7 1 0 0 . 0 .2 .0 5. 158 5 . 3 3 0 4 . 3 5 3 4. 5 3 3 * 21 * * 19 * * 18 * 16 * * _____ . _ . : _ . _ 15 * * 14 * ^ * ; ' ; * * * 13 * * * * ; * * * * 12 * * * * * * * * * * ____ . _ _ _ _ : : . * * * * * 10 * * _J_ » » • ' ' '. * * * * ~ 1 * ~ 1 ; ' .9 * * * * * * * * * * _ _ _ _ x -5 * ] • ; * * * * * 7 * _*_ * * _* ; . * ~ * " * . * • * • _ • 6 * * . * * * * *• . * * * * * ______ ___ — x * * ' : : : * * * * * * . 4 * * * * * * * .* _ _ _ _ _ _ _ _ _ _ _ , X * * 3 * * * * * * * * * * * * * * * * * * * * * * * *. 2 * * * * * * * ? - * * * * * * * * * * * * * * * 1 * * * * * * * * * * * * * * *_ ._ . _ _ _. _ X * * * * * * * * * 0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ' T R A N S I T T I M E ( M I N . I T A B L E TAB 8 E N T R I E S I N TABLE MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS 2 3 6 5 3 . 9 7 3 2 . 3 5 1 9 3 9 7 . 0 0 0 NON-WEIGHI ED UPPER OBSERVED PER CENT C U M U L A T I V E C U M U L A T I V E M U L T I P L E D E V I A T I O N L I M I T FREQUENCY OF TOTAL PERCENTAGE REMAINDER, Of MEAN FROM MEAN 0 78 3.29 3.2 9 6.7 - . 0 0 0 - 1 . 6 89 1 2 3 8 1 0 . 0 6 1 3 . 3 8 6 . 6 . 2 5 1 - 1 . 2 6 4 2 38 2 1 6 . 1 5 2 9 . 5 7 0 . 4 . 5 0 3 - . 8 3 9 3 4 1 5 1 7 . 5 4 4 7.0 5 2 . 9 . 7 5 5 - . 4 1 3 4 3 9 1 1 6 . 5 3 6 3 . 5 3 6 . 4 1 .006 . 0 1 1 5 30 3 1 2 . 8 1 7 6 . 4 2 3 . 5. 1.258 . 4 3 6 6 23 7 1 0 . 0 2 8 6 , 4 1 3 . 5 1.510 . 8 6 1 7 132 5.58 ' 9 2 . 0 7.9 .1.761 1.287 8' 84 3.5 5 9 5 . 5 4.4 2 . 0 1 3 1.712 9 52 2. 19 9 7 . 7 2.2 2 . 2 6 5 2 . 1 3 7 10 20 .84 9.8.6 1.3 2. 5 1 6 2 . 5 6 2 . 11 1 9 .80 9 9 .4 • 5 2 . 7 6 8 • • 2 . 9 8 8 12 8 .33 9 9 . 7 -2 3 . 0 2 0 3 . 4 1 3 13 4 . 1 6 : 9.9.9 ̂  .0 3 . 2 7 1 3.83 8 3.4 2 .08 1 0 0 . 0 .0 3 . 5 2 3 4 . 2 6 3 R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO 21 * * 2 0 ~ * * 18 * * 17 * * • ** ** 16 * ** ** ** * ** ** ** 15 * * ** ** ** ** - *.* ** 14 * * ** ** ** ** ** ** 13 * ** ** ** * ** ** ** 12 * * ** ** ** ** ** ** ** ** . 11 * ** ** ** ** ** ** ** ** 10 * ** ** ** ** ** * ** ** ** ** ** ** 9 * ** ** ** ** ** - 1 -* ** ** ** ** ** ^ «Y» 8 ** ** ** ** ** * ** ** *•* ** ** ** 7 * ** ** ** ** ** ** * ** ** ** ** ** ** 6 * ** ** ** ** ** ** * ** . ** ** ** ** ** 5 * ** ** ** ** ** *•* ** * ** ** ** ** ** ** .** 4 * ** ** ** ** ** ** ** * ** ** ** ' ** ** ** ** 3 * ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** 2 *. ** ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** ** 1 * ** *•* ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** * * * * * * 0 ****************** ******************************************************************************************************** 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 OCCUPANCY "FIGURE 8: R E L . • FREQUENCY OF NUMBER OF JOBS OCCUPYING SIMULTANEOUSLY THE S H E L V E S THE RECORDINGS C O L L E C T I O N ( = DESK _ S H E L V E S ) AS STO RAGE STORAGE C A P A C I T Y AVERAGE AVERAGE E N T R I E S AV ER AGE CURRENT MAXIMUM CONTENTS U T I L I Z A T I O N TIMEVTRAN CONTENTS CONTENTS 11 15 0 5. 3 6 4 .035 5 4 2 1 3.563 1 2 3 T R A N S I T T I M E S THROUGH REC. C O L L . ( M I N . ) , (-DESK _ S H E L V E S ) T A B L E TAB9 E N T R I E S I N TABLE MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS 5 4 2 0 3. 5 6 3 4 . 4 4 1 1 9 3 1 4 . 0 0 0 NON-WEIGHTED UPPER OBSERVED PER CENT C U M U L A T I V E CUMULATIVE M U L T I P L E . D E V I A T I ON L I M I T FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 1 2 0 3 9 3 7.61 3 7 . 6 6 2 . 3 . 2 8 0 - . 5 7 7 2 8 7 7 1 6 . 1 8 5 3.8 46.1 . 5 6 1 - . 3 5 2 •3 6 7 0 1 2 . 3 6 6 6 . 1 : 3 3.8 . 8 4 1 - . 1 2 6 4 52 4 9.66 7 5 . 8 2 4 . 1 . 1.122 .098 5 2 7 7 5.11 8 0 . 9 19.0 1.403 . 3 2 3 6 198 3.65 8 4 . 5 1 5 . 4 1.683 .548 7 153 2-82 8 7.4 12. 5 1. 9 6 4 . i n 8 121 2.23 89 .6 • 1 0 . 3 2 . 2 4 5 . 9 9 8 9 8 4 1. 54 9 1 . 1 . 8.8 2 . 5 2 5 1 . 2 2 4 10 87 1 .60 9 2 . 8 7. 1 2. 8 0 6 1.449 11 9 3 . 1.71 9 4 . 5 5.4 3 . 0 8 6 1.674 12 4 9 .90 9 5 . 4 4. 5 3 . 3 6 7 1.899 13 4 9 .90 9 6 . 3 3.6 3 . 6 4 8 2. 1 2 4 14 3 0 . 5 5 9 6 . 8 3.1 3 . 9 2 8 2 . 3 4 9 15 18 .33 9 7 . 2 2.7 4 . 2 0 9 2 . 5 7 4 16 17 .31 9 7 . 5 2.4 4 . 4 9 0 2. 8 00 17 17 . 3 1 9 7 . 8 2.1 4 . 7 7 0 3 . 0 2 5 18 13 .23 9 8 . 0 1.9 5 . 0 5 1 3 . 2 5 0 19 12 .22 9 8 . 3 1.6 5 . 3 3 1 3 . 4 7 5 20 9 . 16 9 8 . 4 1.5 5.612 3 . 7 0 0 21 13 . .23 9 8 . 7 1.2 5. 8 9 3 3 . 92 5 22 14 .25 98 .9 1.0 6. 173 4 . 1 5 1 23 4 .07 9 9 . 0 .9 6.454 4 . 3 7 6 24 9 , • .16 9 9 . 2 . 7 6.735 4 . 6 0 1 25 4 .07 9 9 . 2 . / /.U15 4.£26 26 6 .11 9 9 . 3 . 6 7 . 2 9 6 5 . 0 5 1 27 5 .09 9 9 . 4 .5 7 . 5 7 6 5.2 76 28 8 .14 9 9 . 6 .3 7.857 5 . 5 0 1 29 7 .12 9 9 . 7 . 2 8. 1 3 8 5 . 7 2 7 30 8 .14 9 9 . 9 .0 8 . 4 1 8 5 . 9 5 2 J i 5 . 09 1 0 0 . 0 .0. 8 . 6 9 9 6.1 R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO 4 5 * 44 _* '4 3 " *~ 42 * 41 * _ _ _ _ _ ; • : : ; : - 39 * 3 8 _* ; , 37" * * ' 3 6 * * 3 5 * * 34 * * 3 3 * * 32 * ; . . • __ • - : 3 1 *" * ' ' • • " — • ~ " ' • ' . " ' " * 3 G * * > • 2 9 * * _ _ _ . _ ; ; r : ; : 27 * * _2_ *_ * ; : . • 2 5 " * . * 24 * * 23 * * 21 * * 20 * . . . . : 1 9 ~ * " ~ * ' •" ~~ •" '. " ~ "~ • " ' ' " 7 18 * * 17 * * [ . 16 * * * 15 * * * 1 4 * * * ; : ; ; "13 * * * 12 * * * * • 1 1 * * ' * * 10 * *~ — * * : '• : g * * * * * 8 * * * * * , ' •_._ _ _ _ _ _ _ __ _____ _ . . . __ : . _ 6 * * * . * * 5 * * * * * * 4 * * * *~ * 5 3 * * * * * * * .2 * * * * * * * * * • ----- - ^ * * * * * * * * * 0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1 2 3 4 5 6 7 8 9 10 11 12 13 , 14 1 5 TRANS IT T I M E ( M I N . ) """FIGURE 9: R E L . FREQUENCY OF TRANS'! T. TI MES THROUGH THE RECORDINGS C O L L E C T I O N : ~ OCCUPANCY OF RECORD. C O L L E C T . {=DESK _ S H E L V E S ) T A B L E TAB 10 E N T R I E S IN T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS / 5 4 2 0 5 . 8 9 7 3 . 5 8 5 3 1 9 6 4 . 0 0 0 NON-WEIGHTED \ UPPER OBSERVED PER CENT CU M U L A T I V E C U M U L A T I V E M U L T I P L E D E V I A T I O N L I M I T 0 1 FREQUENCY OF TOTAL 88 1.62 298 5.49 PERCENTAGE 1 .6 7. 1 REMAINDER 9 8 . 3 9 2 . 8 OF MEAN - . 0 0 0 .169 FROM MEAN - 1 . 6 4 4 - 1 . 3 6 5 2 3 4 505 9 .31 6 3 1 1 1 . 6 4 7 1 3 1 3 . 15 1 6 . 4 2 8 . 0 4 1 . 2 8 3 . 5 7 1 . 9 5 8 . 7 . 3 3 9 .508 .678 - 1 . 0 8 6 - . 807- - . 5 2 9 5 6 7 597 1 1 . 0 1 58 7 1 0 . 8 3 48 7 8.9 8 5 2 . 2 6 3 . 0 7 2 . 0 47 .7 3 6 . 9 2 7 . 9 . 8 4 7 1.017 1. 1 8 6 -.2 50 . 0 2 8 . 3 0 7 8 9 10 i i i 6.88 3 0 1 5.5 5 2 1 4 3.94 7 8.9 8 4 . 5 8 8 . 4 2 1 . 0 1 5 . 4 .11.5 1.356 1 .52 6 1. 6 9 5 . 5 8 6 .865 1.144 11 12 13 183 3 . 3 7 136 2 . 5 0 101 1.86 9 1 . 8 9 4 . 3 9 6 . 1 8.1 5. 6 3.8 1 . 8 6 5 2.03 4 2 . 2 0 4 1.422 1.701 1.980 14 15 16 7 5 1.38 49 .90 37 .68 9 7 . 5 9 8 . 4 9 9 . 1 2 .4 1.5 .8 2 . 3 7 3 2 . 5 4 3 2 . 7 1 3 2 . 2 5 9 2 . 5 3 8 2 . 8 1 7 17 18 19 19 .35 11 .20 4 .07 9 9 . 5 9 9 . 7 99 .7 .4 . 2 .2 2 . 8 8 2 3. 0 5 2 3 . 2 2 1 3 . 0 9 6 3 . 3 7 5 3 . 6 5 3 20 21 22 5 . 0 9 2 .03 4 .07 9 9 . 8 9 9 . 9 1 0 0 . 0 .1 .0 .0 3 . 3 9 1 3 . 5 6 0 3 . 7 3 0 3 .932 4 . 2 1 1 4 . 4 9 0 R E M A I N I N G F R E Q U E N C I E S ARE ALL ZERO < So 15 * * 14 * * * 13 * * ** * ** 12 * ** ** * ** 11 ** ** ** •a. ** ** ** * ** ** . ** 10 •v ** ** ** ** a. ** ** ** ** * ** ** ** ** 9 * ** ** ** ** ** * ** ** ** ** ** * ** ** ** ** ** 8 * ** ' ** ** ** ** ** * ** ** ** ** ** ** * ** ** ** ** v f 7 * ** ** • ** ** ** _» -J' •V f * ** ** ** ** ** ** * ** ** ** ** "** ** 6 * ** ** ** ** ** ** ** * ** ** ** ** ** ** ** * ** ** ** ** :** ** ** 5 * ** ** ** ** ** ** ** ** ** * ** ** ** *•* ** ** ** ** ** * ** ** ** ** ** ** ** ** ** 4 * ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** * ** •** ** ** ** ** ** ** ** 3 * ** - .** ** ** ** ** ** ** ** ** ** * ** ** ** ** *.* ** ** ** ** ** ** * ** . ** ** ** ** ** ** ** ** ** ** 2 * **; ** ** ** ** ** ** ** .** ** ** ** * ** ** ** ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** ** ** 1 ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** 0 ******************************** ***************************** *********************************** o i 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 OCCUPANCY F I G U R E 1 0 : R E L . FREQUENCY OF NUMBER OF JOBS OCCUPYING S I M U L T A N E O U S L Y DESK AND S H E L V E S STORAGE C A P A C I T Y AVERAGE CONTENTS T T 1 5 . 891 AVERAGE UT I L 1 Z A T I O N E N T R I E S T2TT AVERAGE TI ME/TRAN 4 4 . 9 5 3 CURRENT CONTENTS rr~ MAXIMUM CONTENTS Z 3 -4(3 L IST EN IN G ROOM I N T E R A R R I V A L T I M E S ( M I N . ) T A B L E T A B U E N T R I E S IN TABLE 1 2 5 3 MEAN ARGUMENT 2. 8 4 5 STANDARD D E V I A T I O N 2. 9 7 6 SUM OF ARGUMENTS 3 5 6 5 . 0 0 0 NON-WEIGHTED UPPER OBSERVED PER CENT C U M U L A T I V E CUMUL AT IV E M U L T I P L E D E V I A T I O N L I M I T FREQUENCY OF TOTAL PERCENTAGE RE MAINDER OF MEAN • FROM MEAN .1 5 1 2 4 0 . 8 6 4 0 . 8 5 9 . 1 . 3 5 1 - . 6 1 V 2 2 1 8 1 7 . 3 9 5 8 . 2 4 1 . 7 .702 - . 2 83 3 1 6 3 1 3 . 0 0 7 1 . 2 2 8 . 7 1. 0 5 4 .052 4 9 7 7.74 7 9 . 0 2 0 . 9 1.405 .3 87 5 8 5 6. 78 8 5 . 7 1 4 . 2 1.757 . 7 2 3 6 53 4 . 2 2 9 0 . 0 9.9 2 . 1 0 8 1 . 0 5 9 7 4U 3 . 1 9 9 3.2 6. 7 2 . 4 6 0 1.395 8 21 1.67 9 4 . 8 5.1 2 . 8 1 1 1.7 31 9 20 1 .59 9 6 . 4 3. 5 3. 163 2. 0 6 7 10 15 1.19 9 7 . 6 2.3 3 . 5 1 4 2 . 4 0 3 11 8 .63 9 8 . 3 1.6 3 . 8 6 6 2.7 39 12 6 .47 9 8 . 8 1.1 4 . 2 1 7 3 . 0 7 5 13 5 . 39 ^ 9 . 2 .7 4 . 5 6 9 3 . 4 1 1 14 3 . 2 3 9 9 . 4 .5 4 . 9 2 0 3 . 7 4 7 15 0 .00 9 9 . 4 .5 5 . 2 7 2 4 . 0 8 3 16 2 . 15 9 9 . 6 .3 5 . 6 2 3 4 . 4 1 9 17 .0 .00 9 9 . 6 .3 5 . 9 7 5 4 . 7 5 5 18 1 .07 99 .6 .3 6 . 3 2 6 5 . 0 9 1 19 1 . 0 7 9 9 . 7 .2 6.6/7 5 . 4 2 7 2 0 1 .07 9 9 . 8 . 1 7. 0 2 9 5.763 21 0 . 00 9 9 .8 . 1 7 . 3 8 0 6 . 0 9 9 22 0 .00 9 9 . 8 . 1 7.732 6 .435 23 0 .00 9 9 . 8 .1 8 . 0 8 3 6 . 7 7 1 24 1 . 07 9 9 . 9 .0 8 . 4 3 5 7 . 1 0 7 u .00 9 9 . 9 . 0 8. 786 7 . 4 4 3 26 0 .00 9 9 . 9 .0 9. 138 7.7 79 27 0 .00 . 9 9 . 9 .0 9.489 8 . 1 1 5 28 0 .00 9 9 . 9 • 0 9.841 ' 8 . 4 5 0 29 0 .00 9 9 . 9 .0 1 0 . 1 9 2 8. 7 8 6 OVERFLOW 1 . 07 1 0 0 . 0 .0 AVERAGE V A L U E Ub UVfckFLLiW 34.OU * ~% ft 60 * * "*" 56 * * 5 2 * _* 4 8 * * * 4 4 * * *~ 40 * * _ _ , . 36 * * ft • ; ; * * 32 * * * * * * : 28 * * * * ___ . . _ . . __ 24 * * • ft * _ _ . . : . 20 * * * *~~ ~ " 1 " ' ' 16 * * * * # * — * * : 12 * * * * * * * ft __. ^ 5 * * " ; ' ^ ~ ~ ~ 8 * * * * * * ft ft ft * * * *" * : * 4 ft ft ft ft ft ft ft ft • -' ft ft * * ft ft * ft * * ft ft ft 0 ********** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1 2 3 4 5 _ 6_ _ 7 8 9 10 11 12 13 14 15__ : : I N T E R A R R I V A L TIME ( M I N . ) F I G U R E l l : R E L . FREQUENCY OF I N T E R A R R I V A L T I M E S TO L I S T E N I N G ROOM TABLE TAB 12 E N T R I E S IN T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS 3 6 0 " 1. 9 1 4 1252.000 NON-WEIGHTED 3 .477 UPPER L I M I T 0 1 OBSERVED PER CENT C U M U L A T I V E C U M U L A T I V E M U L T I P L E D E V I A T I O N FREQUENCY 2 0 33 OF TOTAL 5 .55 9. 16 PERCENTAGE 5.5 1 4 . 7 REMAINDER 9 4 . 4 85 .2 OF MEAN - . 0 0 0 .287 FROM MEAN - 1 . 8 1 6 - 1 . 2 9 4 18 .33 1 9 . 4 4 18. 61 3 3 . 0 5 2 . 4 7 1 . 1 6 6 . 9 4 7 . 5 2 8 . 8 2 3 4 5 6 7 6 6 70 67 . 5 7 5 . 8 6 2 1 .150 - . 7 7 2 - . 2 4 9 . 2 7 2 49 33 12 1 3 . 6 1 9. 1 6 3.33 8 4 . 7 9 3 . 8 9 7 . 2 1 5 . 2 6.1 2.7 T5" .0 1. 4 3 7 1.7 2 5 2 . 0 1 2 .795 1.317 1 .840 2.362 2 . 8 8 5 8 8 9 2 R E M A I N I N G F R E Q U E N C I E S ARE ALL ZERO 2.22 • 55 9 9 . 4 1 0 0 . 0 2 . 3 0 0 2 . 5 8 7 : . : : . : : : _ , * - 22 * * 21 * •* 20 * 19 * ** * ** 1 8 * ** ** ** ** ** ** 17 * * ** ** ** ** ** ** 16 * ** ** ** * ** ** ** 15 * ** ** ** ** ** ** - 14 * ** ** ** ** ** ** 13 ** ** *•* ** * ** ** ** ** 12 * ** ** ** ** * ** ** ** ** 11 * ** ** ** **-* ** ** ** ** 10 * ** ** ** ** * ** ** ** ** 9 * ** ** ** ** ** , ** * ** ** ** ** ** ** 8 * ** ** ** ** ** ** * ** ** . ** ** ** ** 7 ** ** ** ** ** ** * ** ** ** ** ** ** 6 * ** ** ** ** ** ** ** ** ** ** ** ** 5 * ** ** ** ** ** ** ** * ** ** ** ** ** ** ** 4 * ** ** ** ** *•* ** ** * ** ** ** ** ** ** ** 3 ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** 2 * *-¥ ** ** ** ** ** * -~ ** * ** ** ** ** ** ** ** ** ** 1 * ** - ** ** ** ** ** ** ** ** * ** ** ** ** ** ** * * * * * * 0 ****************** ******************************************************** ************************************************ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 A R R I V A L RATE/10 M I N . F I G U R E 1 2 : R E L . FREQUENCY OF A R R I V A L S TO L I S T E N I N G ROOM DURING 10 MIN. T A B L E T A B 1 3 E N T R I E S I N T A B L E MEAN ARGUMENT .' STANDARD D E V I A T I O N SUM OF ARGUMENTS J 1254 45 ._06 3 5.625 56689.UUU NUN-Wfc It>HI EU UPPER . OBSERVED PER CENT CUMULAT I V E CUMUL A T I V E M U L T I P L E D E V I A T I O N L I M I T FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 7 .55 . 5 99.4 -.000 -1.268 5 57 4. 54 5.1 94.8 .110 -1.128 10 71 5.66 10. 7 89.2 .221 -.988 15 84 6.69 17.4 82.. 5 . 331 -.847 20 95 7.5 7 25 .0 74 .9 .442 -.707 25 104 8.29 ' 3 3 . 3 66.6 .553 -.567 30 105 8.37 41.7 58. 2 . 663 -.426 35 80 6.37 48.0 5 1.9 .774 - .286 40 66 5.26 53. 3 46. 6 .884 - . 146 45 94 7 .49 60.8 39.1 .995 -.005 50 90 7.17 68.0 31.9 1.106 . 134 55 67 5.34 ' 73. 3 26.6 1 .216 .274 60 48 3 .82 77.1 22.8 1.327 .415 65 43 3.42 80.6 19.3 1.437 .555 to 28 2.23 82.8 1 /. 1 1. 548 .69t> 75 24 1.91 84.7 15.2 1.659 .836 80 19 1.51 86.2 13.7 1.769 .976 85 26 2.07 88.3 11. 6 1. 880 1.117 90 15 1.19 89.5 10.4 1.990 1.2 57 95 17 1.35 90.9 9.0 2 .101 1.397 i 00 12 .95 91.8 8. 1 2. 212 1.53 8 10 5 7 . 55 92.4 7.5 2.322 1.678 1 10 7 .55 92.9 7.0 2.433 1 .818 115 11 .87 93.8 6 . 1 . 2.543 1. 959 120 13 1. 03 94.8 5.1 2.654 2.099 ' 125 13 1.03 95. 9 4.0 2.765 2.239 130 6 .47 . 96.4 .3.5 2.875 2.380 135 1 ..07 • 96.4 .3.5 . 2.986 2.520 140 3 .23 96.7 3.2 3. 096 2.660 145 5 .39 9 7 .1 2.8 3.207 2.801 150 4 .31 97.4 2. 5 3.318 2.941 155 4 .31 97.7 2.2 3. 42 8 3.081 160 6 .47 98.2 1 . / 3.53V 3.2 22 165 2 .15 98. 4 1.5 3.649 3.362 170 6 • .47 98.8 1.1 3.760 3. 502 175 4 .31 99.2 .7 3.871 3.643 180 0 .00 9 9 . 2 . 7 3.981 3.783 185 4 .31 99.5 - .4 4.092 3.924 190 6 . 4 / 100. 0 • U 4.202 4.064 R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO % * * 21 * * 20 * 19 * ' 18 * 17 * * ~* 15 * * 14 * : * 1_3_ * "* 12 * * 11 * 1JL_Z . * 9 * * * * * 7 * * * * * -A. T * * * ft * 6 * * * * ft * ft ft * . * * * ft ft ft ft 5 * * * * * ft ft ft * * * * * * ft ft * * * * 4 * * * • * * ft ft ft ft ft * * * * * ft ft ft ft ft ft 3 * * * * * * * ft * * ft ft ft * * * * * * ft * ft ft ft ft ft ft 2 * * * * * ft ft ft ft ft ft ft . ft ft * * * * * * ft ft ft * ft ft ft ft * * 1 . * * * * * ' f t ft * ft * * ft ft ft & ft ft * ft * * * * * * * * ft * ft * ft ft ft * ft ft ft * * & * ft g * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * f t * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ^ ' 5 10 15 20 2 5 3 0 3 5 4 0 45 50 55 6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 5 1 0 0 1 0 5 1 1 0 1 1 5 120 1 2 5 130 1 3 5 1 4 0 1 4 5 1 5 0 T R A N S I T T I M E ( M I N . ) F I G U R E 13: R E L . FREQUENCY OF T R A N S I T TIME OF L I S T E N I N G ROOM T A B L E T A B 1 4 E N T R I E S ' I N T A B L E M E A N A R G U M E N T S T A N D A R D D E V I A T I O N S U M O F A R G U M E N T S J 1 2 5 4 1 5 . 7 0 5 3 . 3 8 2 1 9 6 9 5 . 0 0 0 N U N-Wfc I G H 1 E D U P P E R O B S E R V E D P E R C E N T C U M U L A T I V E C U M U L A T I V E M U L T I P L E D E V I A T I O N L I M I T 0 1 F R E Q U E N C Y 0 0 O F T O T A L . 0 0 . 0 0 P E R C E N T A G E . 0 . 0 R E M A I N D E R 1 0 0 . 0 1 0 0 . 0 O F M E A N - . 0 0 0 . 0 6 3 F R O M M E A N - 4 . 6 4 2 - 4 . 3 4 7 2 3 4 0 0 1 . 0 0 . 0 0 . 0 7 • 0 . 0 . 0 1 0 0 . 0 1 0 0 . 0 9 9 . 9 . 1 2 7 . 1 9 1 . 2 5 4 - 4 . 0 5 1 - 3 . 7 5 5 - 3 . 4 6 0 5 6 7 1 4 8 . 0 7 . 3 1 . 6 3 . 1 . 4 1 . 1 9 9 . 8 9 9 . 5 . 9 8 . 8 . 3 1 8 . 3 8 2 . 4 4 5 - 3 . 1 6 4 - 2 . 8 6 9 - 2 . 5 7 3 8 9 1 0 1 3 2 3 3 5 1 . 0 3 1 . 8 3 2 . 7 9 2 . 1 3 . 9 6 . 7 9 7 . 8 9 6 . 0 9 3 . 2 . 5 0 9 . 5 7 3 . 6 3 6 - 2 . 2 7 7 - 1 . 9 8 2 - 1 . 6 8 6 1 1 1 2 1 3 50 7 7 1 1 3 3 . 9 8 6 . 1 4 9 . 0 1 1 0 . 7 1 6 . 9 2 5 . 9 8 9 . 2 ' 8 3 . 0 7 4 . 0 . 7 0 0 - . 7 6 4 . 8 2 7 - 1 . 3 9 1 - 1 . 0 9 5 - . 7 9 9 1 4 1 5 1 6 1 2 1 1 4 5 1 3 8 9 . 6 4 . 1 1 . 5 6 1 1 . 0 0 3 5 . 5 4 7 . 1 5 8 . 1 6 4 . 4 5 2 . 8 4 1 . 8 . 8 9 1 . 9 5 5 1 . 0 1 8 - . 5 0 4 - . 2 0 8 . 0 8 6 1 7 1 8 1 9 1 2 8 1 2 9 8 6 1 0 . 2 0 1 0 . 2 8 6 . 8 5 6 8 . 3 7 8 . 6 8 5 . 4 3 1 . 6 2 1 . 3 1 4 . 5 1 . 0 8 2 1 . 1 4 6 1 . 2 0 9 . 3 8 2 . 6 7 8 . 9 7 3 2 0 2 1 2 2 7 6 5 9 4 7 6 . 0 6 4 . 7 0 3 . 7 4 9 1 . 5 9 6 . 2 1 0 0 . 0 8 . 4 3 . 7 . 0 1 . 2 T 3 1 . 3 3 7 1 . 4 0 0 1 . 2 6 V 1 . 5 6 5 1 . 8 6 0 R E M A I N I N G F R E Q U E N C I E S A R E A L L Z E R O j 15 * 14 * ft ft" 13 * ft ft 12 * ft ir l l * ft* ft* * * * * * . ~ ~ " * * r " * * ~ ; _ — ~ _ - _ . ; . . - _ _ . 1 0 * * * * * * * * * „ - A . _ -A. 0 , -A. 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OCCUPANCY ~ ~ F I G U R E 1 4 : R E L . FREQUENCY OF NUMBER OF JOBS O C C U P Y I N G S I M U L T A N E O U S L Y THE L I S T E N I N G ROOM STORAGE C A P A C I T Y "4T AV ERAGE CONTENTS ~ . 6 9 0 AVERAGE U T I L I Z A T I O N 77J3T3 E N T R I E S "5T" AVERAGE TIME/TRAN 46 .0 /4 CURRENT CONTENTS MAXIMUM CONTENTS 23 OCCUPANCY OF R E S E R V E L I S T . ROOM T A B L E TAB 1 7 E N T R I E S IN T A B L E 54 UPPER L I M I T TT 1 2 MEAN ARGUMENT 2 .388 STANDARD D E V I A T I O N 2. 191 SUM OF ARGUMENTS 1 2 9 . 0 0 0 NON-WEIGHTED OBSERVED FREQUENCY PER CENT OF TOTAL C U M U L A T I V E PERCENTAGE CU M U L A T I V E REMAINDER M U L T I P L E OF MEAN D E V I A T I O N FROM MEAN T 4 - 11 6 7 4 . 0 5 3 . 7 4 2 . 5 - . 0 0 0 .418 . 8 3 7 - 1 . 0 9 0 - . 6 3 3 -. 177 2 5 . 92 2 0 . 3 7 11 .11 2 5 . 9 46. 2 57.4 3 4 5 "6~ 7 5 7 6 9.25 1 2 . 9 6 1 1 . 1 1 6 6 . 6 7 9 . 6 9 0 .7 33 .3 2 0 . 3 9.2 1 .255 1. 6 7 4 2 . 0 9 3 .278 .73 5 1. 191 1 1 5.55 1.85 1.85 9 6 . 2 9 8 . 1 1 0 0 . 0 ~3T7~ 1.8 .0 2.5 1 1 2. 9 3 0 3 . 3 4 8 1 . 6 4 / 2 . 1 0 4 2 . 5 6 0 R E M A I N I N G F R E Q U E N C I E S ARE ALL ZERO j I GRAPH % * 35 * 34 * 3 3 * 3 2 * 3 1 * 3 0 * 2 9 * 28 * 27 * 26 * 2 5 * 2 4 * 23 * 22 * 21 * 20 * ** ** ** ~**" ** ** ** 19 * 18 * 17 * ** ** ** ** ** ** -*F~ * * * * 16 * 15 * 14 * 13 * 12 * 11 * ** ** ** ** ** ** ** ** *•* ** ** ** ** ~WW ** ** ** ** 10 * 9 * 8 * 7 * 6 * 5 * -2T*" 3 * 2 *_ 0 ** ** ** "**" ** ** ** ** ** ** ** ** ** ** ** ** "WW ** ** ** ** ** -**- ** ** ** ** ** ** ** ** ""*"*- * * * * ~WW ** ** ** ** ** ** ** ** ** •** ** ** ** ** ** ** ** ** ** **, ** i * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 7' 8 9. 10 11 12 13 14 •OCCUPANCY F I G U R E 14A: R E L . FREQUENCY OF NUMBER OF J O B S OCCUPYING SIMULTANEOUSLY THE L I S T E N I N G ROOM STORAGE CAPACITY AVERAGE CONTENTS AVERAGE UTIL IZATION ENTRIES AV ERAGE TIME/TRAN CURRENT CONTENTS MAXIMUM CONTENTS J 10 200 21 .946 .109 3212 24. 604 20 45 S SYSTEM TRANSIT TIMES (MIN. ) (=SERVICE _ WAIT. TIME ) TABLE TAB15 ENTRIES IN TABLE 3 192 MEAN ARGUMENT 4.273 STANDARD DEVIATION 13.2 07 SUM OF ARGUMENTS 13642.000 NON-WEIGHTED UPPER LIMIT OBSERVED FREQUENCY PER OF CENT TOTAL CUMULATIVE CUMULATIVE PERCENTAGE REMAINDER MULTIPLE OF MEAN DEVIATION FROM MEAN 0 5 10 89 7 1882 224 28 . 10 58.95 7.01 28. 1 87.0 94.0 71.8 12.9 5.9 -.000 1.169 2.339 -.323 .054 .433 15 20 25 51 20 15 1.59 .62 .46 95.6 96 .3 96. 7 4.3 3.6 3.2 3.509 4.679 5.849 .812 1.190 1.569 30 35 40 19 10 8 .59 . 31 .25 97.3 97 .6 97.9 2.6 2.3 2.0 7. 019 8.189 9.359 1.947 2.326 2.705 45 50 55 11 4 11 .34 .12 .34 98 .2 98.4 98.7 1.7 1 ,5 1.2 10. 529 11.699 12.869 3.0 83 3.462 3.840 60 65 70 8 3 2 .25 .09 .06 98.9 99.0 99.1 • 1.0 .9 .8 14.038 15.208 16.378 4.219 4.598 4.976 75 80 85 2 3 4 .06 .09 .12 99 .2 99.3 99.4 .7 .6 . 5 17.548 18.718 19.888 5.3 55 5.733 6.112 90 95 100 ' 0 2 1 . 00 .06 .03 99 .4 99.4 99.5 .5 .5 .4 21.058 22 .228 23.398 6.490 6.869 7.248 105 n o 115 2 0 1 . 06 .00 .03 99.5 99.5 99.6 .4 .4 .3 24.568 25.738 26.908 7.626 8 .005 8. 3 83. 120 125 130 2 1 o- .06 .03 .00 99.6 99.7 99.7 .3 .2 .2 28 .077 29.247 30.417 8.762 9.141 9. 519 135 140 145 0 1 0 . 00 .03 . 00 99. 7 99.7 99.7 .2 . 2 .2 31.587 32.757 33.927 9.898 10.276 10.655 150 1 55 160 1 i l. .03 .03 .03 99. f 99 .8 99.8 .2 • J. • JL 35.097 36. 267 37.437 11.033 11.412 11.791 165 170 175 0 0 0 .00 .00 .00 99. 8 99.8 99.8 • i. • i- • i. 38.607 39.777 40.947 12.169 12.548 12.926 180 185 190 0 2 3 .00 .06 . 09 99. 8 99.9 100.0 • J. .0 .0 42.116 43.286 44.456 13.305 13. 684 14.062 REMAINING FREQUENCIES ARE ALL _ERO J ft * 1 0 0 * 9 5 * 9 0 * * 85 * 80 * __ 75 * 70 * ft 6 5 * 60 * 5 5 * ^~ ft * 50 * * 4 5 ft •* ft. * AO *. *~ 3 5 * * 3 0 * * * ft ~ 2 5 ~ ^ *~ ft ft 20 * * .„ x 15 ft ft ft ft 1 0 * - ft ft 5 * * * * ft * 0 * * * * * * * f t f t * * * * * f t * * * * f t * f t f t * f t f t f t f t f t * f t * f t f t f t * * f t f t 5 10 15 20 25 30 3 5 40 45 50 5 5 6 0 6 5 70 7 5 8 0 85 9 0 95 100 10 5 110 1 1 5 1 2 0 1 2 5 1 3 0 1 3 5 140 1 4 5 1 5 0 TRANSIT Tl ME < MIN. ) - ~ T A B L E T A B 1 6 E N T R I E S I N T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS Tm 2 2 . 5 9 7 5.921 000 NUN-WL IGHibU UPPER OBSERVED PER CENT CUMULAT IV E C UMULATIVE M U L T I P L E . D E V I A T I O N L IM IT FREQUENCY O F TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 0 .00 .0 1 0 0 . 0 -. 0 0 0 - 3 . 8 1 5 2 0 . 0 0 .0 1 0 0 . 0 . 0 8 8 - 3 . 4 7 8 4 3 .09 . 0 9 9 . 9 .177 - 3 . 1 4 0 6 6 .18 .2 9 9 . 7 . 2 6 5 - 2 . 8 0 2 8 6 .18 .4 9 9 . 5 . 3 5 4 - 2 . 4 6 5 10 16 .50 ' .9 9 9 . 0 .442 - 2 . 1 2 7 12 62 1 .94 2.9 9 7 . 0 . 531 - 1 . 7 8 9 14 106 3.32 6.2 93 .7 .619 - 1 . 4 5 1 16 2 3 0 7.20 1 3 . 4 8 6 . 5 . 708 - 1 . 1 1 4 18 3 4 5 1 0 . 8 0 2 4 . 2 7 5 . 7 . 7 9 6 - . 7 7 6 20 4 6 1 1 4 . 4 4 3 8 . 6 6 1 . 3 • 8 8 5 - . 4 3 8 22 4 5 8 1 4 . 3 4 5 3 . 0 46.9 . 9 7 3 - . 1 0 0 24 4 4 1 1 3 . 8 1 66 .8 3 3.1 1.062 . 2 3 6 26 358 1 1 . 2 1 7 8 . 0 2 1 . 9 1 . 1 5 0 .574 28 l \ i 6 .67 8 4 . 7 15.2 1. 2 3 9 . 9 1 2 30 153 4 . 7 9 8 9 . 5 10.4 1.327 1 . 2 4 9 32 112 ' 3.50 9 3 . 0 6.9 1 .416 1 .587 34 89 2 .78 9 5 . 8 4.1 1.504 1. 9 2 5 36 61 1.91 9 7 . 7 2 .2 1.593 2 . 2 6 3 38 51 1.59 9 9 . 3 .6 1 . 6 8 1 2 . 6 0 0 40 15 . .46 99 .8 .1 1.770. 2 . 9 3 8 42 4 .12 9 9 . 9 .0 1.858 3 . 2 7 6 44 2 .06 1 0 0 . 0 .0 1.947 3 . 6 1 4 " R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO % * A- T * 40 * A r - 36 * 34 * • A - - r 32 * 30 * 28 1 - A - Ar * ¥ * f A - T A r A - *¥» *v . 1 26 -JU Ar A -* •A. A--v* • * * ** 24 A . •V Ar A . •V -V - A - _U * A r A - A . 22 -»* , A - „ •v -v ftft * -A- Air -¥* <V - A . A , 20 Ar Ar Ar *V " i - A » A - A . Ar Ar •V- -»* - J , Ar 1 8 -A- ftft ftft * A - Ar '1* K* A . A -• f> -V ** 16 * ft* A . A -T" ' V A > A --r* -r- ft ft* A > Ar i r •*•*• Ar Ar 14 ft - _ A r •V -v A r - A , ft A . A - A > Ar 12 Ar Ar Ar- A> A r - < - f ft ** *»' A - A -•V -V ft* 10 A . * v A A - Ar A , A - A , T" -¥• •if- Ar T ft* > » * A , A - Ar ft* 8 Ar •V Ar A - A - Ar •V -«~ Ar- Ar ft* ft Ar A-'1* *•<* A r Ar *«* *V A , -A. *v- ** 6 ft A - Ar •V* v Ar A r • V -Ar- Ar Ar A - 1* A . Ar **•> Ar A * A . A . A . „ ** A - A --V -V- 4 J " r •r -Jr A -V -A- -A- Ar-J_- ** Ar A j -(- A - A . •fc ^ A . A > ft* . . ** A r A - Ar Ar If. .f. -ff. if. . 2 * ftft A - A - * & A r Ar T* ** A -Ar A . A r ft ft ** A , Ar •V -V A r ™ * * ** ft ft 0 A > A A - A- Ar T -V* V * V - V A - V - „ _ - „ „ A - A - _ J . A - . A - -j". A - A - A . • V - V -*»* ' V -V "1* -Y- -*V - , v Jf. *f 1' 3}i 5yt ^ A > A> A / A ~ A * A r 1* <1" "V- -»*> "V •*!- *** ̂ * * ^ "** • J - A - A - A - A J . -v -v* - w -sr-r- ********* **************ft*************************ftftftftftftftftftftftftftft*ftftftftftftftftftftft*ftft 2 6 1 0 14 18 22 26 30 34 38 42 4 6 50 54 58 6 2 66 7 0 74 78 OCCUPANCY FI GURE 16: R E L . FREQUENCY QF NUMBER OF JOBS OCCUPYING S I M U L T A N E O U S L Y THE SYSTEM END CPU T I M E USED: A S S E M B L Y : 3. 173 SECONDS E X E C U T I O N : 6 4 . 8 4 1 SECONDS E X E C U T I O N TERMINATED $ S I G N O F F 7 RFS NO. 771083 UNIVERSITY OF B C COMPUTING CENTRE MTSUN120) 00: 12:48 12-30-70 < USER: WULI DEPARTMENT: COMM **** ON Al 00: 12:49 ~ : OFF AT 00:14:23 **** ELAPSED TIME 94.136 SEC• **** CPU TIME USED 71.257 SEC. **** STORAGE USED 4437.03 PAGE-SEC. **** CARDS READ 406 **** LINES PRINTED 94T_ : **** PAGES PRINTED 280 CARDS PUNCHED 0 ; */.*** DRUM READS . 5 **** RATE FACTOR 0.6 **** APPROX. COST OF THIS RUN C$12.22 * * * * F I L E S T O R A G E 0 P G - H R . .00 * * T A T T ~ T T G T ^ 10:54:13 12-29-70 MMMMM MMMMM TTTTTTTTTTTTTTTTTTTTTTTTT SSSSSSSSS MMMMMM MMMMMM TTTTTTTTTTTTTTTTTTTTTTTTT SSSSSSSSSSSSS MMMMMMM MMMMMMM TTTTTTTTTTTTTTTTTTTTTTTTT SSSSSSSSSSSSSSSSS NMFMMMMM MMMMMMMM TTTTT s s s s s s s s s s s s s MMMMMMMMM MMMMMMMMM TTTTT s s s s s s s s s s KVPMMMMMMM MMMMMMMMMM TTTTT s s s s s MMMMN MMMMM MMMMM MMMMM H I M s s s s s s MMMMM ' MMMMM MMMMM MMMMM TTTTT SSSSSSSSSSSSS MMMMM MMMMM MMMMM MMMMM TTTTT SSSSSSSSSSSSS MMMMM MMMMM MMMMMM' MMMMM TTTTT SSSSSSSSSSSSS MMMMM MMMMMMMMM MMMMM TTTTT SSSSSSS MMMMM MMMMMMM • MMMMM TTTTT s s s s s MMMMM HMMMM • MMMMM ! T T 1 1 s s s s s MMMMM MMM . •MMMMM TTTTT SSSSS SSSSS MMMMM. MMMMM TTTTT SSSSSSS s s s s s s s MMMMM • MMMMM TTTTT SSSSSSSSSSSSSSSSS MMMMM MMMMM TTTTT SSSSSSSSSSSSS MMMMM MMMMM TTTTT SSSSSSSSS R FS NO. 7 7 1 1 8 4 U N I V E R S I T Y OF B C COMPUTING CENTRE M T S ( A N 1 2 0 ) 0 0 : 4 1 : 4 2 1 2 - 3 1 - 7 0 (X ) \ •J, , i , j , _<v -JL, A J, -A J. O, JL, «^ -J» v«r T 1) t C f T -i- 'r -T> T . -r -y -v -v T -i" T v "c •*.* • •*! 1 i l 1 O SSIGNON WULI T = 150 P = 4 0 0 * * L A S T SIGNON WAS: 0 0 : 2 8 : JOB. S U B M I T T E D THROUGH PRIO=V C C P I E S = 4 20 1 2 - 3 0 - 7 0 FRONT DESK READER ******************** / USER "WULI" S I G N E D ON AT $RUN * STATUS PAR =F UL L E X E C U T I O N BEGINS 0 0 : 4 1 : 4 4 CN 1 2 - 3 1 - 7 0 \ STATUS OF WULI AT LAST S I G N O F F USED MAXIMUM R E M A I N I N G C U M U L A T I V E CHARGE CURRENT DISK S P A C E CURRENT C E L L SPACE (•$) {PAGES ) ( P A G E S ) 1 0 6 . 8 7 0 0 1 5 0 . 0 0 4 3 . 1 3 50 50 100 100 C U M U L A T I V E M E M O R Y — C P U C U M U L A T I V E MEMORY--WA IT CUMULATI VE CPU T I M E ( P G - H R ) ( P G - H R ) (HR) 5.91 3.60 0 . 1 1 C U M U L A T I V E L I N E S P R I N T E D C U M U L A T I V E PAGES P R I N T E D C U M U L A T I V E CARDS READ 4 9 6 1 1 1 6 4 3 8 8 1 1 BATCH S E S S I O N S E X P I R A T I O N DATE AND T I M E : 0 5 - 3 1 - 7 1 28 2 4 : 00 .00 • E X E C U T I O N TERMINATED $RUN *GPSS P A R = S I Z E = 8 E X E C U T I O N BEGINS BLOCK CARD NUMBER *LDC O P E R A T I O N A , B , C , 0 , E , F, G COMMENTS S I M U L A T E ' * S I M U L A T I O N OF UBC. RECORDINGS C O L L E C T I O N BY JOHANNES K RAM AR NUMBER 1 2 7 * • * F U N C T I O N D E F I N I T I O N S •A, 3 4 5 s * SYSTEM A R R I V A L T I M E E X P O N E N T I A L L Y D I S T R I B U T E D A R R I V F U N C T I O N R N 1 , C 2 4 NEG- E X P . DISTR ., M E A N - 1MIN.' 0. 0, 0. 0/. 1,. 1 0 4 / . 2 ,. 22 2/. 3 ,. 35 5/. 4,. 5 0 9 / .5 , . 69 / . 6 , .9 15 / .7 , 1 . 2/ 6 7 8 .75,1 . 3 8 / . 8 , 1 . 6 / . 8 4 , 1 . 8 3 / . 8 8 , 2 . 1 2 / .9» 2 . 3 / . 9 2 , 2 . 5 2 / . 9 4 , 2 . 8 1 / . 9 5 , 2 . 9 9 . 9 6 , 3 . 2 / . 9 7 , 3 . 5 / . 9 8 , 3 . 9 / . 9 9 , 4 . 6 / . 9 9 5 , 5 . 3 / . 9 9 8 , 6 . 2 / . 9 9 9 . 7 . 0 / . 9 9 9 7 , 8 . 0 -a- " 9 10 11 * DESK S E R V I C E T I M E EXPONENT I A L L Y D I S T R I B U T E D DESK F U N C T I O N ' R N 1 , C 2 4 NEG, E X P . D I S T R . 0 . 0 , 0 . 0 / . 1 ,. 1 0 4 / . 2 , . 2 2 2 / . 3 , . 35 5 / .4, . 5 0 9 / . 5 , . 6 9 / . 6 t. 9 1 5 / . 7, 1.2/ 12 13 14 . 7 5, 1. 3 8 / . 8, 1. 6/. 8 4 , 1 . 8 3 / . 8 8 ,2 .12 / .9,2 . 3 / . 9 2 , 2 . b 2 / . 9 4 , 2 . 8 1 / . 9 b , 2 . 9 9 .9 6, 3- 2/.9 7, 3 . 5 / . 9 8 , 3. 9 / . 9 9 , 4 . 6 / . 9 9 5 , 5. 3/. 9 9 8 , 6 . 2/.999»7.0/.9997 ,8.0 "v • . ' • 15 16 17 * S H E L F S E R V I C E TIME E X P O N E N T I A L L Y D I S T R I B U T E D S H E L F F U N C T I O N R N 1 , C 2 3 NEG. E X P . D I S T R . 0. 0,0. 0/. 1 5 4 , . 8 4 0 / .2 81 , . 2 5 0 / . 3 9 0 , .4 2 0 / . 48 3, . 5 8 0 / . 5 62 , . .7 5 0 / . 6 2 9 , . 9 2 / 18 19 2 0 . 6 8 5 , 1 . 0 8 / . r 3 3 , 1. 2 5 / . 7 7 4 , 1 . 4 2/. 8 0 8 , 1 . 5 9 / . 8 3 7 ,1 . 7 5 / . 8 6 2 , 1 .9 2 . 8 8 3 , 2 . 0 8 / . 9 , 2 . 2 5 / . 9 1 6 , 2 . 4 2 / . 9 2 7 , 2 . 5 8 / . 9 3 7 f 2 . 7 5 / . 9 4 6 , 2 . 9 2 / . 9 5 3 , 3 . 0 8 / . 9 5 9 , 3.25 21 22 23 . 9 6 4 , 3 . 4 2 / 1 . 0 , 5 . 2 7 '* L I S T E N I N G ROOM S E R V I C E T I M E G E N E R A L L Y D I S T R I B U T E D 24 25 26 L I S T F U N C T I U N K N I , C 2 5 GEN. D I S T R I B U T I O N 0 . 0 , 0 . 0 / . 0 2 4 , .06 3 / . 0 7 1 , . 1 8 7 / . 1 3 1 , . 3 1 2 / . 2 0 5 , . 4 3 7 / . 2 8 9 , . 5 6 3 / . 3 6 6 , . 6 9 0 / . 4 3 6 , . 8 2 0 / . 4 9 8 , . 9 4 0 / . 5 56 , 1 . 0 6 7 . 6 2 3 ,1 . 1 8 / . 6 9 9 , 1 . 3 1 / . 7 5 4 , 1 . 4 4 / . 7 8 6 , 1 .56/ 2 7 28 29 . 8 1 4 , 1 . 6 9 / . 8 3 6 , 1 . 8 1 / . 8 5 5 , 1 . 9 4 / . 8 7 2 , 2 . 0 6 / . 8 8 8 , 2 . 1 8 / . 9 0 3 , 2 . 3 1 / . 9 1 7 , 2 . 4 4 / . 9 2 7 , 2 .5 5 7 . 9 6 2 , 3..19/.989 , 4 . 2 0 / 1 . 0 0 , 4 . 8 2 0 30 31 32 * STORAGE D E F I N I T I O N S 10- STORAGE 2 0 0 D E F I N E S I Z E OF SYSTEM, S STORAGE 11 STORAGE 1 5 0 . D E F I N E -SIZE OF REC. C O L L . 3 3 3 4 35 30 . STORAGE 100 D E F I N E S I Z E OF STOR. 3 0 4 0 STORAGE 23 D E F I N E S I Z E OF STOR. 40 4 1 STORAGE 23 - D E F I N E S I Z E OF STOR. 4 1 36 3 7 38 * T A B L E D E F I N I T I O N S TAB1 T A B L E I A , 1 , 1 , 2 0 I N T E R A R R I V A L T I M E ' TAB2 T A B L E R T , 0 , 1 , 3 0 , 1 0 A R R I V A L RATE 39 4 0 41 TAB3 T A B L E M 1 , I , 1 , 3 0 T R A N S I T TIME T A B L E TAB4 Q T A B L E 2 , 0 , 1 , 3 0 UNITS IN QUE. TAB5 T A B L E I A , 1 , 1 , 3 0 I N T E R A R R I V A L TIME S H E L V E S 42 4 3 4 4 IAB6 l A b L t „kl ,0 , 1 , 2U , 10 A R R I V A L R A 1 b TAB7 T A B L E M l , 1,1,60 T R A N S I T T I M E TAB8 T A B L E S 3 0 , 0, 1,40 STOR. 30 OCCUPANCY 4b 46 47 . ' TA89 T A B L E M l , 1 , 1 , 6 0 TRANS. T I M E S E R V I TAB 10 T A B L E S l l , 0 , l , 6 0 STORAGE 11 OCCUPANCY T A B U T A B L E I A , 1 , 1 , 3 0 . INTERARR. TIME F A C . 4 0 48 49 50 I A B I 2 1 AB Lb R T , 0 , 1 , l b , 1 0 l A R R l V A L S F A C 40 TAB 13 T A B L E M l , 0 , 5 , 6 0 TRANS. TIME F A C . 4 0 TAB 14 T A B L E S 4 0 , 0 , l , 2 6 STORE 40 OCCUPANCY 51 52 5 3 TAB 15 T A B L E M l , 0 , 2 , 8 0 TRANS. TIME I N SYSTEM T A B 1 6 T A B L E S 1 0 , 0 » 2 , 6 0 S Y S T . OCCUPANCY TAB 17 TABLE S 4 1 , 0 , l , 2 6 - STOR. 41 OCCUPANCY 54 55 56 J * G P S S P R O G R A M 58 * 59 1 . . G E N E R A T E ' I, FN $ARR IV A R R I V A L S TO S Y S T E M 60 •2 ' E N T E R 1 0 C U M . S T O R . S Y S T E M 6 1 3 . T R A N S F E R . , 3 6 , S T G 3 , S T G 2 GO TO 3 OR 2 • ' . 62 4 ~ S T G 2 MARK : S E T T R A N S . T I M E = 0 . ~ '. ' 5 T 5. E N T E R 11 CUM. ' S T O R E R C . ' 6 4 ,6 -• . Q U E U E 2 J O I N Q U E . 2 ' 6 5 7 ~ . G A T E NU 1 , S E R 2 66 8. S E R 1 S E I Z E 1 • . " . O C C . DESK -SERV. 1 67 G P S S / 3 6 0 / M T S V E R S I O N ( 4 / 8 / 1 3 ) A > 9 DEPART 2 • • L E A V E QUE. 2 68 10 ADVANCE 1, F N $ D E S K DESK S E R V I C E 69 11 R E L E A S E 1 R E L E A S E DESK SERV. 1 70 12 TRANSFER ,TWO 71 / 13 S ER 2 L INK 2 , F I F 0 , R E S 2 L I N K USER C H A I N 2 11 \ 14 RES 2 S E I Z E 2 OCC. DESK SERV. 2 73 15 D E P A R T 2 L E A V E QUE. 2 74 16 ADVANCE 1, F N $ D E S K DESK S E R V I C E 7 5 17 R E L E A S E 2 R E L E A S E DESK 76 18 TWO U N L I N K • 2 , S E R 1 2 , 1- U N L I N K USER C H A I N 2 77 19 T K A N S F t R , 0 N t 78 20 SER 12 GATE NU 1,RES2 79 21 T RANSFER ,SER1 80 22 ONE T A B U L A T E TAB1 81 23 T A B U L A T E TAB2 T A B . A R R I V A L S 82 24 TABUL ATE TAB 3 TAB. TRANS. TIME . 8 3 25 L E A V E 11 84 26 T A B U L A T E T A 8 9 8 5 27 ' T A B U L A T E T A B 1 0 86 28 ASSIGN. 2,K1 SET P I TO ,1 87 29 T E S T LE C l , K 3 6 0 0 , F I N E TEST T I M E 88 3 0 TEST E P 3 , K 1 , G E H 2 89 31 • TfcST t P 4 , K i , G E H 3 9 0 • 32 TRA N S F E R »E XI T 91 33 GEH2 T E S T E P 4 , K 1 , G E H 4 9 2 34 T R A N S F E R . 7 5 , S T G 3 * E X I T 9 3 35 • GEH3 TRA N S F E R ... 9 6 , S T G 4 , E X I T 9 4 36 GEH4 TRANS FER . 7 3 , G E H 5 , E X I T 9 5 37 GEHb TRANSFER . 1 1 , S ) G 3 , S I G 4 9 6 38 STG3 MARK 97 39 E N T E R 11 CUM. STORE RC. 98 40 ENTER 30 ENTER STOR. 3 0 99 41. ADVANCE 6 ,FN$S H E L F S H E L F S E R V I C E TIME 1 0 0 - 42 L E A V E 30 L E A V E STOR. 30 1 0 1 4 3 T A B U L A T E T A B 5 I N T E R A R R I V A L TIME 102 4 4 T A B U L A T E T A B 6 A R R I V A L RATE 103 45 T A B U L A T E TAB 7 T R A N S I T TIME 1 0 4 46 T A B U L A T E TAB8 STORE. S H E L V E S OCCUPANCY 10 5 47 L E A V E 11 . L E A V E STORE 11 1 0 6 48 T A B U L A T E TAB9 107 49 T A B U L A I E I A B 1 0 STUKE KbCORU. C O L L E C T . 1 0 a 50 A S S I G N 3., K l SET P2 TO 1 1 0 9 51 T E S T L E C l , K 3 6 0 0 , F I N E TEST TIME 1 1 0 52 T E S T . E P2,K1,GE.H7 111 53 TEST E P 4 , K 1 , G E H 8 112 54 TRANS FER , E X I T 1 1 3 bb b t H / 1 ES 1 fc P4 , K l , G E H 9 1 1 4 56 TRANSFER . 2 8 , S T G 2 , E X I T 11 5 57 GEHB T R A N S F E R .2 2, ST G4, E X I T 116 58 GEH9 T R A N S F E R . 1 4 , G E H 1 0 * E X IT 1 17 59 GEH10 TRANSFER . 5 8 , S T G 2 , S T G 4 1 1 8 60 STG4 MARK 1 1 9 61 G A T E SNh 4 0 , 0 F L 0 W 1 2 0 62 ENTER 40 ENTER STOR. 4 0 121 - -- - - - • J G P S S / 3 6 0 / M T S V E R S I O N ( 4 / 8 / 1 3 1 A ̂ | . 63 64 65 66 ADVANCE LE A V E T A BULATE T A B U L A T E 4 0 , F N $ L I S T 4 0 T A B U T A B 1 2 L I S T . ROOM S E R V I C E TIME L E A V E STORAGE 40 I N T E R A R R I V A L T I M E FAC 4 A R R I V A L RATE F A C . 4 122 123 1 2 4 1 2 5 ) 67 68 69 T A B U L A T E T A B U L A T E TRANSFER TAB13 TA B 14 ,BE IDE TRANSIT T I M E F A C . 4 STORE. 40 OCCUPANCY 1 2 6 1 2 7 1 2 8 70 7 l 72 OFLOW ENTER ADVANCE L E A V E 41 4 0 , F N $ L 1 S T 41 L I S T . ROOM S E R V I C E TIME 129 130 1 3 1 73 74 75 BEI DE TABULA IE T R A N S F E R A S S I G N TA B1 7 t BE IDE 4,K1 OCCUP. OF R t S h R V . L I S T . ROOM ' SET P4 TO 1 13 2 133 134 76 77 78 GEH11 TEST E TR A N S F E R TEST LE P 3 , K 1 , G E H 1 1 . 0 9 , S T G 2 . E X I T C l , K 3 6 0 0 , F I N E TEST T I M E 135 136 1 3 7 79 80 81 GEH13 TEST E TRAN S F E R TRANSFER P 2 ,K1,GEH13 .38 ,STG3,EX IT . 0 8 , G E H 1 4 , E X IT 138 1 3 9 . 1 4 0 82 ' 83 84 GEH14 E X I T . TRAN S F E R L E A V E T A B U L A T E . 1 4 , S T G 2 , S T G 3 • 10 TAB 1 5 L E A V E S Y S T . STOR. TRANS. TIME IN S Y S T E M 141 142 143 85 86 87 F I N E T ABULATE T E R M I N A T E L E A V E T A B 1 6 10 SYSTEM OCCUPANCY LEAVE S Y S T . STOR. 144 145 1 4 6 88 89 90 T A B U L A T E T A B U L A T E T E R M I N A T E T A B 1 5 T A B 1 6 1 TRAMS. T I M E . I N SYSTEM SYSTEM OCCUPANCY 14 7 1 4 8 1 4 9 * CONTROL CARD START 1 150 151 1 5 2 ' FAC REPORT EJE C T T I T L E 1 , S T A T I S T I C S CONCERNING THE INFORMATI ON DESK , S E R V . 1 1 5 3 1 5 4 155 F A C SP A C E T I T L E SPACE 3 2 , S T A T I S T I C S CONCERNING THE INFORMATION D E S K , S E R V . 2 3 . 156 157 158 ' QUE C HA T I T L E . SP A C E TI TLE 2 , S T A T I S T I C S CGNC ERNI NG THE DESK QUEUE 3 • . 2 , S T A T I S T I C S CONCERNING THE DESK USER C H A I N 1 5 9 1 6 0 161 TAB E J E C T T I T L E E J E C T I t DESK I N T E R A R R I V A L TIMES ( M I N . ) 162 163 1 6 4 * GRAPH GRAPH TP,TAB 1 165 1 6 6 167 O R I G I N X Y 5 0 , 1 0 »2 f 1 3 ,1 , 1 , 8 0 , 4 , 2 0 , 2 168 1 6 9 170 • 7 1.00 10 STATEMENT STATEMENT STATEMENT 4, 1, % 52 » 2 4 > I N T E R A R R I V A L 55 , 4 6 , F IGUR.E 1 : REL TIME ( M I N . ) . FREQUENCY OF I N T E R A R R I V A L T I M E S 171 172 173 ENDGRAPH 1 7 4 1 7 5 • J TAB TI TLE E J E C T 2,NUMBER OF A R R I V A L S TO DESK/10 M I N . 176 177 -Jr 1 7 8 * GRAPH 179 GRAPH !P,TAB2 180 O R I G I N 5 0 , 1 0 181 X , 2 , 2 , 0 , 1 , 3 0 182 Y 0 , 1 , 2 1 , 2 183 7 STATEMENT 4,1.,? 1 8 4 100 STATEMENT 5 2 . 2 0 » A R R I V A L R A T E / 1 0 M I N . 1 85 10 STATEMENT 55 , 6 4 , F I G U R E 2 : R E L . FREQUENCY OF A R R I V A L S TO I N F . DEI 1 8 6 SK OUR ING 10 M I N . 18 7 ENDGRAPH 188 1 8 9 TAB T I T L E E J E C T 3,DESK T R A N S I T T I M E S ( M I N . ) (=WAIT. £.SERVICE TIME.) 190 191 * 192 GRAPH 193 GRAPH TP ,TAB3 1 9 4 . O R I G I N . 5 0 , 1 0 1 9 5 X , , 1 4 , 1 , 1 , 8 196 Y 0 , 3 , 2 0 , 2 197 ! S 1 A I t M bN r 4, I , * 198 100 STATEMENT 5 2 t 1 9 f T R A N S I T TIME ( M I N . ) 1 9 9 1.0 STATEMENT 55 , 6 0 , F I G U R E 3 : R E L . FREQUENCY OF TRANST TIMES AT INF1 2 0 0 ORMATION DESK 2 0 1 ENDGRAPH 2 02 •V 2 0 3 T AB T I T L E E J E C T 4,NUMBER OF JOBS WAITING FOR S E R V I C E AT DESK 2 0 4 2 0 5 rf. 2 0 6 * GRAPH 2 0 7 GRAPH T P , T A B 4 2 08 O R I G I N . 5 0 , 1 0 2 0 9 X » 2f 1 3 , 0, 1,8 2 1 0 Y 0 , 3 , 2 0 , 2 2 1 1 7 STATEMENT 4,1 ,% 2 1 2 100 STATEMENT 52,13»JOBS I N QUEUE 2 1 3 10 . STATEMENT 55 , 7 2 , F I G U R E 4: R E L . FREQUENCY OF J O B S WAITING FOR S E I 2 1 4 R V I C E AT I N F O R M A T I O N DESK 2 1 5 ENDGRAPH 2 1 6 •X-'r 2 1 7 STO T I T L E 30,THE S H E L V E S AS STORAGE 2 1 8 S P A C E 3 2 1 9 TAB T I TLE E J E C T 5 , S H E L F I N T E R A R R I V A L TIMES ( M I N . ) 2 2 0 221 2 2 2 * GRAPH 2 2 3 GRAPH TP , TAB 5 2 2 4 O R I G I N 5 0 , 1 0 2 2 5 X , 2 , 1 8 , 1 , 1 , 6 . 2 2 6 Y 0 , 4 , 2 0 , 2 2 2 7 • 7 S I A T E M b N T 4, I , * 228 100 STATEMENT 5 2 » 2 4 » I N T E R A R R I V A L T I M E ( M I N . ) 2 2 9 GPSS/360/MTS VERSION ( 4 / 8 / 1 3 ) A ^ 10 TAB STATEMENT ENDGRAPH T I T L E 55,46,FIGURE 5: REL. FREQUENCY OF INTERARRIVAL TIMES 6,NUMBER OF A R R I V A L S TO SHELVES/10 MIN. 2 3 0 2 3 1 232 2 3 3 EJECT * GRAPH GRAPH T P,T AB6 2 3 4 2 3 5 2 3 6 O R I G I N X Y 5 0 , 1 0 , 2 , 4 , 0 , 1,20 0,1,20,2 2 3 7 238 2 3 9 7 100 10 STATEMENT STATEMENT STATEMENT' 4,1,56 52 » 2 0» ARR I VAL RATE/10 MIN-.. 55 ,62,FIGURE 6: R E L . FREQUENCY OF A R R I V A L S TO SHE LVE SI 240 241 2 42 DURING 10 MIN. ENDGRAPH 243 2 4 4 2 4 5 TAB T I T L E EJECT 7,SHELF TRANSIT TIMES (MIN. 246 247 248 * GRAPH GRAPH O R I G I N TP,TAB7 5 0 , 1 0 249 2 50 251 7 X Y STA TE ME NT , ,5• 1, 1, 15 0,1,24,2 4,1 ,56 • 252 2 53 2 5 4 100 10 ELVES STATEMENT STATEMENT •52,19,TRANSIT TIME (MIN.) 55 ,52 , FIGURE .7: REL . FREQUENCY OF TRANSIT TIMES AT SHI 255 2 5 6 2 57 TAB ENDGRAPH TI TLE 8,OCCUPANCY OF SHELVES 258 2 5 9 260 EJECT * GRAPH 261 262 2 63 GRAPH O R I G I N X TH,TAB8 5 0 , 1 0 , 2 J 6 , 0 , 1 , 1 5 26 4 265 266 7 100 Y STATEMENT STATEMENT 0,1,24,2 4,1,56 52,9.OCCUPANCY 267 268 269 10 PYING STATEMENT 55,79,FIGURE 8: REL. FREQUENCY OF NUMBER OF JOBS 0CCU1 SIMULTANEOUSLY THE SHELVES ENDGRAPH 2 70 271 272 ~i, -r STO RAGE T I T L E 11,THE RECORDINGS COLLECTION (=DESK _ SHELVES) AS ST01 273 2 7 4 275 SPACE TAB T I T L E SHELVE S) 3 9,TRANSIT TIMES THROUGH REC. COLL. (MIN.) , i-DESK _ 1 276 2 7 7 278 EJECT * GRAPH 279 280 281 GRAPH O R I G I N TP ,T AB9 5 0 , 1 0 2 82 283 GPSS/3 60/MTS • V E R S I O N { 4 / 8 / 1 3 1 . • A ^ 7 ' 100 X Y STATEMENT STATEMENT , , 7 , 1 , 1 , 1 5 0, 1, 4 5 , 1 - • 4 , 1 , <g •52»1.9, T R A N S I T TIME ( M I N . ) • 2 8 4 2 8 5 2 86 2 8 7 / 10 GH t H E STATEMENT R E C O R D I N G S ENDGRAPH 5 5 , 7 5 , F I G U R E 9: R E L . FREQUENCY OF TRANS I t T I M E S THR0U1 C O L L E C T I O N 2 8 8 2 8 9 2 9 0 \ TAB T I TL E E J E C T 10,OCCUPANCY OF RECORD, C O L L E C T . (=DESK _ S H E L V E S ) 2 9 1 . 2 9 2 . 2 9 3 * GRAPH GRAPH T P , T A B 1 0 2 9 4 2 9 5 ' 2 9 6 O R I G I N . X Y 5 0 , 1 0 , 2 , 4 , 0 , 1 , 2 0 0 , 1 , 1 5 , 3 . ; 2 9 7 2 9 8 2 99 7 •100 10 STATEMENT STATEMENT STATEMENT 4,1 ,% 5 2 , 9, OCCUPANCY 55 ,85,.FIGURE 1 0 : REL . FREQUENCY. OF NUMBER OF J 0 8 S . 0 C C 1 3 0 0 3 0 1 3 0 2 U P Y I N G S I M U L T A N E O U S L Y DESK. AND S H E L V E S ENDGRAPH ' : . • -• 3 0 3 3 0 4 3 0 5 S TO TAB T I T L E S P A C E T I T L E 4 0 , THE LISTENING.-R-UUM-AS STORAGE • - 3 '•'. ."• • ' '• ,' .11 , L I S T E N I N G RCOM' I N T E R A R R I V A L T I M E S ( M I N . ) 3 0 6 30,7 3 0 8 * GR AP E J E C T H 3 0 9 3 1 0 3 1 1 GRAPH O R I G I N . X TP, I A B U 5 0 , 1 0 , , 7 , 1 , 1 , 1 5 - 3 1 2 3 13 3 1 4 7 1 0 0 Y STATEMENT STATEMENT 0, 4 , 1 5 , 3 4 , 1 , % 52 » 25».INTERARRIVAL ' TIME ( M I N . ) ' 3 1 5 3 1 6 3 1 7 10. STATEMENT 5 5 , 6 4 , F I G U R E 1 1 : REL .. FREQUENCY OF I N1ERARRI VAL T I M E S l " . .TO LI S T E N I N G ROOM • ' ' • • • " . ENDGRAPH 31 8 319 3 2 0 *: .TAB T I T L E E J E C T 12,NUMBER OF A R R I V A L S TO . L I S T . ROOM/10 MIN 3 2 1 32 2 3 2 3 •*>* . * GRAPH • ' GRAPH T P , TAB. 12, ' . - 3 2 4 3 2 5 3 2 6 O R I G I N X- Y 50 ,10 . , 2 , 6 , 0 , 1 , 1 5 0, 1,24,2 . 32 7 3 2 8 3 2 9 i 1 0 0 10 S1ATbtobNT STATEMENT STATEMENT 4, 1,;56 . 52 ,.2 0» A R R I V A L RATE/ 10 M I N . 5 5 , 7 0 , F I G U R E 1 2 : R E L . FREQUENCY ..OF A R R I V A L S TO L ISTEN1 330 331 3 3 2 , . ING ROOM DUR ING 10 ' ENDGRAPH •A. M I N . - • 3 3 3 3 3 4 3 3 5 TAB T I T L E E J E C T 1 3 , L I S T . ROOM S E R V I C E TIMES. (MIN.}. 3 3 6 3 3 7 J GRAPH GRAPH O R I G I N TP ,TAB13 5 0 , 10 3 3 8 3 3 9 3 4 0 3 4 1 X , , 3 , 5 , 1 , 3 0 3 4 2 Y 0 , 1 , 1 5 , 3 3 4 3 7 STATEMENT 4, 1, % 3 4 4 1 0 0 STATEMENT 5 2 , 1 9 , T R A N S IT T I M E (MIN.) 3 4 5 10 STATEMENT 55 , 5 8 , F I G U R E 1 3 : R E L . FREQUENCY OF TRANS IT T I M E OF L 1 1 .346 S T E N I N G ROOM • ' 3 4 7 ENDGRAPH. • 3 4 8 - » . . T 3 4 9 • T A B T I T L E • 14, OCCUPANCY OF L I S T . ROOM 3 50 E J E C T 351 3 5 2 - * GRAPH 3 53 GRAPH T P , T A B 1 4 . 3 54 O R I G I N :. 5 0 , 10 3 5 5 X , 2 , 4 , 6 , 1 , 1 8 3 5 6 Y 0 , 1 , 1 6 , 3 3 5 7 7 STATEMENT 4,1*3, 3 58 100 STATEMENT 52 , 9 , O C C U P A N C Y 3 5 9 10 STATEMENT. 5 5 , 8 7 , F I G U R E 1 4 : R E L . FREQUENCY OF NUMBER UF JOBS U C C l 3 6 0 •.UPYJNG S I M U L T A N E O U S L Y THE L I S T E N I N G ROOM .361 ENDGRAPH- 362 * 3 6 3 STO T I T L E . S P A C E • 41 , THE. R E S E R V . L I S T E N I N G ROOM.AS STORAGE' 3 . 3 6 4 3 6 5 . • TAB T I T L E E J E C T 17,OCCUPANCY OF RESERVE L I S T . ROOM 3 6 6 3 6 7 . 3 6 8 * GRAPH 3 6 9 GRAPH T P , T A 6 1 7 3 7 0 O R I G I N 50,10. . : 3 7 1 x • • • , 2 , 6 , 0 , 1,1 5 3 7 2 Y . 0 , 1 , 2 4 , 2 . 3 7 3 7 ' STATEMENT 4,1 ,% 3 74 100 STATEMENT 52 , 9 , OCCUPANCY ' .; ' ..• 3 7 5 10 STATEMENT. 5 5 , 9 6 , F T C U R E 1 4 A : R E L . F R E Q U E N C Y OF NUMBER OF-JOBS 0C1 '• ! - - 3 7 6 ; C O P Y I N G S I M U L T A N E O U S L Y THE L I S T E N I N G ROOM 3 7 7 ENDGRAPH 3 7 8 •if 3 7 9 STO T I TLE 1 0 , T H E S Y S T E M AS STORAGE - 3 8 0 SPACE 3 3 8 1 TAB T I T L E 1 5 , S Y S T E M T R A N S I T TIMES'(MIN..) ( - S E R V I C E 5, WAIT. TIME 1 3 8 2 ) 3 83 t J t CT 3 8 4 •A- 3 85 * GRAPH 38 6 GRAPH TP,TAB 15 . 3 8 7 O R I G I N 5 0 , 1 0 3 8 8 X , ,11 ,0,1 ,9 3 8 9 Y 0 , 2 , 1 5 , 3 3 9 0 7 STATEMENT 4, 1, * . 3 9 1 G P 5 S / 3 6 0 / M T S V E R S I O N ( 4 / 8 / 1 3 ) A >| 1 0 0 •• 1 0 E S S T A T E M E N T S T A T E M E N T E N D G R A P H 5 2 , 1 9 , T R A N S I T T I M E ( M I N . ) 5 5 , 4 9 , F I G U R E 1 5 : R E L . F R E Q U E N C Y O F S Y S T E M T R A N S I T T I M 1 3 9 2 3 9 3 3 9 4 3 9 5 / n' T A B . ' : T I T L E E J E C T 1 6 , O C C U P A N C Y O F S Y S T E M ( = D E S K , S H E L V E S , L I S T . R O O M ) 3 9 6 3 9 7 3 9 8 1- *• G R A P H G R A P H T P , T A B 1 6 • . •' • : ' * • . '. ' • . ' ' 3 9 9 4 0 0 4 0 1 O R I G I N X Y 5 0 , 1 0 ' . , 2 , 4 , 2 , 2 , 2 0 " ' . • " .' 0 , 2 , 2 0 , 2 . 4 0 2 4 0 3 4 0 4 7 1 0 0 1 0 S T A T E M E N T S T A T E M E N T S T A T E M E N T 4 , 1 , % ' 5 2 » 9 , O C C U P A N C Y 5 5 , 7 9 , ' F I G U R E 1 6 : . R E L . F R E Q U E N C Y O F N U M B E R O F J O B S 0 C C 1 4 0 5 4 0 6 4 0 7 U P Y I N G S I M U L 1 A N E O U S L Y - T H E S Y S T E M E N D G R A P H 4 0 8 4 0 9 4 1 0 E N D 4 1 1 BLOCK NUMBER SYMBOL R E F E R E N C E S BY CARD NUMBER 75 BEI DE 128 133 83 E XI T 91 9 3 94 95 113 115 116 117 136 139 140 87 F I N E 88 110 137 59 G E H 1 0 117 78 GEH11 135 81 GEH13 138 82 GEH14 1 4 0 33 GEH2.' 89 35 GEH3 90 36 GEH4 92 37 GEH5 95, • • • 55 . Gbh7 111 57 GEH8 1 12 58 GEH 9 114 70 OF LOW 120 22 ONE 78 14 R E S 2 72 7 9 8 S E R 1 80 20 SER12 77 13 SER 2 66 4 STG2 62 115 118 136 141 38 STG3 62 9 3 96 139 141 60 STG4 94 96 116 118 18 TWO 71 SI : ' • • •' . • T A B L E SYMBOLS AND CORRESPONDING NUMBERS 1 TAB1 10 TAB 10 11 T A B U 12 T A B 1 2 13 TAB 13 14 . TAB 14 15 TAB 15 16 . TAB 16 17 TAB 17 2 TAB2 ' 3 TAB 3 4 T A B 4 •5 TABS • 6 TAB6 . 7 TAB 7 8 T A B 8 9 TAB 9 F U N C T I O N SYMBOLS AND CORRESPONDING NUMBERS 1 A R R I V 2 DESK _4 L I S T 3 S H E L F * FUNCTION D E F I N I T I O N S . A . * SYSTEM A R R I V A L TIME E X P O N E N T I A L L Y D I S T R I B U T E D 1 F U N C T I O N K N I L 2 4 0.0 0 .0 . 1 . 104 .2 .222 '• . 3 ' . 3 5 5 .4 .5 09 .5 .69 .6 . 9 1 5 .7 1.2 . 75 1.38 . 8 1 .6 .84 1.83 .88 2.12 .9 2.3 . 92 2.52 .94 2.81 .95 2 .99 .96 3.2 .97 3.5 . 98 3.9 .99 4.6 .99 5 5.3 . 99 8 6.2 . 9 9 9 7. 0 . 9 9 9 7 8.0 * * DESK S E R V I C E T I M E EXPONENT I A L L Y . D l S T R I B U T ED 2 F U N C T I O N R N l C 2 4 0.0 0 .0 . 1 -.104 -.2 .222 .3 . 3 5 5 .4 .5 09 .5 .69 . . . .6 . 9 1 5 .7 1.2 .75 1.38 . 8 1.6 . .84 1 .83 .88 2.12 .9 '2.3 . 92 2.5 2 .94 2.81 ' • • ' . .95 2.99 .96 3.2 . 97 3. 5 .98 3 .9 • 99 4.6 .99 b 5.3 . 9 9 8 * 6.2. . 9 9 9 7.0 . 9 9 9 7 8.0 * SHELF S E R V I C E TIME E X P O N E N T I A L L Y D I S T R I B U T E D - 3 F U N C T I O N R N l - C 2 3 0.0 0.0 .154 .840 .28 1 .25 0 . . 3 9 0 . 4 2 0 . 4 8 3 . 5 8 0 .562 .7 50 .629 .92 . 6 8 5 1.08 .73 3 1.25 . 7 7 4 1 .42 .808 1 .59 . 837 1.75 . 8 6 2 1.92 . 8 83 2. 0 8 .9 2.25 . 9 1 6 2 .42 .927 2 . 5 8 . 9 3 7 2.75 .94 6 2 .92 .953 3.08 .959 3.25 .964 " A " 3.42 1 . 0 5. 27 •V * L I S T E N I N G • R O O M S E R V I C E T I M E G E N E R A L L Y D I S T R I B U T E D 4 F U N C T I O N . R N l C2 5 0.0. 0.0 .0 24 .063 .071 .18 7 . 131 • . . 3 1 2 . 2 0 5 .43 7 .289 .563 .366 . 6 9 0 .4 36 . 8 2 0 .49 8 . 9 4 0 . 5 5 6 1 .06 .623 1.18 . 6 9 9 1-31 . 754 1.44. . 786 1 .56 .814 1.6 9 .836 1 .81 . 8 5 5 1.94 . 8 7 2 2.06 . 8 8 8 2. 1 8 .903 2 . 3 1 .917 2.44 .927 2.55 . 9 6 2 3 . 1 9 . 9 8 9 . 4.20 1 .00 Ar 4 . 8 2 0 *• STORAGE D E F I N I T I O N S 10 STORAGE 200 11 STORAGE 150 3 0 STORAGE 1 0 0 4 0 STORAGE 23 41 STORAGE 23 * T A B L E D E F I N I T I O N S 1 T A B L E IA 1 1 20 2 TABLE R T : 0 1 30 10 3- T A B L E M l 1 1 30 J 4 QTABLE 2 0 1 30 \ 5 TABL E IA 1 1 30 6 T A B L E RT 0 1 20 10 7 TA B L E M l 1 1 60 8 T A B L E •• S3 0 0 1 40 • 9 T A B L E Ml 1 1 60 / , 10 TABLE S l l 0 1 60 \ 11 T A B L E IA 1 1 30 12 T A B L E RT 0 1 15 10 13 T A B L E . M l 0 5 60 14 T A B L E S 4 0 0 1. 26 1 5 TA B L E M l 0 2 80 16 T A B L E S 1 0 0 2 60 17 T A B L E S 4 1 0 1 26 * GPSS & PROGRAM . 1 G E NERATE 1 FN1 • 2 EN 1 ER 10 3 T R A N S F E R .360 38 4 4 MARK 5 ENTER 11 6 QUEUE 2 7 GATE NU • 1 13 8 S E I Z E 1 9 DEPART 2 10 ADVANCE 1 FN2 - 1 1 R E L E A S E 1 12 TRANSFER 18 .13' L I N K 2 F I F O 14 14 S E I Z E 2 15 DEPART 2 16 ADVANCE 1 . FN2 17 R E L E A S E 2 18 U N L I N K 2 2 0 1 19 T R A N S F E R 2.2 20 GATE NU 1 1-4 - 21 TRANSFER 8 22 T A B U L A T E 1 23 T A B U L A T E 2 24 T A B U L A T E 3 25 L E A V E 11 26 T A B U L A T E . g 27 T A B U L A T E 10 28 A S S I G N 2 K l 2 9 TEST LE C l K 3 6 0 0 87 30 T E S T E P3 K l 33 3 1 TEST E P4 K l 3 5 32 T R A N S F E R 83 33 T E S T E P 4 K l 36 3 4 T R A N S F E R .750 3 8 83 35 T R A N S F E R . . 9 6 0 6 0 83 36 TRANSFER . 7 3 0 37 83 37 T R A N S F E R .110 38 60 3 8 MARK 39 .ENTER 11 4 0 ENTER 30 41 ADVANCE 6 FN 3 42 L E A V E 30 4 3 T A B U L A T E 5 . J 4 4 T A B U L A T E 6 4 5 T A B U L A T E 7 4 6 T A BULATE 8 4 7 L E A V E 11 48 T A B U L A T E 9 4 9 T A B U L A T E 10 J 50 A S S I G N 3 K l 51 TEST LE C l K 3 6 0 0 87 , ' 52 TEST E P2 K l 55 53 TEST E P4 K l 57 54 TRANSFER 83 • 55 TEST E P 4 K l 58 • • 56 T R A N S F E R .280 4 83 57 TRANSFER . 2 2 0 6 0 83 58 TRANSFER .1 4 0 59 83 59 ; TRANSFER .580 4 60 ' 6 0 MARK 61 GATE SN F 40 70 62 ENTER 40 6 3 ADVANCE 40 F N 4 64 L E A V E 40 6 5 T A B ULATE 11 66 TABULATE • 12 6 7 T A B U L A T E 13 • . 68 T A B U L A T E 14 69 TRANSFER 75 7 0 ENTER 41 71 ADVANCE 4 0 FN4 72 L E A V E 41 73 T A B U L A T E ' 17 74 TRANSFER 75 7 5 A S S I G N 4 K l 76 TEST E P3 K l 7 8 7 7 T R A N S F E R . 0 9 0 4 83 78 T E S T L E C l K 3 6 0 C 87 7 9 TEST E P2 K l 81 80 • TRANSFER .380- 3 8 83 8 1 . TRANSFER . 0 8 0 82 83 8 2 TRANS FER .140 4 38 83 L E A V E 10 84 T A B U L A T E 15 85 T A B U L A T E 16 86 TERMINATE 8 7 . L E A V E TO •8 8 T A B U L A T E 15 89 T A B U L A T E 16 9 0 T E R M I N A T E 1 * CONTROL CARD s iAkr r S T A T I S T I C S CONCERNING THE I N F O R M A T I O N D E S K , S E R V . 1 F A C I L I T Y AVERAGE NUMBER AVERAGE S E I Z I N G P R E E M P T I N G U T I L I Z A T I O N E N T R I E S T I M E / T R A N T R A N S . NO. TRANS. NO. 1 .557 3 3 7 9 . 5 9 3 69 S T A T I S T I C S CONCERNING THE INFORMATION D E S K , S E R V . 2 F A C I L ITY AVERAGE NUMBER ; , AVERAGE S E I Z I N G P R E E M P T I N G U T I L I Z A T I O N 2 . 3 8 5 E N T R I E S T I M E / T R A N 2 4 3 9 . 5 6 9 TRANS . NO. TRANS- NO . S T A T I S T I C S CONCERNING THE DESK QUEUE QUEUE MAXIMUM AVERAGE CONTENTS CONTENTS TOTAL ZERO E N T R I E S ' . E N T R I E S PERCENT ZEROS AVERAGE TIME/TRANS $AVERAGE TABLE TIME/TRANS NUMBER CURRENT CONTENTS 2 20 .777 $AVERAGE T I M E / T R A N S = AVERAGE 5 8 1 8 4537. T I M E / T R A N S EX C LU DI NG Z ERO 77. 9 E N T R I E S .481 2 . 1 8 6 4 S T A T I S T I C S CONCERNING THE DESK USER C H A I N .. USER C H A I N TOTAL E N T R I E S AVERAGE CURRENT TIME/TRANS . CONTENTS AVERAGE CONTENTS MAXIMUM CONTENTS 2 T T 6 8 : 1.176 : : : . 5 7 7 IE DESK I N T E R A R R I V A L T I M E S ( M I N . ) T A B L E TAB 1 . E N T R I E S IN T A B L E 5 8 1 6 MEAN ARGUMENT .618 STANDARD D E V I A T I O N .808 SUM OF ARGUMENTS 3 5 9 8 . 0 0 0 NON-WEIGHTED UPPER OBSERVED PER CENT C U M U L A T I V E CUMULATIVE M U L T I P L E D E V I A T I O N L I M I T ' FREQUENCY OF TOTAL PERCENTAGE • REMAINDER OF MEAN FROM MEAN 1 5 1 2 9 8 8 . 1 8 88 .1 11.8 1.616 . 4 7 1 2 528 9 .07 9 7 . 2 2.7 3 . 2 3 2 1.708 3 111 1 .90 9 9 . 1 .8 4 . 8 4 9 2. 9 4 5 4 37 .63 9 9 . 8 .1 6 . 4 6 5 .4. 1 8 3 . 5 8 . 13 9 9 . 9 .0 8 . 0 8 2 5 . 4 2 0 6 2 .03 9 9 . 9 .0 9.698 6. 6 5 7 7 1 • 01 ' 1 0 0 . 0 .0 1 1 . 3 1 5 7 . 8 9 4 R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO 80 * •  00 A- Ar A - 1" -V- •»_• 7 6 * * * _ 7 2 * * * . i . A - Ar - A « 4r . _ . — 6 0 ^ , * ^ ̂ A - A * A - *v* or--v 56 * : ~ ~ ~ * ft ft 52 * A- -x- .. 4 3 ft , .ftft ** Ar A , •V -v> A. A. - V A - -A-. - I - 1* 4 4 * 4 0 * A- 3 6 * • Ar . , _____ _ A. 2 8 ,*. A- 2 4 ft A- 20 * Ar 1 6 » A. I" 12 . * ' • Ar '* ^ sic sic 4 A. • „ Ar Ar Ar ' . • 'f • • y * f *J" -V * A. Ar _t Ar .. -*"]*•-_• i r *v O Ar X ^- J V .V A A A A A - A _ -Ar Ar A. A. Ar -Ar v'r -A- Ar A* A- A- A-A- A* Ar Ar Ar Ar A- A- AJ- Ar _» Ar Ar Ar Ar Ar A« Ar A» Ar A» Ar Ar _U -A> -Ar A Ar A* Ar Ar Jr Ar Ar A- A» Ar Ar Ar A* Ar A Ar Ar Ar Ar -Ar Ar __• Ar Ar A» __• A * -A. -Lr A -A. A* A» "X- A r A A_ A* -A» Ar Ar A r •__• -A" A-A - ( r A * A * A » A_ A_ __• Ar <>_  A r A A r -J_ A - A r A j __" ifr Ay _r jfe j _ 2 ; ' 3 ' '•. 4- 5 6 7 8 _ - ~ ~ : I N T E R A R R I V A L TIME ( M I N . ) *i_• Ar Ar Ar F I G U R E l : R E L . FREQUENCY OF I N T E R A R R I V A L T I M E S NUMBER OF A R R I V A L S TO D E S K / 1 0 M I N . T A B L E TAB2 • E N T R I E S I N T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS J 360 16 . l t o 5 . 0 8 9 5 8 1 6 . 0 0 0 NON-WEIGHTfcO \ UPPER OBSERVED PER CENT CUMULAT IVE CUMULATIVE M U L T I P L E DEVI A T I ON L I M I T 0 1 FREQUENCY 0 0 OF TOTAL .00 .00 PERCENTAGE . 0 .0 REMAINDER 1 0 0 . 0 1 0 0 . 0 OF MEAN - . 0 0 0 . 0 6 1 FROM MEAN -3 .1 74 - 2 . 9 7 7 2 3 4 0 0 0 .00 .00 .00 .0 .0 .0 1 0 0 .0 100.0 1 0 0 . 0 . 1 2 3 . 1 8 5 • 2 4 7 - 2 . 7 8 1 - 2 . 5 8 4 - 2 . 3 8 8 5 6 7 1 4 5 . 2 7 1.11 1.38 .2 . 1.3 2.7 9 9 . 7 9 8 . 6 9 7 . 2 . .309 . 3 7 1 .433 - 2 . 1 9 1 - 1 . 9 9 5 - 1.798 8 9 10 12 10 11 3 . 3 3 2 .7.7 3.05 6. 1 8.8 1 1 . 9 9 3 . 8 9 1 . 1 88 .0 .495 . 5 5 7 .618 - 1 . 6 0 2 - 1 . 4 0 5 - 1 . 2 0 9 11 12 13 20 23 34 . 5.55 .'" 6.3-8 9.44 17. 4 .23.8 3 3 . 3 8 2 . 5 7 6 . 1 6 6 . 6 .680' . 7 4 2 . 8 0 4 - 1 . 0 1 2 . - . 8 1 6 - . 6 1 9 14 15 16 27 25 25 7.49 • 6 . 9 4 . 6.94 4 0 . 8 47 .7 5 4 . 7 5 9 . 1 5 2 . 2 4 5 . 2 . 8 6 6 • 92 8 .990 - . 4 2 3 - . 2 2 7 -.0 30 17 18 19 33 2 0 18 9.16 5.55' . . 4 . 9 9 6 3 . 8 6 9 . 4 7 4 . 4 3 6 . 1 30 .5 2 5.5 1.05 2 1.114 1.176 . 1 6 5 .362 .558 20 21 22 21 15 15 5 . 8 3 ' '. 4. 16 4.1 6 8 0 . 2 8 4 . 4 8 8 . 6 19.7 15 .5 1 1 . 3 1. 23 / 1.299 1 . 3 6 1 . 7 5 5 . 9 5 1 1.148 23 24 25 10 13 5 2.77 3 . 6 1 1.38 91 .3 9 4 . 9 9 6 . 3 8 .6 5 .0 3.6 1 . 4 2 3 1 .485 1. 54 7 1. 3 4 4 1.541 1 .737 26 27 28 5 3 1 1.3 8 . 8 3 • .27 9 7 .7 9 8 . 6 9 8 . 8 2.2 1.3 1.1 1 . 6 0 9 1 .671 1. 7 3 3 1.9 34 2.130 2 . 3 2 7 OVERFLOW AVERAGE V A L U E 4 OF OVERFLOW 1.11 3 2 . 7 5 1 0 0 . 0 . .0 J * * . _ 21 * 2.0 * * 19 * 18 * 1 6 * 15 * I T T • * 13 * * . 12 * . ' * 11. * •. * 10 * g- * ' ' • * * ' * * * • . ** ** 8 *. : — ~ ~ : ~- : ~~" : ; • ** : ~ww * r * * • . . . . . . . * * 7 * . ' ** ** / ** '* ** ** ** 6 .* . ' • ** ** . * * * * ** ** '** ** ** *'* ** ** b * • . * ** ** ** ** ** '**• ** ** ** ** ** ** ** ** ** ** ** ** ** 4 '** ** ** . ** ** ** ** ** ** ** ** ** • * ** *'* ' ** ** ** .** ** ** ** ** ** " 3 * * * ' ** ** ** ** **' ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** 2 * . ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** * ** ** ** ** ** .** ** ** ** ** ** ** ** ** ** ** " 1 ** ** ** ** ** ** **' ** ** ** ** • ** ** ** ** ** ** •** ** ** * ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** *# ** ** ** o ********************************* 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2 3 2 4 25 2 6 27 28 2 9 " ' : : : : • - . 7 A R R I V A L R A T E / 1 0 M I N . F I G U R E 2: R E L . FREQUENCY OF A R R I V A L S TO I N F . DESK DURING -10 MIN. DESK T R A N S I T T I M E S ( M I N . ) , ( = WAIT . S SERV I C E T I M E ) TABLE. T A'B'3 .". E N T R I E S I N T A B L E MEAN ARGUMENT . .STANDARD D E V I A T I O N >' . SUM OF ARGUMENTS ) 5 8 1 / 1 . U6i> . l . b f O 6 1 9 6 . 0 0 0 NUN-WEIGH IbU • UPPER OBSERVED PER CENT CUMUL A T I V E CUMULATIVE M U L T I P L E D E V I A T I O N , L I M I T FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN • . 1 4 3 3 8 74. 5 7 7 4 . 5. 2 5 . 4 . .938 - . 0 4 1 ... . ; 2 7 0 8 1 2 . 1 7 8 6.7 13.2 1.877 .5 95 3 3 3 3 5 . 7 2 9 2 . 4 7 . 5 • 2.W16 1.232 4 19 3 3 . 3 1 .-: 9 5.7 •4.2 3 . 7 5 5 1.868 5 117 2 . 0 1 9 7 . 7 2.2 4 . 6 9 4 2 . 5 0 5 6 4 9 .84 ' 9 8 . 6 1 . 3 5 . 6 3 2 3 . 1 4 2 . 7 26 .44 9 9 . 0 .9 . 6.571 3 . 7 7 9 • • • , 8 1 8 .30 9 9 . 3 . 6 7 . 5 1 0 4 . 4 1 6 . . . 9 .16 . 2 7 • 9 9 . 6 .3 8 .449 ; 10 ". '' 6 • 10 9 9 . 7 .2 9.388 5.6 89 11 U .18 9 9 . 9 ' . 0 1 0 . 3 2 7 6 .326 12 •' • " 2 . 0 3 1 0 0 . 0 . 0 11 .265 6 . 9 6 3 REMAINING. F R E Q U E N C I E S ARE A L L ZERO T »U * •A. • T •J* 1 * ; y.. 60 kL-IT- af* 0 57 * - 4 . * f 5 4 J» -f si. -1* a . •V- 5 1 •J* - r **: 4 8 o , * 4 5 J , -c 42 • •A* 'V -J* 3 9 *v T j , •• 3 6 s»» - i - s>- •V * 3 3 A* •V A. f 30 •r •j~ 27 s>, * 1* »u -*/* 24 •V J , ŷ . ' 21 sfc, •V* ~v -V- 18 y, s»- sJv -V 15 - * r %** s«* •V 12 ' P J> •v 9 V -t- i - *** -a, -or si, K* •sir • s». 6 sV *»• * -sl, sV " V -A. •3 -Y* •** •V sA, *v J r S.V 0 y, s». * l - -J- -sV si. -J- •V- " V " V • • » -1""Y* si, '«* , 1 , si, sr. sr* sA- s>0 s»„ s4, s», s>, s*» -v* - i - --•«•• 'i- "t- *(• -v ' r -v -»* •*(* l " sis. • -X s ' , sI-sS- J, «V J, A J , J, T -v -r -v -v -*v - v *f * * * ^ •"_> " i " *r -V* -v* *v m* "t- ir- •*»"• •4- *JU S*» , **- T- -Y» - y -r- ^ - ' f - J - - f -y* - i - - J * *r f '-r- •*»» T f T ^ ^ V » ^ ^ <r -V* *»* ' A -"r- ' c - -v V - v* ^ - r * ^ - v ' • 1 2 3 : 4 5 6 7 8 T R A N S I T T I M E ( M I N . ) F I G U R E 3: R E L . FRE QUENCY OF• TRANST T I M E S AT INFORMATION DESK T A B L E TAB A E N T R I E S IN TABLE MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS 3 8 1 8 .481 1. 2 2 6 2 8 - I . O O u NON-WEIGHTED UPPER OBSERVED PER CENT CU M U L A T I V E CUMULAT IV E M U L T I P L E D E V I A T I O N L I M I T FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 4 53 7 77 .98 7 7 . 9 2 2 . 0 - . 0 0 0 - . 3 9 2 1 6 5 5 1 1 . 2 5 89.2 10 .7 2 .077 .42 2 2 2 6 6 4.5 7 9 3 . 8 6.1 4. 154 1 .238 3 134 2. 30 96 .1 3.8 6.2 3 1 2. 0 5 3 4 100 1.71 9 7 . 8 2.1 8 . 3 0 8 2 .868 5 56 .96 9 8 . 7 1.2 1 0 . 3 8 5 3 . 6 8 3 6 22 .37 99 .1 .8 1 2 . 4 6 2 4 . 4 9 9 7 16 .27 9 9 . 4 . 5 1 4 . 5 3 9 5 .314 8 12 .20 9 9 . 6 . 3 1 6 . 6 1 6 6. 129 9 12 .20 9 9 . 8 .1 1 8 . 6 9 4 6 . 9 4 5 10 4 .06 9 9 . 9 . 0 2 0 . 7 7 1 7 . 7 6 0 a 11 4 .06 1 0 0 . 0 .0 2 2 . 8 4 8 8. 5 7 5 R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO { A- V- * I V Ar . -_• • * 6 0 I f A r 00 A r A r . 57 V „_ "l™ -<* Ar Ar 1- -V* A. *¥* • A r A r ,54 Ay A r Ar Ar Ar 1' -V -r>r '1* A r -Ar A r . *¥- 4 8 * -*»' Ar A r -A- ftft • . 4 5 * A r A . A Ar A . 't- *r . 4 2 A r f rj - rJC wV-Ar •"*'*-*•*• 39. v Ar A. 36 A r •y A r '1C • A. Ar A r A * •V 1- A r A r • _ .33 K * A r _lr A . "V* r j - rJC ' 3 0 ft • -A- Ar • 2 7 ' A r -v -A- A r -*»' -V ' A, Ar " ' - . "1- *¥* 24 ft A r : x~C : :— :—7 . *** 21 A . t" A r A r •v -»* 18 A r * A r A r Ar ' Ar Ar '<"• -V- J . A -v -V-.15 -A- ft r , - -j< ft* . 1.2 A r Ar A r -1- *¥* A r A r - A r -I- I 4 A r " A_ - T-.-r 9 A r - f A- Jr A r A r •V •T* A r A r -Ar 1" 6 _—_ . -(* A r A r A r A r f A r Ar -Ar . A r A r -I* - ' ' 3 A r A r -Ar Ar- A r A r Ar • V f 0 A r f • . A r A r A - A r A r A - Ar Ar A. A r T " ! " "V- -r- -r ' j * ^ £ # ^ # # 3*: sj- .v A , £ ^ _Jc ̂  £ ;{c -Jr Ar • v **#- Ar A- Ar Ar Ar r p r,- r^ ̂ » ^ Ar Ar A r Ar ' 0 1 1 . 2 3 4 . 5 6 ' 7 JOBS I N QUEUE F I G U R E 4: R E L . FREQUENCY OF JOBS, W A I T I N G FOR S E R V I C E - AT INFORMATION DESK , GRAPH V J , 'f J % •JU 'f •Jr -v Jr • j , ' * * * . • • j , . " . ' *** •A. 80 *. J , 00 ' J , i j ; 76 1* v«, -r* -.V JV -V "»* 7 2 -e- JV J , *V >A--V •** 6 8 •** -J , X- -JU n> -o - j , j . 64 **r* * J * 6 0 J , -v * r J ~ •v* •A. '«* * r vt, a . •V* "V J , ' • -T 'r» 56 •- •••• ' 52 %v * r J > •V *«- -1' J , j . 4 8 V JV ->V sO T* j , •V *•*• A, JV •"•*" 1" A, J l , 1* I T 4-4 v>, 1" J - >'r •40 ' r •*•»* •*»*• 1* 36 v l , * - J v •V vV J , T> J , Jl, •r- '1* u. vt, •1* T> 3 2 Jr f JV j , J, •***• Jv J , 28 •*Y» J> T JV -<- «y 24 y - J , ' r J. j> 0* . V j , J, •v --v , u 2 0 16 •v JV -JV -v J . J , "I" JL, a . 12 * * JV . "T* Jr Jr • '<* -v -A, JV 'r* -v- j - j> • •» rf 8 * J . J , -Jr •Jr -Jr •Jr J , •JV J , 4 ' i» J . . -Y* '**• ")*• J f •*»*• i » • -V -V JV JV -T* '€* 0 J , -y -A. -a* »o ju y* A* J , - J ' y, J - »*£ Ji, Jv -vV. v l , V* JV J - JV -JV J . < ,,v 1 - T *V* •***. *V* *¥* 1* -"l* V 1 Jr -Jr vV J - J  ->» »V -V Jo- -V J . J . J - X J i , J , J , v l , J , J , ̂  -A, J , JV J , J , J), J , J i , JV -A* J - JV J ' jjjj* J l , J , Jyv , r ^v ̂ v ^ v ^s , r ,,v jfci rf, rf. Jp. JOv -ov rp. rf. rf. JCv ^ 'V' -T" ->" *V» • If* -^s 2 3 ******************************** 4 5 6 I N T E R A R R I V A L T I M E ( M I N . ) F I G U R E 5: REL.- FREQUENCY OF I N T E R A R R I V A L T I M E S > STORAGE C A P A C I T Y AVERAGE AVERAGE E N T R I E S AVERAGE CURRENT MAXIMUM CONTENTS . U T I L I Z A T I O N ' T l M E / T R A N CONTENTS CONTENTS 30 1 0 0 / .34 3 . 0 / 3 4 5 3 4 6 2 4 S S H E L F I N T E R A R R I V A L T IM.ES ( MI N . ) T A B L E TAB 5 E N T R I E S IN T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS 4 5 2 7 .794 • 9 7 4 3 5 9 8 . 0 0 0 NON-WEIGHTED ' UPPER OBSERVED PER CENT C U M U L A T I V E CUMULATIVE M U L T I P L E D E V I A T I O N L I M I T FREQUENCY OF.TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 1 3 8 1 5 8 4 . 2 7 , . • 8 4 . 2 1 5 . / 1.258 .21U 2 47 3 1 0 . 4 4 9 4 . 7 5.2 2 .516 1 .2 37 3 1 5 4 3 .40 9 8.1 1.8 3 . 7 7 4 2 . 2 6 3 4 52 1.14 9 9 . 2 .7 5 .032 3 . 2 9 0 5 16 .35 . 9 9 . 6 .3 6.290 4 . 3 1 6 - 6 8 .17 9 9 . 8 - .1 7. 5 4 9 5 . 3 4 3 ( 5 .. 1 1 9 9 . 9 .0 8 . 8 0 ( • 6.3C0 •8 2 .04 9 9 . 9 . .0 10. 0 6 5 7.3 96 9 1 .02 9 9 . 9 .0 1 1 . 3 2 3 8 . 4 2 3 10 0 .00 . 9 9 . 9 .0 1 2 . 5 8 1 9 .449 11 • 1 .02 1 0 0 . 0 .0 1 3 . 8 4 0 1 0 . 4 7 6 • R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO T A B L E TAB6 E N T R I E S ' I N T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS J 3 6 0 1 2 . 5 7 2 4 . 7 8 5 4 5 2 6 . U U U NON-WEIGHTED s UPPER OBSERVED PER CENT CUMULATIVE CUMULATIVE M U L T I P L E D E V I A T I O N L I M I T FREQUENCY OF TOTAL PERCENTAGE REMAINDER ' OF MEAN FROM MEAN 0 0 • .00 . 0 1 0 0 . 0 - . 0 0 0 - 2 . 6 2 7 1 0 .00 .0 1 0 0 . 0 . 0 7 9 - 2 . 4 1 8 2 0 . 00 .0 • 100 .0 .159 - 2 . 2 0 9 3 8 2.22 2.2 9 7 . 7 . 2 3 8 - 2 . 0 0 0 4 2 .55 2.7 9 7 . 2 . 3 1 8 - 1 . 7 9 1 5 9 2 . 4 9 5.2 9 4 . 7 .397 - 1 . 5 8 2 6 13 3 . 6 1 8.8 9 1 . 1 . 4 7 7 - 1 . 3 73 7 14 • 3.88 12 .7 8 7 . 2 . 5 5 6 - 1 . 1 6 4 . 8 20 5 . 5 5 1 3 . 3 UJ..6 .636 - . 9 5 5 9 . 37 1 0 . 2 7 2 8 . 6 7 1 . 3 . 7 1 5 - . 7 4 6 10 24 6.66 3 5.2 6 4 . 7 . 7 9 5 - . 5 3 7 11 27 7.49 4 2 . 7 57.2 .874 - . 3 2 8 12 3 5 9 .72 5 2.4 4 7 . 5 . 9 5 4 - . 1 1 9 13 22 6.11 " 5 8.6 41 .3 1.034 . 0 8 9 14 38 1 0 . 5 5 ' 6 9 . 1 3 0 . 8 1.113 . 2 9 8 15 31 8.61 7 7.7 2 2 . 2 1 . 1 9 3 . 5 0 7 16 18 4 . 9 9 8 2 . 7 17.2 1.272 .716 17 15 4. 16 8 6 . 9 13.0 1. 3 5 2 . 9 2 5 18 8 2.22 8 9 . 1 10.8 1.431 1 .134 OVERFLOW 39 1 0 . 8 3 1 0 0 . 0 . 0 AVERAGE VALUE OF OVERFLOW 2 1 . 8 7 % * * * ~ *~ 20 * ~ 19 * * 18 * 17 * 16 * 15 * * 14 * 13 * 12 * 11 * • 10 * ** -r- *r* ** * ** ** ** 9 * ** ** ** ** * ftft * * ** ** 8 * ** ft* ft* ** ** ft* ft* ** ft* ** 7 * ft* ** ft* * * ** ft* ** ** ** ** #* .6 * " ** ** *ft ** **. ** ** * ft* ** ** ftft ** ** ** ** • 5. * ft* ** . ** ** ft* ** ** ** * ** ftft * * * * ** ft* ** ** ** ** 4 ** ,** ** ft ft- ** ** ** ** ft* ** ** * ** ft* ft* ** **' ** ** ft* ** ** ** 3 * ft* ** ** ft* ** ** ** ft* ft* ft* ** ** ** * •** ft* ** ft* ftft ft* ft* ** ** ** ft* ** ** 2 * ft* ** ft* ft* ft* ** ft* ** ** ** ft* ** ** ** ** ** * ** ** ** ** ** ** ft* . ** ** ** ** ** ** ** ** ** 1 * ** ** ** * * * ft- ft* ft* ft* _v -_• ** ** ** ft* ** ft* ** ** ** ** ft* ft* ft* ft* <Ar A r ft* ft* ** ** ** ** 0 * * * * * * * * * * * * * * * * 4 * * * * * * * * * * * * * * * * * ****** ******** *************************** 0 1 2 3 4 . 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 A R R I V A L R A T E / 1 0 M I N . F I G U R E 6: R E L . FREQUENCY OF A R R I V A L S TO S H E L V E S DURING 10 M I N . S H E L F T R A N S I T T I M E S ( M I N ) T A B L E TAB7 E N T R I E S I N TABLE MEAN ARGU ME NT STANDARD D E V I A T I O N SUM OF ARGUMENTS 4 5 2 8 5 .8 33 b . 6 U i 2O415.0UU N U N - W b l G H I E U s UPPER 'OBSERVED PER CENT CUMULAT IV E CUMULATIVE M U L T I P L E D E V I A T I O N L I M I T FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 1 60 2 1 3 . 2 9 13.2 8 6 . 7 . 1 7 1 - . 8 6 2 2 7 6 5 1 6 . 89 3 0 . 1 6 9 . 8 . 3 4 2 - . 6 8 4 3 67 4 1 4 . 88 4 5 . 0 - 5 4 . 9 .514 - . 5 0 5 4 571 1 2 . 6 1 5 7 . 6 4 2 . 3 . 6 8 5 - . 3 2 7 5 3 0 4 6.71 6 4 . 3 3 5 .6 .857 - . 1 4 8 6 2 6 4 5.83 1 7 0 . 2 2 9 . 7 1 .02 8 .0 2 9 7 196 4 . 3 2 7 4 . 5 2 5.4 1. 199 . 2 0 8 8 192 4. 24 7 8 . 7 2 1 . 2 1.37 1 . 3 8 6 9 LZti 2.82 ' 8 1.6 18.3 1. 542 10 12 6 2.78 8 4 . 4 1 5 . 5 1.714 . 7 4 3 11 12 2 2. 69 8 7.1 12.8 1 . 8 8 5 .922 12 8 5 1.87 8 8 . 9 1 1 . 0 2. 0 5 7 1 . 1 0 0 13 64 1.41 9 0 . 3 9 .6 2 . 2 2 8 1.279 14 62 1.36 9 1 . 7 8.2 2 . 3 9 9 1.457 15 b6 1.2 3 9 2 . 9 / .0 2 . 5 / 1 1.6 36 16 50 1 . 10 9 4 . 1 5.8 2. 7 4 2 1 .814 17 43 .94 9 5 . 0 4.9 2 . 9 1 4 1.993 • 18 37 .81 9 5 . 8 4.1 3 . 0 8 5 2 . 1 7 1 .19 17 .37 9 6 . 2 3.7 3 . 2 5 6 2 . 3 5 0 20 13 .28 9 6 . 5 3.4 3.42 8 2 . 5 2 8 21 15 .33 9 6 . 8 3.1 3 .59 9 2 . 70"/ 22 22 .48 9 7 . 3 2.6 3 . 7 7 1 2 . 8 8 6 23 12 .26 9 7 . 6 2.3 3 . 9 4 2 3 . 0 6 4 24 18 .39 9 8 . 0 1.9 4 . 1 1 4 3 . 2 4 3 25 11 .24 9 8 . 2 . 1.7 4 . 2 8 5 3 . 4 2 1 26 16 .35 . 9-8.6 1 .3 4 . 4 5 6 3 . 6 0 0 2 7 12 • .26 - 9 8 . 8 1.1 4 . 6 2 b 3 . ( m 28 • 17 .37 99 .2 .7 4 . 7 9 9 3 . 9 5 7 29 8 .17 9 9 . 4 .5 4 . 9 7 1 4 . 1 3 5 3 0 18 .39 9 9 . 8 . 1 5. 142 4 . 3 1 4 31 8 .17 - 1 0 0 . 0 .0 5 . 3 1 3 4 . 4 9 2 R E M A I N I N G F R E Q U E N C I E S ARE ALL ZERO J % 22 * * 21 * * * 20 19 * * * 18 * * 17 16 . * * * ft • 15 * * ft * * 14 13 * * * * * * * * ft ft 12 * * ft * ft .. ft ft ' f t * ft . * ft ft . 1 1 10 ft * ft ft * * • ft * * ft ft * ft ft ft - g ft ft- ft * ft * .. ft * ft ft ft ft ft '*. • 8 7 ft ft- ft . ft * * - .ft * * ft * ft * * 6 ft ft ft ft ft * * ft ft- ft ft ft * ft ft- • * ft 5 ft ft ft * ft • ft ft • • * ft ft * .ft ft ft ft ft * , ft ft *- * * •Ar f '. 3 ft * ft * ft ft ft • * * ' ft * ft A' ft * ft ft * * * . ft ft ft ft •A- -{- 2 1 * ft ft ft ft ft ft * * ft ft ft ft ft ft ft . . ft * * * ft ft ft ft ft ft ft *' ft * * ft ft ft ft * ft ft * • 0 ft ft ft ft * * * * ftft ft ft ft ft ft ft * ft ft ft ft ft ftft ft ft ft ft 1 2 3 ft 4 ft 5 * 6 ft 7 * 8 ft ' 9 * 10 ft. 11 ft 12 ft ft ft *** * * * * * * * * * * * * * * * * 13 14 15 TRANSI T TI ME ( M I N . ) F I G U R E 7: R E L . FREQUENCY OF T R A N S I T T I M E S AT S H E L V E S J OCCUPANCY OF S H E L V E S T A B L E TAB8 E N T R I E S IN T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS ) 4 5 2 8 7.407 3 . 3 6 3 3 3 5 4 3 . 0 0 0 NON-WEIGH IfcD U PPER ' OBSERVED PER CENT CUMULATIVE CUMULATI VE M U L T I P L E D E V I A T I O N L I M I T F REQUENCY CF TOTAL • PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 9 . 19 ' .1 9 9 . 8 - . 0 0 0 - 2 . 2 0 2 1 7 0 1.54, 1.7 • 9 8 . 2 . 134 - 1 . 9 0 5 2 158 3 . 4 8 5.2 9 4 . 7 .269 -1 .607 3 278 6.13 1 1 . 3 88.6 .404 - 1 . 3 1 0 4 3 8 7 8 .54 1 9 . 9 8 0 . 0 . 5 3 9 - 1 . 0 1 3 5 4 7 3 10. 4 4 3 0 . 3 69.6 .674 - . 7 1 5 6 5 5 2 1 2 . 1 9 4 2 . 5 5 7 . 4 . 8 0 9 - . 4 1 8 7 5 3 6 1 1 . 8 3 5 4 . 3 4 5 . 6 . 9 4 4 - . 1 2 1 8 526 1 1 . 6 1 6 6 . 0 3 3 .9 1.079 .1 /6 9 4 3 1 9.51 7 5 . 5 2 4 . 4 1.214 .473 10 3 4 2 7.55 3 3 . 0 16.9 1.349 . 7 7 0 11 2 4 7 5.45 88.5 1 1 . 4 1 .484 1 .068 12 176 3 .88 9 2 . 4 7.5 1. 6 1 9 1.365 13 118 2 . 60 9 5 . 0 4.9 1.754 1.662 14 88 1 .94 9 6 . 9 3.0 i . 889 1 .960 15 58 1 .28 9 8.2 1.7 2 . 0 2 4 2 . 2 5 7 16 33 . 7 2 9 8.9 1 .0 2 . 1 5 9 2 . 5 5 4 17 17 .37 9 9 . 3 . 6 2 . 2 9 4 2 . 8 5 2 18 11 .24 9 9 . 6 .3 2 . 4 2 9 3 . 1 4 9 19 . 8 . 17 9 9 . 7 .2 2 . 5 6 4 3.446 2 0 6. .13 9 9 . 9 .0 2 . 6 9 9 3 . 743 21 2 . 04 9 9 . 9 .0 2. 8 3 4 4 . 0 4 1 22 1. . 02 9 9 . 9 .0 2 . 9 6 9 4 .338 23 1 .02 1 0 0 . 0 .0 . 3. 104 4.63 5 R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO 22 * 21 * * 2 0 ~ * ~ 1.9 * 18 * TT~*~ * 16 * 15 * 14 * * 13 * *~ 12 * ** * ** 11 * — : ww ~ww ww  : : * . . * * * * * * 10 * . * * ** ** * * *~ • ~** ' ; * * * * " * * • ~~ • " g * ** ** ** ** ** * . * * • * * ** * * ** — g - i r '• : ww 5 * - * * WW. WW—; WW : ; — * ** ** * * * * * * ** . • 7 * ** ** _ _ _ _ _ . . * * ~ * * * * * * r * * * * ~ — — — - - — . 6 * ** ** ** ** ** ** ** ** * ** . ** ** ** ** ** ** ** - 5—* ww ** ** ~ ww~ ** ww ww  ! ww ww ' * * * * * * * * * * * * * * * * * * * 4 * * * * * * * * * * * ' * * * * * * _ __ - — ** ** ** ' ** ~** ** ' 3 * ** *•* ** ** ** ** ** ** * * ** ** * ** ** ** ** ** ** ** ** ** ** ** —2~w ww w% wwr "~^W : ww~ ww WW ww ww ww ww ww * ** ** ** ** ** ** ** ** ** ** ** ** 1 * ** ** ** ** * * ** ** ** ** ** ** ** ** * * * ** ** ** **" ** "** ** ** ** ** ** ** ** * * ~ 0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 0 - 1 • 2 3 4 5 6 7 8_ 9 10 11 12 13 14 . . . OCCUPANCY : F I G U R E 8: R E L . FREQUENCY OF NUMBER OF JOBS OCCUPYING S I M U L T A N E O U S L Y THE S H E L V E S STORAGE C A P A C I T Y AVERAGE CONTENTS . AVERAGE E N T R I E S U T I L I Z A T I O N AVERAGE TIME/TRAN CURRENT CONTENTS MAXIMUM CONTENTS ) 11 1 5 0 9 . 0 64 .060 1 0 3 5 2 3. l b i / 34 T R A N S I T T I M E S THROUGH RE C . C O L L . I MIN . ) , {= DESK £ S H E L V E S ) T A B L E TAB9 E N T R I E S I N TABLE 10 34 5 MEAN ARGUMENT 3 . 1 5 2 STANDARD D E V I A T I O N 4 . 5 5 0 SUM OF ARGUMENTS 3 2 6 1 1 . 0 0 0 NON-WE IGHTED UPPER L I M I T OBSERVED FREQUENCY PER OF CENT TOTAL C U M U L A T I V E CUMULATIVE PERCENTAGE REMAINDER M U L T I P L E OF MEAN D E V I A T I O N FROM MEAN 1 2 .3 4 9 4 0 . 1 4 7 3 1 0 C 7 4/./5 1 4 . 2 3 9.73 4 /. / 6 1 . 9 7 1 . 7 52.2 3 8 . 0 2 8 . 2 .31 / . 6 3 4 .951 - . 4 ^ 2 -.2 53 - . 0 3 3 4 5 6 7 6 4 4 2 1 3 1 3 7.38 4.06 3.0 2. 7 9 . 1 8 3 . 1 8 6 . 2 2 0 . 8 16.8 1 3 . 7 1 . 2 6 8 1. 5 8 6 1.903 .186 . 4 0 6 .625 f 8 9 2 2 2 2 1 0 1 4 4 2 .14 2.02 1 .39 8 8.3 9 0 . 3 9 1 . 7 11.6 9.6 8.2 2 . 2 2 0 2 . 5 3 7 2. 8 5 5 . 84b 1.065 1.284 10 11 12 132 133 87 1.27 1.28 .84 9 3 . 0 9 4 . 3 9 5 . 1 6.9 5.6 4.8 3 . 1 7 2 3 .489 3 . 8 0 6 1.504 1.724 1.944 13 • 14 15' 6 4 6 2 5 6 .61 , .59 .54 9 5 . / 9 6 . 3 . 9 6 . 9 4 .2 3.6 3.0 4 . 1 2 3 4 . 4 4 1 4 . 7 5 8 2. 1 6 3 2 . 3 8 3 2 . 6 0 3 16 •17 18 • 50 4 3 37 . 4 8 .41 .35 9 7 . 4 9 7 . 8 9 8.1 2.5 2.1 1.8 5 . 0 7 5 5. 39 2 5 . 7 1 0 2 . 8 2 3 3 .042 3. 2 6 2 19 20 21 17 13 15 . 16 .12 .14 9 8.3 9 8 . 4 9 8 . 6 1 .6 1.5 1.3 6.02 / 6.344 6 . 6 6 1 3 .482 3 . 7 0 2 3 . 9 2 1 22 23 24 22 12 18 .21 .11 .17 9 8 . 8 9 8 . 9 9 9 . 1 1.1 1.0 .8 6.97 8 7 . 2 9 6 7 . 6 1 3 4 . 1 4 1 4 . 3 6 1 4 . 5 8 1 25 26 27 11 16 12 . 10 • 15 . 11 9 9 . 2 9 9 . 3 9 9 . 5 .7 .6 .4 / . 9 3 0 8 . 2 4 7 8 . 5 6 5 4 . 8 0 0 5 . 0 2 0 5 . 2 4 0 28 29 30 17 8 18 .16 .07 . 17 9 9 . 6 9 9 .7 9 9 . 9 .3 .2 .0 8. 8 8 2 9. 199 9.516 5 . 4 6 0 5 . 6 7 9 5 . 8 9 9 31 R E M A I N I N G F R E Q U E N C I E S ARE 8 A L L ZERO .0 / 1 0 0 . 0 .0 9. 8 3 3 6 . 1 1 9 • J % * 4 5 0 4 4 A r 1» 4 3 A r 'r* 42 A r 41 4 0 A . -T 39 A. 1 " 38 J , -V: Ar -1* • 3 7 36 I r 3 5 A r ***• 3 4 •V- • V 33 A . 1 " 32 * 't* 31 •V Ar 3 0 # 2 9 J . A r t " 28 J . •V -,_ 2 7 ' '(* A r " V 26 A r ' O 2 5 A r 2 4 23 A r •v 2 2 Ar T A r "V" 21 ft ' 20 - r A. 19 A * ^Ar • 18 ft 17 •A. Ar 16 A r 15 ft 14 A . A r •*>*• Ar 13 "<* Ar 12 A - -.̂  A r *v- 11 Ar Ar *v A r -v- 10 •A. A r •v A r 9 „ Ar '1- A r Ar 8 * A r A r 7 -A- A r -.*• A Ar "1* -V- * 6 Ar -V" A A l Ar 5 A . I - '1- A r A r A-*T* 4 A* •V Ar * f -V* • L J , **«•* * 3 -Ar *V "f A r Ar A r A r Ar T* 2 A T -A--» v A r A r -|> -_* Ar ' « * A r A r ft * 1 A - V A r A r A r Ar **» A r A r 'J- •¥* ft * ft ft * 0 A A r -A* A A r Ar -Ar ^r" "V* -** *V- 1 ' Ar J r A ->*•-." Ar Ar Ar A r Ar A r A r A r -J* < * -A J » * _ *?r *»* -\- 'i- --i- -*.* -v* -v -*»v •**» *v* *v* «,*• -*r* 'r* *•** *»- r k r_I A- A Ar A . A r A . *!C *|- r , - r , - r j * r ( A r A. Ar A> -A-r -A- Ar A . A, vO A r Ar « V >l 1" -V- "C f -v •*)*• *V -V -V * l * T I * _* 1 :********************** ************************************ 1 2 3 4 5 6 7 8 9 10 U 12 13 14 1 5 TRANS IT T I M E ( M I N . ) F I G U R E 9: R E L . FREQUENCY OF TRANS IT T I M E S THROUGH THE RECORDINGS C O L L E C T I O N OCCUPANCY OF RECORD. C O L L E C T . ( = DESK £ S H E L V E S ) T A B L E T A B I D E N T R I E S IN T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS ) 1 0 3 4 5 9. 402 4 . 7 0 7 9 7 2 6 7 . 0 0 0 NON-WEIGHTED UPPER OBSERVED PER CENT CU M U L A T I V E CUMULATI VE MULT I P L E D E V I A T I O N L I M I T 0 1 FREQUENCY 12 74 OF TOTAL . 11 .71 PERCENTAGE . 1 .8 REMAINDER 9 9 . 8 9 9 . 1 . OF MEAN - . 0 0 0 . 1 0 6 FROM MEAN -1 .997 - 1 . 7 8 5 2 3 4 2 1 9 4 1 1 5 5 0 2.11 3 . 9 7 5 . 3 1 . 2.9 ' 6. 9 1 2 . 2 9 7 . 0 9 3 . 0 8 7 . 7 .212 . 3 1 9 . 4 2 5 - 1.572 -1 .360 - 1 . 1 4 7 5 6 7 7 8 8 8 7 6 1 021 7.61 8.46 9.86 1 9 . 8 2 8 . 3 3 8.1 8 0.1 • 7 1 . 6 6 1 . 8 . 5 3 1 . 6 38 . 7 4 4 - . 9 3 5 - . 7 2 2 - . 5 1 0 a 9 10 1 0 2 3 9 5 8 8 8 3 9.88 9.26 8.53 48.0' 5 7 . 3 6 5 . 8 5 1 .9 4 2 . 6 3 4 . 1 .8 50 . 9 5 7 1. 0 6 3 - . 2 9 Z - . 0 8 5 . 1 2 6 11 12 13 7 0 6 6 4 5 4 7 1 6. 82 6 .23 4. 55 7 2 . 7 7 8 . 9 8 3 . 4 2 7 . 2 2 1 . 0 1 6 . 5 1 . 1 6 9 1.276 1.382 .3 39 . 5 5 1 . 7 6 4 14 15 ' 16 3.5 t 3 0 4 2 4 8 3 . 4 5 2 . 9 3 2. 39 8 6 . 9 8 9 . 8 9 2 . 2 1 3 . 0 10.1 7 .7 1 .488 1. 5 9 5 1.701 .976 1 . 1 8 9 1.401 17 18 19 2 1 4 1 3 5 8 5 2 .06 1.30 . 82 9 4 . 3 9 5 . 6 9 6 . 4 5.6 4 . 3 3.5 1.808 1.914 2 . 0 2 0 1.614 1 . 8 2 6 2 . 0 3 9 2 0 21 22 7 3 6 0 6 1 .70 .57 .58 9 7 . 1 9 7 . 7 9 8 . 3 2.8 . 2 . 2 1.6 2. 1 2 7 2 . 2 3 3 2 . 3 3 9 2 . 2 5 1 2 . 4 6 3 2 . 6 7 6 23 24 25 3 6 •26 27 • .34 .25 .'26 9 8 . 6 9 8 . 9 9 9 . 2 1.3 1.0 .7 2 . 4 4 6 2 . 5 5 2 2 * 6 5 8 2 . 8 8 8 3 . 1 0 1 3 . 3 1 3 26 • 27 28 2 0 17 12 • 19 . 16 .11 9 9 . 4 9 9 . 5 9 9 . 6 .5 .4 ' .3 2. 7 6 5 2 . 8 7 1 2 . 9 7 7 3. 5 2 6 3 . 7 3 8 3 . 9 5 1 29 30 31 13 8 4 .12 .07 .03 9 9 . 8 9 9 . 8 9 9 . 9 . 1 .1 . 0 3 . 0 8 4 3 . 1 9 0 3.297 4 . 1 6 3 4 . 3 7 5 4 . 5 8 8 32 4 33 .4 R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO .03 .03 99 .9 1 0 0 . 0 .0 .0 3 . 4 0 3 3 .509 4 . 8 0 0 5 . 0 1 3 * J 15 * 14 * 13 "*~ * 12 * 11 10 9 * * ** ** ** ** ** ** * ** ** ** 8 * ** ** ** ** ** ** ** ** ** ** ** ** ** ** 7 * * . ** ** ** ** ** ** ** ** * ** ** ** ** ** ** : 6 ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** 5 * ** ** ** ** ** . ** ** Jv J> If* -v- ** .. ** ** ** ** ** ** ** ** * ** ** ** ** **" ** ** * • 4 * ** ** . ** ** ** ** ** ** ** ** ** ** ** ** ** ** -J, -Ju. ** ** ** ** ** ** ** ** ** ** 3 * * * * * ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** 2 * * * * * * * ** ** ** * * ** ** ** ** ** ** ** * ** *'* ** ** ** ** ** ** ** ** ** ** ** ** * ** *•* ** ** ** ** ** ** ** ** ** ** ** ** ** 1 * ** ** ** * * ** ** ** ** ** **  **  ** ** * ** ** ** ** ** ** . ** ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** 10 11 ************************************ 12 13 14 15 16 17 1 8 19 OCCUPANCY F I G U R E 1 0 : R E L . FREQUENCY OF NUMBER OF JOBS OCCUPYING S I M U L T A N E O U S L Y DESK AND S H E L V E S STORAGE C A P A C I T Y AVERAGE AVERAGE E N T R I E S AVERAGE CURRENT MAXIMUM CONTENTS UTI L I Z A T I O N : TIME/TRAN CONTENTS CONTENTS J 40 23 2 0 . 9 2 5 .909 1 6 3 4 4 6 . 1 1 6 21 23 L I S T E N I N G ROOM I N T E R A R R I V A L T I M E S ( M I N . ) T A B L E T A B U E N T R I E S I N T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS 1 6 1 2 2 . 2 1 6 2 . 1 9 1 3 5 7 3 . 0 0 0 NON-WEIGHTED UP P E R OBSERVED P ER CENT C U M U L A T I V E CUMULATIVE M U L T I P L E D E V I A T I O N L I M I T FREQUENCY OF TOTAL PERCENTAGE . REMAINDER OF MEAN FROM MEAN 1 7 7 6 4 8 . 1 3 ' 4 8 . 1 51.8 .451 - . 5 5 5 2 2 9 9 1 8 . 5 4 6 6 . 6 3 3.3 . 9 0 2 - . 0 9 8 3 2 1 1 1 3 . 0 8 79 .7 2 0 . 2 1 . 3 5 3 .357 4 144 8.93 8 8 . 7 11.2 1 .804 .8 13 5 54 3 .34 9 2 . 0 7. 9 2. 2 5 5 1 . 2 7 0 6 3 6 2 .23 9 4 . 2 5.7 2 . 7 0 6 1.726 7 3 5 2.17 9 6 . 4 3.5 3 . 1 5 8 2 . 1 8 2 8 17 1 .05 9 7 . 5 2.4 3 . 6 0 9 2 . 6 3 9 9 16 . 9 9 9 8 . 5 1 .4 4 . 0 6 0 3 . 0 9 5 10 12 .74 9 9 . 2 . .7 4 . 5 1 1 3 . 5 5 1 11 6 .37 9 9 . 6 • . .3 4.962 4 . 0 0 8 ' • . 12 1 . 06 9 9 . 6 .3 5 . 4 1 3 4 . 4 6 4 13 2 .12 9 9 . 8 . 1 5. 8 6 5 4.92.0 14 2 .12 9 9 .9 .0 6. 3 1 6 5 . 3 7 7 15 1 .06 1 0 0 . 0 .0 6.767 5 . 8 3 3 R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO wooy 9 - N i i M 3 i s n 01 sawn l V A r n a v n a i N i J O A0N3n03yj * i a y :TI 3^0013 CNItW) 3WI1 3VAI yyVHBlNI : ; ; ST *fl £1 Zl U OT 6 8 1 9 5 V £ Z I *********************************** ****************** 0 * * * * * * * * * * ; * * * * ••* * *• * * *7 * *_ * * * * * * * * * * * * * 8 *__ * * * * * * * * * * * ZT ' , _4 * , * * * * * * * 91 ' * . » * * * * * OZ : . * : £ * * * * <7Z. ; - • - ] * * * * * * ez : : * £ * * * * Z£ * * * * * . * .9£ . 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' ; \ * » * * * . * ; : : * : •_* * * * * 8+7 * * * Z5 * * * 95 *  * 09 T A B L E TAB 12 • E N T R I E S I N T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS 3 6 0 4 .474 2.0 39 1 6 1 1 . 0 0 0 NON-WEIGHTED UPPER OBSERVED PER CENT CU M U L A T I V E C U M U L A T I V E M U L T I P L E D E V I A T ION L I M I T 0 1 FREQUENCY 5 1.9 OF TOTAL 1.38 5 .27 PERCENTAGE 1.3 6. 6 REMAINDER 9 8 . 6 9 3 . 3 OF MEAN - . 0 0 0 .223 FROM MEAN - 2 . 1 9 4 - 1 . 7 0 4 2 3 4 3 6 57 7 4 9 .99 1 5 . 8 3 2 0 . 5 5 16 . 6 3 2 . 4 5 3 . 0 8 3 . 3 6 7.5 4 6 . 9 . 4 4 6 . 6 7 0 . 8 9 3 -1.213 - . 7 2 3 - . 2 3 2 5 6 7 67 3 7 39 1 8 . 6 1 1 0 . 2 7 10 .83 71 .6 8 1 . 9 9 2 . 7 2 8 . 3 1 8 . 0 7. 2 1. 117 1.340 1.564 . 2 5 7 .747 1 .238 1. -28 2 . 2 1 9 2. 7 0 9 8^ 9 10 15 7 4 4.16 1.94 1.11 9 6 .9 9 8 . 8 1 0 0 . 0 3V0 1 . 1 .0 1 7 7 8 7 2 .011 2. 2 3 4 R E M A I N I N G F R E Q U E N C I E S ARE A L L ZERO / "1 *- .* 22 * 21 * * "ftftT ft* 20 T 19 * ft* 18 * ** ** ft ** ** 17 * . ** ** ft ft* ' f t * 16 . * . ft* ** * ** ** V 15 ft ft* ft* ** * ft* ** ** 14 * ft* ftft ft* * . • . t* ** t* ' ' 13 * ft* * ft- ** * ** ft ft *ft 12 ft ** ft* * * ft* ft* . 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ROOM S E R V I C E T IMES ( M I N . ) TA B L E TAB 13 E N T R I E S IN T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N . SUM OF ARGUMENTS J 1 6 1 3 46 .275 3 6 . ^ 5 0 / 4 6 4 2 . 0 U 0 NUN-WEIGH!tU UPPER OBSERVED PER CENT CU M U L A T I V E CUMULATIVE MULT I P L E D E V I A T I O N L I M I T 0 5 FREQUENCY 9 89 OF TOTAL .55 5.51 PERCENTAGE .5 6. 0 REMAINDER 9 9 . 4 9 3 . 9 OF MEAN - . 0 0 0 .108 FROM MEAN - 1 . 2 5 9 - 1 . 1 2 3 10 15 20 ' 79 9 2. 13 2 4 .89 5.70 8.18 10.9 1.6.6 2 4 . 8 8 9 . 0 ' 8 3 . 3 75-1 . 2 1 6 .324 .432 - . 9 8 7 - . 8 5 1 - . 7 1 4 25 30 35 122 119 1 1 4 7 . 5 6 " 7.37 7.06 3 2 . 4 3 9 . 8 4 6 . 8 6 7 . 5 6 0 . 1 53.1 . 5 4 0 .648 . 7 5 6 - . 5 7 8 - . 4 4 2 -.3 06 40 45 50 V3 105 1 2 5 5. lb 6. 50 7 .74 • 5 2.6' 5 9 . 1 6 6 . 8 4/.3 4 0 . 8 3 3 . 1 • 8 6 4 .972 1. 0 8 0 - . 1 fU - . 0 3 4 . . 1 0 1 55 60 65 9 9 56 4 6 6.13 3.47 2 .85 7 3.0 7 6. 5 7 9 . 3 2 6 . 9 2 3 . 4 2 0 . 6 1.188 1 .296 1.404 . 2 3 7 .373 . 5 0 9 /O 75 80 4 4 18 2 5 2. 12 1.11 1.54 8 2 . 0 8.3.T 8 4 . 7 17 .9 16.8 15.2 1.512 1.620 1. 7 2 8 . 6 4 5 .781 . 9 1 7 . 8 5 90 . 95 3 4 3 4 2 5 2. 10 2.10 1. 54 8 6 . 8 8 8 . 9 9 0 . 5 13.1 11.0 9.4 1.8 3 6 1.944 2 . 0 5 2 1 . 0 5 3 1 . 1 8 9 1.325 100 105 1 10 2 6 15 7 1.61 .92 . 43 9 2 . 1 9 3 . 0 9 3 . 4 7. 8 6.9 6.5 2 . 1 6 0 2 . 2 6 9 2.37 7 1.461 1.597 1.734 115 120 1 2 5 6 3 • 12 .37 .18 . 74 93.-8 94.0 9 4 . 7 6. 1 5.9 5.2 2 . 4 8 5 2 . 5 9 3 2 . 7 0 1 1 . 8 7 0 2 . 0 0 6 2 . 1 4 2 1 3 0 . . 1 3 5 140 10 4 5 .61 .24 .30 9 5 . 4 9 5 . 6 9 5 . 9 4. 5 4.3 4.0 2 . 8 0 9 2 . 9 1 7 3 .02 5 2 . 2 7 8 2 . 4 1 4 2 . 5 5 0 145 150 . 1 55 8 7 5 .49 .43 .30 9 6 . 4 9 6 . 8 9 7 . 2 3.5 3.1 2.7 3 . 1 3 3 3 . 2 4 1 3 . 3 4 9 2. 6 86 2 . 8 2 2 2 . 9 5 8 160 165 170 9 '-8 , 10 .55 .49 .61 9 7 ..7 9 8 . 2 9 8 . 8 2.2 1.7 1. 1 3.457 3.56 5 3 . 6 7 3 3. 0 9 4 3 . 2 3 0 3 . 3 6 6 175 180 185 4 ' . 5 3 .24 .30 .18 99 .1 9 9 . 4 9 9 . 6 .8 .5 .3 3 . 7 8 1 3 .389 3 . 9 9 7 3 . 5 0 2 3 .638 3 . 7 7 4 190 6 .37 100.0 .0 4 . 1 0 5 3 . 9 1 0 R E M A I N I N G F R E Q U E N C I E S ARE ALL ZERO 15 * _ 14 * _ 13 * * . 12 * * 11 * ' * 10 * _ g * * 8 * ' .' *' * * —•* : ~ 1 ••* * * * * * * * * * 6 * * * * * * * * * . * * * . * * * * * * * 5 * * * * * * * * * * * * * * * * * * * * * * * * * 4 * * * * •*. * * * * * * '* * * * * * * * * • * * * * * * * 3 * * * •* * * * * * * * N * * * * * * * * * * * * * * •* * * * * * 2 * * * * * *" * * * * A. * * * * * * * * * * * * * * * * * * * * * * .1 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * o * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 5' 10 15 20 2 5 3 0 35 4 0 45 50 55 60 6 5 70 75 80 85 9 0 95 100 105 110 1 1 5 120 125 1 3 0 1 3 5 1 4 0 145 1 5 0 T R A N S I T TIME ( M I N . ) F I G U R E 1 3 : R E L . FREQUENCY OF T R A N S I T TIME OF L I S T E N I N G ROOM • ; ; • ; J OCCUPANCY OF LIST. ROOM • TABLE TAB 14 ENTRIES IN TABLE MEAN ARGUMENT . STANDARD DEVIATION SUM OF ARGUMENTS J 1613 20 .050 2. 238 32341.000 NON-WEIGHTED \ UPPER OBSERVED PER CENT CUMULATIVE CUMULATIVE MULT I PLE DEV IATION LIMIT FREQUENCY OF TOTAL PERCENTAGE- REMAINDER OF MEAN FROM MEAN • 0 '0 .00 .0 100.0 -.000 -8.957 1 0 . 00 .0 100.0 .049 -8.511 2 0 .00 . 0 100.0 .099 -8.064 3 -• o .00 .0 100.0 . 149 -7-617 4 0 .00 .0 100.0 . 199 -7.170 5 . - o .00 .0 100.0 .249 -6.724 6 0 . 00 .0 100.0 .299 -6.277 7 0 .00 . 0 100.0 .349 -5.830 8 0 .00 .0 100.0 .398 -5.3 83 . . 9 . 1 . 06 .0 . 99.9 .448 -4.936 10 1 .06 . 1 99.8 .498 -4.490 11 3 .18' • .3 99.6 . 548 -4. 043 12 5 .30 . .6 99 .3 .598 . -3.596 13 19 1 .17 1.7 98.2 .648 -3.149 14 24 1 .48 3.2. 96.7 . 698 -2. 703 15 44 2. 72 6.0 93-9 .748 -2.256 16 47 2.91 8.9 91.0 .797 -1.809 17 71 4.40 13.3 86.6 . 847 - 1.362 18 101 6. 26 19. 5 80.J4 .897 -.915 19 150 9 .29 28.8 -• 71.|l .947 -.469 20 255 15.80 44.6 55. B .997 -.022 ' 21 365 22.62 67.3 32.6 1.047 .424 22 527 32.67 100. 0 .'o 1 .097 .871 REMAINING FREQUENCIES ARE ALL _ERO 0 0 ** ** ** 00 ** ** 15 '* • * 1 4 * * ** ** ** ** ** ** 13 * * . • ** ** ** ** J V - J V f ***• * J - JV -*»* **- ** ** . 12 * * J U J v ** ** ** ** ** * ** J V J v ** 11 * ** ** ** J v J V Jr- ** ** * ** •A. * 7 V ** 10 * ** ** ** ** * ** Jv J V ** 9 * * ** ** ** ** ** ** ** ** * ** ** ** ** 8 * ** ** ** ** ** ** ** ** * ** ** ** ** 7 * * . . . ** ** ** ** ** ** ** ** * ** ** J V J V 6 * ** ** 3r & * . • ** ** J V J V •V "i» ** * •A. J V *-r» *r- ** OV J V -v -V ** ** 5 * ** ** ** ** * J V - J V *v •***• ** ** ** J V J v T» -V * J V J V ** J V J v TT V- ** J v J v 'f 4 * ** ** ** J V Jv ** J V J V *V f * ** ** ** J * J v ** * ** ** ** ** ** **. 3 * ** ** ** ** ** • * ** ** ** ** ** ** * ** ** ** : J V J v - f I f 4 ** ** 2 * :** ** ** ** ** J v J r ** ** * ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** ** 1 * ** ** ** ** ** ** ** ** ** ** * ** ** ** ** ** ** ** - J v J v ** ** * ** ** ** t * ** ** ** ** ** 10 11 12 13 14 15 r.* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 16 17 18 19 2 0 2 1 22 2 3 OCCUPANCY F I G U R E 1 4 : R E L . FREQUENCY OF NUMBER OF JOBS • OCCUPYING SIMULTANEOUSLY THE L I S T E N I N G ROOM THE R E S E R V . L I S T E N I N G ROOM AS STORAGE STORAGE C A P A C I T Y AVERAGE AVERAGE E N T R I E S AVERAGE CURRENT MAXIMUM CONTENTS U T I L I Z A T I O N TIME/TRAN CONTENTS CONTENTS ) 41 23 1 0 . 2 8 1 . 4 4 7 8 4 6 4 3 . /63 9 2 3 OCCUPANCY OF R E S E R V E L I S T . ROOM T A B L E TAB 1.7 E N T R I E S I N T A B L E 837 MEAN ARGUMENT 1 2 . 5 4 9 STANDARD D E V I A T I O N • SUM 5.50 7 OF ARGUMENTS 1 0 5 0 4 . 0 0 0 NON-WEIGHTED • UPPER ' L I M I T OBSERVED PER FREQUENCY ' OF CENT' TOTAL C U M U L A T I V E CUMULATIVE PERCENTAGE REMAINDER M U L T I P L E OF MEAN D E V I A T I O N FROM MEAN U 1 2 2 . 4 9 .23 .47 1 .07 .2 9 9 . / .7 9 9 . 2 1.7 9 8 . 2 -.QUO .079 . 1 5 9 - z . 2 /a -2 .096 - 1 . 9 1 5 3 4 5 12 16 32 1.43 1.91 3.82 • 3.2 9 6 . 7 5. 1 9 4 . 8 • 8.9 9 1 . 0 .239 .318 . 3 9 8 - 1 . 7 3 3 - 1 . 5 5 2 - 1 . 3 7 0 •6 . 7 8 47 57. 54 5.61 6.81 6.45 14 . b 8 5 . 4 2 1 . 3 7 8 . 6 2 7 . 8 7 2.1 .4/8 . 5 5 7 . 6 3 7 - 1 . 1 8 9 - 1 . 0 0 7 - . 8 2 6 9 10 11 53 ' 4 7 . 56 6.33 5.61 6. 69 3 4 . 1 6 5 . 8 39 . 7 6 0 . 2 ' 46 .4 5 3 . 5 .717 . 7 9 6 .876 - . 6 4 4 - . 4 6 2 - . 2 8 1 12 . 1 3 \ . 14 5 2 51 39 6.21 6 .09 4.65 5 2 . 6 4 7 . 3 5 8.7 4 1 . 2 63 . 4 3 6.5 .956 1.03 5 1.11 5 - . 0 9 9 . 0 8 1 . 2 6 3 . 1 5 16 17 4 0 41 ' 35 • 4.7 7 4.89 4. 18 6 8 . 2 3 1 . 7 7 3 . 1 2 6 . 8 7 7 . 2 2 2 . 7 1.19 5 1.274 1.354 .444 . 6 2 6 .808 • 18 19 20 32 2 9 34 3.82 3.46 4. 06 8 1 . 1 -18.8 8 4 . 5 1 5 . 4 8 8 . 6 1 1 . 3 1.434 1.513 1 . 5 9 3 . 9 8 y 1 . 1 7 1 1.352 21 3 5 ' 2 2 ' 6 0 R E M A I N I N G FREQUENCIES. ARE A L L ZERO 4.18 7.16 9 2 . 8 7.1 1 0 0 . 0 .0 1.673 1.753 1.534 1.715 J % '22 * * 21 * * * ,20 19 * * 18 ft * ft 17 16 * ft ft 15 ft ft ft 14 13 ft . ft •* 12 ft * * 11 10 * ft • ft 9 * ft ft 8 7 * ft * ' 6 ft ft * ** ** ** * * * * * * - Ar Air - J r -V f T* ** ** 5 4 ft ft * ** ** ** ft* ** ** ** ** ** ** ** ** ** ft* ** ** ** ft* ** ** ** ** ** ** ** 3 ft ft ft ** ft* ** ** ** ** ftft ** ** ** ** ** ** ** ** ** ** ** ** •\- * * * * ft* ** ** ft* ** ** 2 1 * ft ft- ** . ** . ••. ** ft* *ft ** ** ** ** ** ft* ** ** ** ** ** ** ** ** , ** ** ** ** ** ** ** ** ** ft* * * ** ** ** - •' . 0 ft ftft ** ft* ** ** ** ** ft* ft* ****************************************************************************************** 0 1 2 3 4 5 6 7 8 9 10 ** ** ****************** 11 12 ** ** ************ * * 13 14 OCCUPANCY F I G U R E 1 4 A : R E L . FREQUENCY OF NUMBER OF J O B S O C C U P Y I N G SIMULTANEOUSLY THE L I S T E N I N G ROOM J STORAGE C A P A C I T Y AVERAGE AVERAGE E N T R I E S AVERAGE CURRENT MAXIMUM CONTENTS U T I L I Z A T I O N TIME/TRAN CONTENTS CONT ENTS / 10 200 4 0 . 3 1 8 .201 6 1 2 3 2 3 . 7 1 1 37 78 \ S Y S T E M T R A N S I T T I M E S ( M I N . ) ( = S E R V I C E & WAIT. TIME ) T A B L E T A B 1 5 E N T R I E S I N T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS 6 0 8 6 3 . 3 67 1 1 . 7 0 7 2 0 4 9 3 . 0 0 0 NON-WEIGHTED UPPER OBSERVED PER CENT CUMULATIVE CUMULATIVE M U L T I P L E D E V I A T I O N L I M I T FREQUENCY OF .TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 2 58 5 4 2 . 4 7 4 2 . 4 5 7 . 5 - . 0 0 0 -.2 87 - • 2 2 1 1 2 .34.7 0 7 7 . 1 2 2 .8 . 5 9 3 - . 1 1 6 . 4 6 5 5 1 0 . 7 6 8 7 . 9 1 2 . 0 1 .187 .054 6 2 2 9 3 . 7 6 9 1 . 7 8. 2 1. 781 .224 8 .112 1 . 84 9 3 . 5 6.4 2 . 3 7 5 .3 95 10 6 4 1 .05 9 4 . 5 5.4 2 .969 .566 12 4 4 .72 9 5 . 3 4. 6 3. 5 6 3 . 7 3 7 14 3 0 .49 9 5 . 8 4.1 4 . 1 5 7 .908 16 25 .41 9 6 . 2 3.7 4 . 7 5 1 1.079 18 1 8 .29 9 6 . 5 3.4 5 . 3 4 5 1. 2 4 9 20 11 .18 9 6 . 6 3 .3 5 . 9 3 9 . 1 . 4 2 0 22 9 . 14 9 6 . 8 3. 1 6.533 1 .591 24 7 .11 96 .9 3.0 7. 1 2 7 1.762 26 1 1 . 18 9 7. 1 2 .8 7 . 7 2 1 1.933 28 9 .14 9 7.2 2.7 8. 3 1 5 2 . 1 0 4 30 17 .27 9 7 . 5 2.4 8 . 9 0 9 2 . 2 7 4 32 .11 • 18 9 7 . 7 2.2 9.503 2 . 4 4 5 , 3 4 8 .13 9 7.8 2. 1 1 0 . 0 9 7 2 . 6 1 6 36 4 . 06 9 7 . 9 2 . 0 1 0 . 6 9 1 2 . 7 8 7 • ' 38 , 15 .24 9 8.1 , 1.8 11 .285 2.958 40 3 .04 9 8 . 2 1.7 U . 8 7 9 3. 1 2 9 42 •• 6 .09 9 8.3 1 .6 1 2 . 4 7 3 3 . 2 9 9 •44 6 .09 9 8. 4 1 . 5 ' 1 3.067 3 . 4 7 0 46 9 .14 9 8 . 5 1.4 1 3 . 6 6 1 3 . 6 4 1 48 11 . 1 8 .98.7 1.2 1 4 . 2 5 5 3 . 8 1 2 50 • 7 .11 9 8 . 8 1. 1 1 4 . 8 4 8 3 . 9 8 3 52 3 .04 9 8 .9 1 . 0 1 5 . 4 4 2 4 . 1 5 4 54 2 . 0 3 9 8 . 9 1 .0 1 6 . 03 6 4 . 3 2 4 56 6 .09 9 9 . 0 . 9 1 6 . 6 3 0 4.4 95 58 '2 .03 9 9 . 0 .9 1 7 . 2 2 4 4 . 6 6 6 60 2 .03 9 9 . 1 . 8 1 7 . 8 1 8 4 . 8 3 7 62 3 .04 9 9 . 1 .8 1 8 . 4 1 2 5 . 0 0 8 . 6 4 . . 2 .03 • 9 9 . 2 .7 19 .006 5 . 1 7 9 66 3 • .04 9 9 . 2 . 7 1 9 . 6 0 0 5 . 3 5 0 68 0 .00 • 9 9 . 2 .7 2 0 . 1 9 4 5. 5 2 0 70 : 2 . 0 3 9 9 . 2 .7 2 0 . 7 8 8 5.691 , 72 0 .00 9 9 . 2 . 7 2 1 . 3 8 2 5.862 74 l . 01 9 9 . 3 .6 2 1 . 9 7 6 6 . 0 3 3 76 2 . 0 3 9 9 . 3 .6 22 . 5 7 0 6 . 2 0 4 78 2 .03 9 9 . 3 . 6 2 3 . 164 6.375 80 1 .01 . 9 9 . 3 ' .6 2 3 . 7 5 8 6 . 5 4 5 8 2 • 2 .03 9 9 . 4 .5 2 4 . 3 5 2 6 .716 J 84 2 .03 99 .4 .5 2 4 . 9 4 6 6 . 8 8 7 8.6 5 .08 9 9 . 5 .4 2 5 . 5 4 0 7 .058 88 0 .00 9 9 . 5 .4 2 6 . 1 3 4 7 . 2 2 9 90 1 .01 99 .5 .4 2 6 . 7 2 8 7 . 4 0 0 92 0 .00 9 9 . 5 .4 2 7 . 3 2 2 7 . 5 7 0 9 4 1 .01 9 9 . 5 .4 2 7 . 9 1 6 7. 7 4 1 J 96 1 .01 y y . 5 .4 2 8 . 5 1 0 f-,912 98 1 .01 9 9 . 6 • 3 2 9.10 3 8 .083 100 1 .01. 9 9 . 6 . .3 2 9 . 6 9 7 8 . 2 5 4 102 4 .06 9 9 . 6 .3 3 0 . 2 9 1 8 . 4 2 5 104 1 .01 9 9 . 7 .2 3 0 . 8 8 5 8 . 5 9 5 106 0 .00 .99.7 .2 3 1 . 4 7 9 8 . 7 6 6 108 . 0 .00 9 9 . 7 .2 3 2 . 0 7 3 8 . 9 3 7 1 1 0 • 1. .01 9 9 . 7 . 2 3 2 . 6 6 7 9 . 1 0 8 \ • 112 1 .01 " 9 9 . 7 • .2 3 3 . 2 6 1 9 . 2 7 9 / . 1 1 4 0 .00 ' 9 9 . 7 .2 3 3 . 8 5 5 9 . 4 5 0 116 0 .00 9 9 . 7 .2 3 4 . 4 4 9 9 . 6 2 0 118 0 .00 9 9 . 7 .2 3 5 . 0 4 3 9 . 7 9 1 120 0 .00 '. 9 9 . 7 .2 3 5 . 6 3 7 9 .962 122 0 .00 9 9 . 7 .2 3 6 . 2 3 1 1 0 . 1 3 3 124 0 . 00 9 9 . 7 .2 3 6 . 8 2 5 1 0 . 3 0 4 126 0 .00 9 9 . 7 .2 3 7 . 4 1 9 1 0 . 4 7 5 128 0 .00 9 9 . 7 .2 3 8 . 0 1 3 1 0 . 6 4 5 130 2 . 03 9 9 . 7 .2 3 8 . 6 0 7 1 0 . 8 1 6 132 0 ' .00 9 9 . 7 .2 3 9 . 2 0 1 1 0 . 9 8 7 13 4 ' 1 .01 9 9 . 7 .2 3 9 . 7 9 5 1 1 . 1 5 8 136 2 . 03 9 9 . 8 .1 4 0 . 3 8 9 1 1 . 3 2 9 138 0 .00 9 9 . 8 . 1 4 0 . 9 8 3 1 1 . 5 0 0 140 1 .01 - 9 9 . 8 .1 4 1 . 5 7 7 1 1 . 6 7 0 1 4 2 . 1 .01 9 9 . 8 .1 4 2 . 1 7 1 11 .841 144 0 .00 9 9 . 8 ' .1 4 2 . 7 6 b 1 2 . 0 12 • • 1 4 6 . • 0 .00 : . 9 9 . 8 .1 4 3 . 3 5 8 : 1 2 . 1 8 3 .148 . • • .1 . .01 9 9 . 8. .1 4 3 . 9 5 2 1 2 . 3 5 4 150 0 .00 9 9 . 8 .1 4 4 . 5 4 6 1 2 . 5 2 5 . 152 . 0 . 00 9 9 . 8 ' .1 . 4 5 . 1 4 0 1 2 . 6 9 6 • . 154 1 .01 9 9 . 8 .1 4 5 . 7 3 4 1 2 . 8 6 6 . 156 0 .00 99 .8 . 1 4 6 . 3 2 8 1 3 . 0 3 7 .  • OVERFLOW 7 .11 1 0 0 . 0 .0 AVERAGE V A L U E OF OVERFLOW 1 6 7 . 0 0 30 2 8 * * * 2 6 * 0 * * * ~*~ *. * 0 * "*~ ft ft * 24 ft * ft ft ft ft ft * ft " f t - * ft I T ft 2 2 ft ft ft 20 ft ft * ft ft ft ft ft ft 18 ft- ft ft ft ft ft * ft 16 ft ft * ft ft ft ft ft ft 14 ft ft ft ft ft ft * ft ft ft * 12 ft ft- ft ft ft 10 " * " * ft ft ft * ft ft ft 8 * ' ft * ft ft * ft * ft ft * ft * ft * ft 6 •* * ft ft ft ft ft ft- ft ft ft. ft ft- ft ft ft ft " f t " * ft "ft - * ft * ft 2 * ft- ft ft ft. ft ft ft :****** ****** ********************** ******************************** 6 8 10 12 14. 16 TRANS IT T I M E ( M I N . ) F I G U R E 15: R E L . FREQUENCY OF SYSTEM T R A N S I T TIMES OCCUPANCY OF S Y S T E M ( = O E S K . S H E L V E S , L 1 S T . ROOM) T A B L E TAB 1 6 E N T R I E S IN T A B L E MEAN ARGUMENT STANDARD D E V I A T I O N SUM OF ARGUMENTS J 6 08 6 4 0 .922 9.2 30 2 4 9 0 5 5 . 0 0 0 NON-WEIGHTED \ UPPER OBSERVED PER CENT C U M U L A T I V E C U M U L A T I V E M U L T I P L E D E V I A T I O N L I M I T FREQUENCY OF TOTAL PERCENTAGE REMAINDER OF MEAN FROM MEAN 0 0 .00 .0 1 0 0 .0 - . 0 0 0 - 4 . 4 3 3 2 2 .0 3 . 0 9 9 . 9 . 0 4 8 - 4 . 2 1 6 4 3 - .04 .0 9 9 . 9 .09 7 - 4 . 0 0 0 6 1 ' . Q i .0 99 .9 . 1 4 6 - 3 . 7 8 3 8 4 .06 . 1 9 9 . 8 . 1 9 5 - 3 . 5 6 6 10 2 , .03 .1 ' 9 9 . 8 . 2 4 4 - 3 . 3 5 0 12 1 .01 .2 9 9 . 7 . 2 9 3 - 3 . 1 3 3 14 4 .06 . 2 9 9 . 7 . 3 4 2 - 2 . 9 1 6 16 5 .08. . .3 9 9 . 6 .39 0 - 2 . 7 0 0 18 11 .18 . 5 9 9 . 4 . 4 3 9 -2 .483 20 4 0 .65 1.1 9 8 . 8 . 4 8 8 - 2 . 2 6 6 22 86 1 .41 2.6 97 .3 .537 - 2 . 0 5 0 24 9 0 1.47 4. 0 9 5 . 9 .586 - 1 . 8 3 3 26 98 1.61 5.7 9 4 . 2 . 6 3 5 - 1 . 6 1 6 28 13 3 2.18 ' 7. 8 9 2 . 1 . 6 8 4 - 1.399 30 2 2 0 3.61 1 1 . 5 8 8 . 4 . 7 3 3 - 1 . 1 8 3 32 . . 2 7 0 4.4,3 1 5 . 9 8 4 . 0 . 7 8 1 - . 9 6 6 34 365 5. 99 •• 2 1 . 9 78 .0 .830 -.7 49 36 48 8 .8.01 2 9 . 9 7 0 . 0 . 8 7 9 - . 5 3 3 38 594 • 9.76 3 9 . 7 6 0 . 2 . 9 2 8 - .316 40 64 1 1 0 . 5 3 5 0 . 2 4 9 . 7 .977 - .099 42 5 5 4 9.10 5 9 . 3 4 0 . 6 1.02 6 .1 16 44 4 8 4 7. 95 6 7 . 3 3 2 . 6 1.075 . 3 3 3 46 44 0 7 .22 7 4 . 5 2 5 . 4 1. 124 . 5 5 0 48 364 5. 9 8 8 0 . 5 1 9 . 4 1 . 1 7 2 .766 50 3 3 6 • 5.52 8 6 . 0 1 3 . 9 1 .221 .983 52 2 4 9 4. 09 9 0 .1 9.8 1.270 1.200 54 18 5 3.03 • 9 3 . 1 6.8 1 . 3 1 9 ' 1 . 4 1 6 56 146 2 .39 9 5.5 4.4 1.368 1.633 58 95 1.56 • - 9 7 . 1 2 .8 1.417 1.8 50 60 4 2 .69 : 9 7 . 8 2.1 1.46 6 2 . 0 6 6 62 34 .55 9 8 . 3 1.6 1.515 2.2 83 64 25 . 4 1 9 8 . 7 1 .2 1 . 5 6 3 2 . 5 0 0 66 16 .26 9 9 . 0 .9 1.612 2 . 7 1 6 68 10 .16 9 9 .2 .7 1.661 2. 9 3 3 70 17 .27 9 9 . 4 .5 1 .710 3 .150 72 • 14 .23 9 9 . 7 . . 2 1 . 7 5 9 3 . 3 6 6 74 11 .18 9 9 . 9 .0 1.808 3.5 83 fh 5 .U8 : 9 9 . V .0 1 .857 3 . 8 0 0 78 1 -.01 10 0.0 . 0 1. 9 0 6 4 . 0 1 6 R E M A I N I N G F R E Q U E N C I E S ARE ALL ZERO 40 * 3 8 * 36 34 32 30 * 28 * Ar 2 6 * 24 * 2 2 * 2 0 * 18 * A . -v A- •v A r Ar -T> *¥• ** ** A r A r •-»*• 16 V A. Ar Ar 1" A r Ar Ar A> •*#*• -v* A r J r A r A r 14 T* J- *v A r A r ** -**• * * 12 Ar '>- Ar *V ** Ar A- v -v- A r A r •V 1" A r A- "i* f- «<r A r •V 1" -Ar A r -!*• - i * ** J r A r * * ** 10 8 s- *V Ar Ar T Ar «*r * f -*>» A r Ar -T* -V ** A r A, T -v Ar A r Ar Ar ->•• 1» Ar Ar *v V A , Ar -V- T -Ar A r ft* * * * * ** Ar A r -v* A r -Ar 6 V -Ar T V A r A r T- Ar -A- •*V> -TT-** ft* Ar A r "f -V* Ar A r ** ft* Ar A r A r Ar * * * * A r A r Ar A r Ar A r A r A r T" -V ** ** A r Ar *<*• -v 4 . •' , 2 A r T A r Ar A r -V ** A r A - I - •A- v«, J r A r 1" V *v -A- Ar A r -Jr -v- -V* '1- J ; A r A r j l r ** * * -»"*-»*• Ar A. "T-'f -A- A. A r A r V *V ^ rjjl X5 ** ** A r A r T T- Ar Ar ** ** * * • ' 0 Or '|- A r A r A- Ar Ar- A r -Ar Ar A r Ar '»*" -lv 1" 'f "V 'i- *V- *V "V" I"' 2 A r A r A r A- -A- A r A r A r A» A- -Ar ,J J _(,. ** -V- "V* "V -*»** J4W/* •*»* "V" -»*• r,» J j s r f V f - 6 10 . 14 Ar A r 3jc:«{e 'r ^ ^ 18 .. A r A r -»* rp Ar A r A r •V T-*T\ 22 A r A r •V A. Ar Ar Ar A- 2 6 ' A r Ay A A r J r J r „«, J - A r A- A- Ar A r A. Ar A r I - •***• T - - I * *t* -V* "7* T 3 0 34 ** ******** 38 A r Ar -V- A r A r A. Ar 42 ** ft* ft* ** * 4 6 - * * A r Ar A r Jj* A r *i> - i 1 r r T * 5 0 . ft* A> -Ar A r A r A r A r •V* - V -V •V'.T'T"' : 54 * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 58 62 66 70 74 78 . . . OCCUPANCY FIGURE 165 R E L . FREQUENCY OF NUMBER OF JOBS OCCUPYING SIMULTANEOUSLY THE SYSTEM R F S NO. 7 7 1 1 8 4 U N I V E R S I T Y OF B C COMPUT ING.CENTRE M T S I A N 1 2 0 ) 0 0 : 4 1 :42 1 2 - 3 1 - 7 0 < USER: WULI DEPARTMENT: COMM *** * ON AI 0 0 : 4 1 : 4 4 ' * * * * OFF AT 0 0 : 5 1 : 0 4 * * * * E L A P S E D TIME 5 6 0 . 043 SEC. **** C P U . T I M E USED 1 3 0 . 9 3 4 S E C . **** STORAGE USED 8 3 4 9 . 1 8 P A G E - S E C . CARDS READ 4 1 8 * * * * L I N E S P R I N T E D 9 9 0 4 **** PAGES P R I N T E D 2 84 **** CARDS PUNCHED' 0 * * * * DRUM READS 9 5 * * * * RATE FACTOR 0.6 APPROX. COST OF T H I S RUN C $ 1 5 . 17' * * * * F I L E STORAGE 0 PG-HR. .00 * * L A S T SIGNON WAS: 0 0 : 2 3 : 2 0 1 2 - 3 0 - 7 0 END C P U TIME USED: A S S E M B L Y : 3.262 SECONDS E X E C U T I O N : 1 2 3 . 8 5 7 SECONDS E X E C U T I O N TERM IN AT ED $ S I G N O F F MMMMM MMMMM T T T T T T T T T T T T T T T T T T T T T T T T T S S S S S S S S S MMMMMM MMMMMM T T T T T T T T T T T T T T T T T T T T T T T T T S S S S S S S S S S S S S MMMMMMM. MMMMMMM T T T T T T T T T T T T T T T T T T T T T T T T T S S S S S S S S S S S S S S S S S MMMMMMMM MMMMMMMM •- TTTTT S S S S S S S S S S S S S • ' • MMN'NNMMMM KMMMMMMMM TTTTT S S S S S S S S S S MMMMMMMMMM MMMMMMMMMM TTTTT s s s s s MMMMM MMMMM 1 I.J TT S S S S S S MMMMM NtMMMM MMMMM MMMMM TTTTT S S S S S S S S S S S S S MMMMM MMMMM MMMMM MMMMM TTTTT S S S S S S S S S S S S S MMMMM • MMMMMMMMMMM MMMMM TTTTT . S S S S S S S S S S S S S MMMMM MM MM MMMMM .MMMMM TTTTT S S S S S S S MMMMM MMMMMMM MMMMM TTTTT s s s s s MMMMM MMMMM .MMMMM TTTTT s s s s s MMMMM MMM MMMMM TTTTT s s s s s s s s s s MMMMM MMMMM TTTTT S S S S S S S S S S S S S S MMMMM MMMMM TTTTT S S S S S S S S S S S S S S S S S MMMMM MMMMM TTTTT S S S S S S S S S S S S S MMMMM MMMMM. TTTTT S S S S S S S S S J

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