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A simulation model of marine traffic flow with particular application to Rosario Strait Braem, Trevor Arthur 1974

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A SIMULATION MODEL OF MARINE TRAFFIC FLOW WITH PARTICULAR APPLICATION TO ROSARIO STRAIT by TREVOR ARTHUR BRAEM B.Sc.(Hons.), Simon Fraser University, 1971 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN BUSINESS ADMINISTRATION in the Faculty of COMMERCE AND BUSINESS ADMINISTRATION We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1974 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l l m e n t o f the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h C olumbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Depart-ment o-f by h i s r e p r e s e n t a t i v e . I t i s u n d e r s t o o d t h a t copy-i n g or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . T. A. Braem Department o f Commerce and B u s i n e s s A d m i n i s t r a t i o n The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date: August, 1974 ABSTRACT The o b j e c t i v e of t h i s r e s e a r c h i s to develop a s i m u l a t i o n model which can be used as a q u a n t i t a t i v e t o o l i n d e t e r m i n i n g o p t i m a l r o u t i n g and s c h e d u l i n g o f marine t r a f f i c f l o w s . A s i m u l a t i o n model of marine t r a f f i c f l o w t h rough Haro S t r a i t , Boundary Pass and R o s a r i o S t r a i t was d e v e l o p e d u s i n g the IBM G e n e r a l Purpose S i m u l a t i o n System. The model a l l o w s e x p e r i m e n t a t i o n w i t h r o u t i n g , v e s s e l p o p u l a t i o n growth, and the e f f e c t of a shore-based r a d a r marine a d v i s o r y system on the i n c i d e n c e of c o l l i s i o n s , p a r t i c u l a r l y t a n k e r c o l l i s i o n s . S e v e r a l experiments were conducted t o i l l u s t r a t e the model concept and e x p e r i m e n t a l p o s s i b i l i t i e s . The c o n c l u s i o n drawn i s t h a t the model i s a v a l u a b l e p l a n n i n g t o o l f o r marine t r a f f i c c o n t r o l and can be extended to s i m u l a t e o t h e r f a c e t s o f marine n a v i g a t i o n and t r a f f i c c o n t r o l . TABLE OF CONTENTS Page L i s t o f T a b l e s i v L i s t o f F i g u r e s v i CHAPTER I INTRODUCTION 1 Need f o r the Study 1 L i t e r a t u r e Review 6 A. D i s c u s s i o n s 7 B. Surveys 8 C. Q u a n t i t a t i v e Models 11 I I THE MODEL 26 Development o f the Model 26 The S i m u l a t i o n Language 30 Data G a t h e r i n g 33 D e s c r i p t i o n o f the Model 35 A. D e s c r i p t i o n o f T r a f f i c Flow 35 B. A r r i v a l Rates 39 C. T r a n s i t Time 40 D. Encounters and C o l l i s i o n s i n the Model 41 E. R e c o r d i n g E n counters 43 i i I l l VALIDATION 53 IV EXPERIMENTS 69 A. Experiment One 69 B. Experiment Two 76 C. Experiment Three 78 D. Experiment Four 81 E. Experiment F i v e 86 F. Experiment S i x 8 9 V CONCLUSIONS 93 1. Growth Rate o f C o l l i s i o n s 93 2. Radar, M a r i n e Guidance Systems 94 3. R o u t i n g 95 4. F o r e c a s t 95 5. Areas o f F u t u r e R e s e a r c h 97 BIBLIOGRAPHY 98 APPENDIX I E v a l u a t i o n o f E x p o n e n t i a l Growth Rate 101 APPENDIX I I F l o w c h a r t s o f S i m u l a t i o n Model HO APPENDIX I I I Programme L i s t i n g s and Sample Output 115 i i i LIST OF TABLES TABLE Page 1.1 Comparison o f Observed and C a l c u l a t e d E n c ounters per Hour per Square N a u t i -c a l m i l e 13 2.1 Segmentation o f R o s a r i o S t r a i t 35 3.1 Comparison o f S t a t i s t i c s on Marine T r a f f i c Flow i n E n g l i s h Channel 66 4.1 Segmentation o f R o s a r i o S t r a i t 69 4.2 S i m u l a t e d V e s s e l E n c o u n t e r s 70 4.3 T h e o r e t i c a l V e s s e l E n c o u n t e r s 70 4.4 Types o f E n c o u n t e r s - Year 1 71 4.5 Types of Encounters - Year 2 72 4.6 Expected Number C o l l i s i o n s - Experiment 1. 73 4.7 Expected Number C o l l i s i o n s - Experiment 3. 79 4.8 S i m u l a t e d V e s s e l E n c o u n t e r s -Experiment 4 83 4.9 T h e o r e t i c a l Number o f Encounters -Experiment 4 83 i v 4.10 Expected Number of C o l l i s i o n s -Experiment 4 84 4.11 Simulated Vessel Encounters -Experiment 5 86 4.12 Expected Number of C o l l i s i o n s -Experiment 5 87 4.13 Simulated Vessel Encounters -Experiment 6 89 4.14 Expected Number of C o l l i s i o n s -Experiment 6 90 v LIST OF FIGURES FIGURE Page 1.1 Tanker Routes 2 1.2 Near M i s s Volume or Encounter Volume 14 1.3 E f f e c t i v e NMAC Volume 15 1.4 C o l l i s i o n E n c l o s u r e A r e a 16 1.5 Channel 19 2.1 T r a n s i t S t o r a g e s i n R o s a r i o S t r a i t 43 2.2 System L o g i c f o r T r a f f i c Flow 46 2.3 System L o g i c f o r T r a f f i c Flow c o n t ' d 49 2.4 System L o g i c f o r T r a f f i c Flow c o n t ' d 50 2.5 System L o g i c f o r T r a f f i c Flow c o n t ' d 51 3.1 A r e a o f I n v e s t i g a t i o n Showing T r a f f i c S e p a r a t i o n i n the Dover S t r a i t P r i o r t o 3 A p r i l , 1972 . 55 3.2 Method o f C o n d u c t i n g T r a f f i c Flow Survey (Decca Radar - 1971) 56 3.3 H o u r l y T r a f f i c Volume o f f F o l k s t o n e / C a p G r i s Nez ( E n g l i s h S i d e Northbound) 58 v i 3.4 H o u r l y T r a f f i c Volume o f f F o l k s t o n e / C a p G r i s Nez ( E n g l i s h S i d e Southbound) 59 3.5 H o u r l y T r a f f i c Volume o f f F o l k s t o n e / C a p G r i s Nez (French S i d e Northbound) 60 3.6 H o u r l y T r a f f i c Volume o f f F o l k s t o n e / C a p G r i s Nez (Fr e n c h S i d e Southbound) 61 3.7 Track Route D i s c i p l i n e and T r a f f i c S e p a r a t i o n - F o l k s t o n e / C a p G r i s Nez 62 3.8 Average Ground Speed o f 376 V e s s e l s -F o l k s t o n e / C a p G r i s Nez 63 4.1 S i m u l a t i o n F o r e c a s t o f Number o f Ex p e c t e d C o l l i s i o n s i n R o s a r i o S t r a i t 74 4.2 S i m u l a t i o n F o r e c a s t ( E x p o n e n t i a l l y Smoothed) o f Number o f E x p e c t e d C o l l i s i o n s i n R o s a r i o S t r a i t 77 v i i ACKNOWLEDGEMENTS The a u t h o r i s i n d e b t e d t o D o c t o r D.H. Uyeno o f t h e F a c u l t y o f Commerce and B u s i n e s s A d m i n i s t r a t i o n , U n i v e r s i t y o f B r i t i s h C o l u m b i a , and t o D o c t o r J . B . S i d n e y , f o r m e r l y o f t h e d e p a r t m e n t , f o r t h e i r g u i d a n c e and e n c o u r a g e m e n t i n t h e d e v e l o p e m e n t o f t h i s t h e s i s . He i s a l s o g r a t e f u l f o r t h e c o o p e r a t i o n a n d a s s i s t a n c e p r o v i d e d b y Mr. R o g e r A. P e t e r s o n , a f o r m e r g r a d u a t e s t u d e n t i n t h e d e p a r t m e n t . The a u t h o r w o u l d a l s o l i k e t o t h a n k M i s s W. Anne M e r c e r f o r h e r h e l p i n e d i t i n g a n d t y p i n g t h i s t h e s i s . v i i i CHAPTER I INTRODUCTION NEED FOR THE STUDY The d e c i s i o n t o move o i l from A l a s k a t o the C h e r r y P o i n t r e f i n e r y i n Washington S t a t e v i a t a n k e r s has g r e a t l y i n c r e a s e d the r i s k o f a c c i d e n t s r e s u l t i n g i n o i l s p i l l s , p a r t i c u l a r l y i n the wate r s s u r r o u n d i n g the San Juan I s l a n d s w hich l i e e n r o u t e t o C h e r r y P o i n t . T h i s t h e s i s i s concerned w i t h the development o f a model w h i c h w i l l y i e l d the ex p e c t e d number o f v e s s e l c o l l i -s i o n s c a l c u l a t e d from a computer s i m u l a t i o n o f marine t r a f -f i c f l o w p a t t e r n s . By s i m u l a t i n g a l t e r n a t i v e r o u t i n g schemes o f marine t r a f f i c f l o w and by f o r e c a s t i n g t h e i r r e s p e c t i v e i n c i d e n c e o f c o l l i s i o n , the model can be employed as a quan-t i t a t i v e t o o l i n the p l a n n i n g and i m p l e m e n t a t i o n o f c o l l i s i o n a v o idance r o u t e s . R o s a r i o S t r a i t l i e s on the e a s t e r n s i d e o f the i s -l a n d s . I t i s 20 m i l e s l o n g and v a r i e s i n w i d t h from 5 m i l e s to 1-1/2 m i l e s . The s t r a i t i s i n c o n s t a n t use by v e s s e l s ( f r e i g h t e r s , t a n k e r s , tows, commercial f i s h b o a t s , and p l e a s u r e c r a f t ) bound f o r B e l l i n g h a m , A n a c o r t e s , the San Juan I s l a n d s , and C h e r r y P o i n t . V e s s e l s bound f o r B. C. p o r t s , p a r t i c u l a r l y Vancouver and New W e s t m i n s t e r , o f t e n use R o s a r i o i n p r e f e r e n c e FIGURE 1 . 1 _ 2 . TANKER ROUTES 3. to Haro S t r a i t , (the passage on the west s i d e o f the San Juan I s l a n d s ) , when g r e a t e r advantage can be t a k e n o f t i d a l c u r r e n t s , which r u n up to 3.7 k n o t s . A l t h o u g h R o s a r i o S t r a i t has s u f f i c i e n t depth t o accommodate l a r g e v e s s e l s , p a r t i c u -l a r l y l a d e n t a n k e r s , i t s r o u t e i s f a r from s t r a i g h t and i t s waters c o n t a i n b o t h r o c k s and s h o a l s ; thus making i t s passage somewhat d i f f i c u l t f o r l a r g e r v e s s e l s to n a v i g a t e , e s p e c i a l l y i n poor v i s i b i l i t y . " ' " The a l t e r n a t i v e t a n k e r r o u t e from Juan de Fuca S t r a i t t o the r e f i n e r y at C h e r r y P o i n t i s t h r o u g h Haro S t r a i t t o Boundary P a s s , t h r o u g h the pass i n t o the G u l f o f G e o r g i a , and then a c r o s s the g u l f t o the r e f i n e r y . Because t h i s r o u t e i s r e l a t i v e l y wide, (a w i d t h o f 2 m i l e s a t i t s narrow-e s t p o i n t , l y i n g i n Boundary P a s s ) , and because i t i s r e l a -t i v e l y f r e e o f r o c k s and s h o a l s , i t s e r v e s the m a j o r i t y o f 2 s e a - g o i n g v e s s e l s bound f o r B. C. p o r t s . T h i s i s the p r o -posed d e p a r t u r e r o u t e from C h e r r y P o i n t . S i n c e 1948, t a n k e r s have grown i n s i z e from v e s s e l s of a modest 10,000 deadweight tons (dwt) to behemoths o f 500,000 or more deadweight t o n s . The v e s s e l s proposed f o r use i n the West Coast Run (Valdez t o C h e r r y P o i n t ) are p r i -m a r i l y i n the 120 thousand and 250 thousand dwt. c l a s s e s . C o n s i d e r i n g the s i z e o f t h e s e v e s s e l s and the r e l a t i v e l y narrow c h a n n e l s ( R o s a r i o S t r a i t ) i n which t h e y w i l l be t r a -v e l l i n g on the f i n a l l e g o f t h e i r j o u r n e y t o C h e r r y P o i n t , 4. major o i l s p i l l s appear imminent u n l e s s e v e r y e f f o r t i s made to reduce the r i s k o f c o l l i s i o n . A b r i e f d e s c r i p t i o n o f the m a n e u v e r a b i l i t y o f t a n k e r s proposed t o c a r r y the A l a s k a n o i l i s r e l e v a n t a t t h i s p o i n t . f A 250 thousand t o n (dwt) t a n k e r r e q u i r e s about 6 m i l e s i n which t o s t o p . In a c r a s h emergency s t o p , i t w i l l t r a v e l about two m i l e s , l o s i n g s t e e r i n g c o n t r o l v e r y q u i c k l y ( i n about 2 minutes i f c r a s h s t o p p i n g from 15 k n o t s ) and g e n e r a l l y ending up s t a r b o a r d o f the o r i g i n a l t r a c t , a t an an g l e to i t i n the o r d e r o f 90°. These v e s s e l s are not c o n s i d e r e d t o be under s t e e r a g e c o n t r o l f o r speeds o f l e s s than 5 k n o t s . In o r d e r t o a v o i d an o b s t a c l e o r an oncoming v e s s e l , t h e y r e q u i r e a p p r o x i m a t e l y 1 m i l e o f advance d i s t a n c e and about 630 f e e t of t r a n s f e r ( l a t e r a l d i s t a n c e ) i n o r d e r t o make a 30° change of h e a d i n g . I n open seas t h i s l a c k o f m a n e u v e r a b i l i t y i s o f l i t t l e consequence. But c o n s i d e r the event o f a f u l l y l a d e n 250 thousand (dwt.) t a n k e r e n c o u n t e r i n g an oncoming v e s s e l o f s i m i l a r s i z e on a c o l l i s i o n c o u r s e i n a narrow c h a n n e l d u r i n g c o n d i t i o n s o f poor v i s i b i l i t y . "A careful examination of c o l l i s i o n records reveals that c o l l i s i o n s occur, time after time, in the same geographic area, under the same weather conditions, and as a result of the same rule v i o l a t i o n s . " ^ The i n c i d e n c e o f o i l t a n k e r s b e i n g i n v o l v e d i n a c c i -d e n t s i s h i g h . They comprise l e s s t h a n 10% o f the w o r l d ' s s h i p p o p u l a t i o n and y e t a p p r o x i m a t e l y 25% o f the major marine a c c i d e n t s i n v o l v e t a n k e r s . ^ A c c o r d i n g t o a s u r v e y o f w o r l d -wide marine a c c i d e n t s , 33.7% o f a l l t a n k e r a c c i d e n t s are due to c o l l i s i o n s . ^ T h i s i s h i g h e r than any o t h e r s i n g l e c o n t r i -b u t o r i n c l u d i n g s t r a n d i n g s , w h i c h have d e c l i n e d . T h i s d e c l i n e was a t t r i b u t e d t o the use o f r a d a r w h i c h , i r o n i c a l l y , was a l s o e x p e c t e d to reduce c o l l i s i o n s . In N o r t h American w a t e r s , o n l y 7% o f c o l l i s i o n s o c c u r r e d i n the open sea whereas 13% o c c u r r e d i n c o n g e s t e d w a t e r s and, s u r p r i s i n g l y , 80% o f a l l c o l l i s i o n s o c c u r r e d i n p i l o t a g e w a t e r s such as R o s a r i o S t r a i t . LITERATURE REVIEW E x c e l l e n t j o u r n a l s e x i s t w hich c o v e r a l l a s p e c t s o f marine and a e r o n a u t i c a l n a v i g a t i o n . T o p i c s range from i n -depth d e s c r i p t i o n s o f d a t a s u r v e y s , t o d e s c r i p t i o n s o f h i g h l y s o p h i s t i c a t e d q u a n t i t a t i v e p r e d i c t i o n models, t o d i s c u s s i o n s on c o l l i s i o n a v o i d a n c e . The most s i n g u l a r l y comprehensive j o u r n a l on marine r e l a t e d s u b j e c t s appears t o be the m u l t i -n a t i o n a l J o u r n a l o f N a v i g a t i o n , p u b l i s h e d i n London, E n g l a n d , and sponsored by the R o y a l I n s t i t u t e o f N a v i g a t i o n . Conse-q u e n t l y , u n l e s s o t h e r w i s e s t a t e d , the a r t i c l e s r e f e r e n c e d i n t h i s r e v i e w a re p u b l i c a t i o n s o f t h i s j o u r n a l . A l t h o u g h marine s a f e t y i s the c o n c e r n o f eve r y m a r i -time n a t i o n , o n l y f i v e c o u n t r i e s appear t o be e x t e n s i v e l y engaged i n i t s r e s e a r c h . Norway and the N e t h e r l a n d s have made s i g n i f i c a n t c o n t r i b u t i o n s i n the areas o f p o r t and t e r -m i n a l n a v i g a t i o n c o n t r o l s but the m a j o r i t y o f c o r e r e s e a r c h on c o l l i s i o n s , c o l l i s i o n a v o i d a n c e systems, and t r a f f i c r egu-l a t i o n schemes has been c o n t r i b u t e d by E n g l a n d , Japan and the U.S.A. (which, i n c i d e n t a l l y , i s the l e a d i n g c o u n t r y i n a i r c o l l i s i o n r e s e a r c h ) . T h i s i s not s u r p r i s i n g c o n s i d e r i n g t h e s e f i v e c o u n t r i e s have e x t r e m e l y l a r g e m e r c a n t i l e n a v i e s . England and Japan, i n a d d i t i o n , have the most h i g h l y c o n g e s t e d w a t e r s i n the w o r l d . The r e l e v a n t l i t e r a t u r e can be d i v i d e d i n t o t h r e e 7. b a s i c c a t e g o r i e s : (1) D i s c u s s i o n s : - on r o u t i n g schemes and t r a f f i c l a n e s (2) S t a t i s t i c s : - s u r v e y s on t r a f f i c f l o w p a t t e r n s - d a t a on c o l l i s i o n s , b o t h raw and c a t e g o r i z e d - s t a t i s t i c a l a n a l y s i s o f t r a f f i c , c o l l i s i o n s , d e n s i t y d i s t r i b u t i o n s , and m e t e o r o l o g i c a l e f f e c t s ( 3 ) Q u a n t i t a t i v e Models Because o f the v a s t amount o f l i t e r a t u r e i n t h e a r e a of c o l l i s i o n a v oidance systems and because o f the r e p e t i t i o n o f much o f i t s c o n t e n t , o n l y the major a r t i c l e s most p e r t i n e n t to t h i s paper w i l l be r e v i e w e d . DISCUSSIONS There i s a p r o f u s i o n o f l i t e r a t u r e on s a f e t y i n marine n a v i g a t i o n . There are a r t i c l e s d i s c u s s i n g the m e r i t s o f new e l e c t r o n i c n a v i g a t i o n a l a i d s y , b o t h ashore and aboard s h i p , some o f which a re computer a s s i s t e d , ( s i m i l a r t o d e v i c e s now b e i n g used i n a v i a t i o n ) , and a l l o f which are e l e c t r o n i c c o l l i s i o n a v o i d a n c e systems. One such system i s a s e r i e s o f towers which p r o v i d e a complete r a d a r coverage o f a con g e s t e d a r e a o f water f o r the purpose o f m o n i t o r i n g t r a f f i c . T h i s system i s proposed f o r A d m i r a l t y I n l e t at the head o f Puget 7 Sound i n Washington S t a t e . Other a r t i c l e s d i s c u s s the e f f e c t s o f c o l l i s i o n a v o i d -8. ance systems such as s e p a r a t i n g and r o u t i n g t r a f f i c f l o w . A l t h o u g h the e f f e c t o f such systems has been t o reduce the number of marine' a c c i d e n t s , p a r t i c u l a r l y i n Dover S t r a i t o f the E n g l i s h Channel, the l i t e r a t u r e a l s o c o n t a i n s numerous d i s c u s s i o n s and p r o p o s a l s on how t o f u r t h e r reduce the i n c i -dence o f c o l l i s i o n u s i n g s e p a r a t i o n and r o u t i n g schemes. There are even a r t i c l e s a p p e a r i n g on c o s t - b e n e f i t a n a l y s i s 9 o f t h e s e systems. SURVEYS : 1 In F e b r u a r y o f 1971 an e x p l o r a t o r y s u r v e y o f marine t r a f f i c on the E n g l i s h .side o f the Dover S t r a i t was o r g a n i z e d and conducted by the N a t i o n a l P h y s i c a l L a b o r a t o r y o f the Department o f Trade and I n d u s t r y (U.K.). The s u r v e y showed t h a t f u r t h e r d a t a on t r a f f i c f l o w would be u s e f u l . Decca Radar L t d . d e c i d e d to c o n t i n u e the s t u d y and s o , i n March 1971, one o f t h e most e x t e n s i v e and s i g n i f i c a n t marine t r a f f i c s u r v e y s t o date was u n d e r t a k e n i n the n a r r o w e s t p a r t o f the Dover S t r a i t . B e a t t i e (1972) d e s c r i b e d the r e s u l t s o f t h i s s u r v e y w h i c h y i e l d e d d a t a on t h e volume, speed, d e n s i t y , and s e p a r a t i o n o f t r a f f i c i n the s t r a i t . I t a l s o e s t a b l i s h e d t h a t a p p r o x i m a t e l y 400 v e s s e l s move th r o u g h the Channel d a i l y . . U n t i l t h e n , i t had been thought t h a t between 800 and 1,000 v e s s e l s moved t h r o u g h d a i l y . F u j i i and Yamanouchi (1973) of the Japanese M i n i s t r y o f T r a n s p o r t d e s c r i b e d the d i s t r i b u t i o n o f c o l l i s i o n s i n Japan f o r the y e a r s 1966 t o 1968. They produced a c a t e g o r i z e d t a b l e f o r the number of v e s s e l s i n c o l l i s i o n and the number o f v e s s e l s e n t e r i n g Japanese Harbours. From the s t u d y t h e y deduced t h a t c o l l i s i o n danger and v e s s e l s i z e are c l o s e l y r e l a t e d . C. Grimes of the Defense O p e r a t i o n a l A n a l y s i s E s t a b -l i s h m e n t made a r a t h e r e x t e n s i v e s u r v e y o f marine a c c i d e n t s w i t h p a r t i c u l a r r e f e r e n c e t o t a n k e r s , (1973). The s t u d y was aimed at p r e d i c t i n g the f u t u r e f r e q u e n c y o f a c c i d e n t s l i k e l y t o r e s u l t i n p o l l u t i o n o f the U.Ki c o a s t l i n e . The s u r v e y c o v e r e d a l l marine a c c i d e n t s i n the N o r t h w e s t e r n European ar e a and a l l world-wide t a n k e r a c c i d e n t s f o r the y e a r s 1959 t o 1968 i n c l u s i v e . L l o y d s Weekly C a s u a l t y R e p o r t s were used as the p r i m a r y d a t a source i n the Survey. l£ i n d i c a t e d t h a t a c c i d e n t s due t o s t r a n d i n g had d e c r e a s e d s i g n i f i c a n t l y whereas c o l l i s i o n s c o n s t i t u t e d 47.21 o f a l l s h i p p i n g a c c i d e n t s i n N o r t h w e s t e r n European waters and 33.7% o f w o r l d - w i d e t a n k e r a c c i d e n t s . U n t i l 1971 most o f the e x t e n s i v e marine s u r v e y s were concerned w i t h t r a f f i c f l o w p a t t e r n s , the volume o f t r a f f i c , and the number o f v e s s e l c o l l i s i o n s f o r a g i v e n a r e a . Con-t i n u i n g c o l l i s i o n s i n the E n g l i s h Channel a f t e r the i m p o s i t i o n o f t r a f f i c - s e p a r a t i o n i n 1967 prompted i n v e s t i g a t i o n i n t o the 10. c i r c u m s t a n c e s b e h i n d c o l l i s i o n s and s t r a n d i n g s . Such a s u r v e y was performed by J . H. Wheatly of the N a t i o n a l P h y s i -c a l L a b o r a t o r y (1973). Data p e r t a i n i n g t o the e f f e c t s o f weather and t i d e on c o l l i s i o n s was c o l l e c t e d and s t u d i e d . E. R. Hargreaves of the Department of Trade and I n d u s t r y o f the U.K. (1973), upon f u r t h e r a n a l y s i s o f the d a t a g a t h e r e d by Wheatly, c o n c l u d e d t h a t 82% o f c o l l i s i o n s i n the E n g l i s h Channel o c c u r e d i n c o n d i t i o n s o f poor v i s i b i l i t y . In f a c t , t w o - t h i r d s o c c u r r e d i n t h i c k or dense f o g . By comparing c o l -l i s i o n s o c c u r r i n g b e f o r e and a f t e r the i n t r o d u c t i o n o f the 1967 r o u t i n g scheme, he deduced t h a t the p r o p o r t i o n o f head-on c o l l i s i o n s f e l l from 73% t o 62% o f the t o t a l , a r e d u c t i o n o f 21%. However, he a l s o found t h a t the number of c o l l i s i o n s i n v o l v e d i n o v e r t a k i n g s i t u a t i o n s had more than d o u b l e d t o 18% o f the t o t a l . These and numerous o t h e r s u r v e y s i n d i c a t e t h a t the g r e a t e s t s i n g l e c o n t r i b u t o r t o marine a c c i d e n t s i s c o l l i s i o n and t h a t the v a s t m a j o r i t y o f c o l l i s i o n s o c c u r i n p i l o t a g e or c o n gested w a t e r s . F r i c k e r o f the U. S. N a v a l Oceanographic O f f i c e , i n h i s a r t i c l e , " R e g i o n a l I n c i d e n c e o f C o l l i s i o n s " , ( V o l . 18 - 1965), s t a t e s t h a t 95, 93, and 88 per cent of a l l c o l l i s i o n s i n Europe, N o r t h A m e r i c a , and Japan, r e s p e c t i v e l y , o c c u r r e d i n p i l o t a g e or c o n g e s t e d w a t e r s . Surveys a l s o i n d i -c a t e t h a t the w o r l d s h i p p i n g p o p u l a t i o n i s i n c r e a s i n g a n n u a l l y a t a r a t e o f about 4% (Thompson - 1973) and t h a t the p r e s e n t t r e n d i n s h i p b u i l d i n g i s towards l a r g e r v e s s e l s w i t h g r e a t e r p a y l o a d s , ( i . e . , c o n t a i n e r cargo s h i p s and s u p e r - t a n k e r s ) . The i n c r e a s e d s i z e and speed o f t h e s e v e s s e l s has s i g n i f i c a n t l y i m p a i r e d t h e i r a b i l i t y t o maneuver and a v o i d c o l l i s i o n s , p a r t i c u l a r l y i n c o n g e s t e d w a t e r s . So, s i n c e 1967, r o u t i n g schemes have been s t u d i e d q u i t e e x t e n s i v e l y i n marine t r a f f i c e n g i n e e r i n g . A l t h o u g h the shipowner's views on t r a f f i c r e -g u l a t i o n have not a l l been f a v o u r a b l e , the s u r v e y s and the s t a t i s t i c a l s t u d i e s do show t h a t a s i g n i f i c a n t r e d u c t i o n i n c o l l i s i o n s has o c c u r r e d s i n c e the i m p l e m e n t a t i o n o f r o u t i n g and t h e y f u r t h e r suggest t h a t e n f o r c e d d i r e c t i o n a l r o u t i n g 11 w i l l f u r t h e r reduce the number o f c o l l i s i o n s . QUANTITATIVE MODELS Rese a r c h i n marine t r a f f i c e n g i n e e r i n g has converged t o one p a r t i c u l a r a r e a o f i n t e r e s t , t h a t o f c o l l i s i o n s ; how t o p r e d i c t them and how t o reduce them. The a v a i l a b i l i t y o f f d a t a on f l o w p a t t e r n s , t r a f f i c d e n s i t y , v e s s e l speeds, c o l l i -s i o n c i r c u m s t a n c e s , e t c . , has s t i m u l a t e d more t h e o r e t i c a l r e s e a r c h . M a t h e m a t i c a l models are b e i n g d e s i g n e d and b u i l t w h i c h , when i n p u t t e d w i t h the p r o v i d e d d a t a , can be used t o f o r e c a s t c o l l i s i o n s and, c o n s e q u e n t l y , be used i n t u r n as q u a n t i t a t i v e t o o l s i n d e c i s i o n making. Many o f the g u i d e l i n e s have been l a i d out by r e s e a r c h i n a i r t r a f f i c e n g i n e e r i n g . A l t h o u g h many a r t i c l e s on model b u i l d i n g f o r marine t r a f f i c e n g i n e e r i n g are a v a i l a b l e , n o t h i n g appears t o have been p u b l i s h e d i n the a r e a o f computer s i m u l a t i o n , per se. However, t h e r e are a n a i o g models, such as Draper and B e n n e t t ' (to be d e s c r i b e d ) which use computers t o r e a d d a t a i n p u t , p e r f o r m programmed c a l c u l a t i o n s , and p r i n t the r e s u l t s . T h i s r e v i e w w i l l b r i e f l y d e s c r i b e f o u r models, w h i c h are mathema-t i c a l , and a l l o f which were r e l e v a n t i n the b a s i c d e s i g n o f the computer s i m u l a t i o n model d e s c r i b e d l a t e r i n t h i s paper. J . Draper and C. B e n n e t t (Department o f Trade and I n d u s t r y Management S e r v i c e s /OR) i n t h e i r a r t i c l e " M o d e l l i n g Encounter Rates i n M a r i n e T r a f f i c Flows w i t h P a r t i c u l a r A p p l i c a t i o n t o the Dover S t r a i t " , ( V o l . 25, 1972) d e s c r i b e an a n a l o g model developed by the O p e r a t i o n s R esearch U n i t i n the Department o f Trade and I n d u s t r y (U.K.) whose o v e r a l l aim was t o reduce the i n c i d e n c e o f c o l l i s i o n i n the Dover S t r a i t . The model a s s e s s e d the l i k e l y e n counter r a t e s i n d i f f e r e n t areas of the Dover S t r a i t f o r v a r i o u s p a t t e r n s o f t r a f f i c f l o w . An encounter was d e f i n e d t o o c c u r when two s h i p s passed w i t h i n a s p e c i f i e d d i s t a n c e o f each o t h e r , say 1/2 n a u t i c a l m i l e . The s h i p s were c o n s i d e r e d t o be t r a v e l -l i n g i n p a r a l l e l p a t h s t o each o t h e r and w i t h c o n s t a n t v e l o -c i t y . ; The f o l l o w i n g t a b l e d e s c r i b i n g the r e s u l t s o f the 13. model, was e x t r a c t e d from the Draper and Bennett a r t i c l e . TABLE 1.1 Comparison o f Observed and C a l c u l a t e d E n c o u n t e r s per Hour per Square N a u t i c a l M i l e Areas o f Area A r e a A r e a A r e a A r e a Dover S t r a i t A B C D E ' Observed Rate 0.033 0.044 0.029 0.076 0.072 C a l c u l a t e d Rate 0.027 0.048 0.031 0.073 0.160 The g e n e r a l f i n d i n g o f the model was t h a t the head-on encounter r a t e i s d i r e c t l y p r o p o r t i o n a l t o the p e r c e n t a g e o f t r a f f i c t r a v e l l i n g a g a i n s t the main stream. G. May, i n h i s a r t i c l e "A Method f o r P r e d i c t i n g the Number o f Near M i d - A i r C o l l i s i o n s i n a D e f i n e d A i r s p a c e " , ( O p e r a t i o n s R e s e a r c h Q u a r t e r l y , V o l . 22, No. 3, Sept. 1971, pp.237-252) proposed a method f o r c a l c u l a t i n g the number o f NMAC's (Near M i d - A i r C o l l i s i o n s ) o r c o l l i s i o n e n c o u n t e r s t h a t c o u l d be expected i n a column o f a i r s p a c e about which t r a f f i c p a t t e r n s are known. May assumed t r a f f i c t o be a t l e v e l f l i g h t and d e f i n e d an NMAC to have o c c u r r e d when two a i r c r a f t came w i t h i n a s p e c i f i e d d i s t a n c e o f each o t h e r . T h e i r d i s t a n c e s , i n the h o r i z o n t a l and v e r t i c a l d i r e c t i o n s , were c a l l e d h o r i z o n t a l near miss d i s t a n c e M, , and v e r t i c a l near miss d i s t a n c e M . n v 14. A volume of a i r about each a i r c r a f t c a l l e d the "near miss volume" was d e s c r i b e d to be c y l i n d r i c a l i n shape, o f r a d i u s M^, and h e i g h t 2M v. FIGURE 1.2 Near M i s s Volume or Encounter Volume May c o n s i d e r e d two a i r c r a f t a t p o i n t s ( x ^ , y^, z^) and (X2, Y2 > ~-n a § i v e n volume, h a v i n g v e l o c i t i e s o f V" and V~ r e s p e c t i v e l y , and hence a r e l a t i v e v e l o c i t y o f V He c o n s i d e r e d the second a i r c r a f t as f i x e d and hence r I -> the f i r s t as h a v i n g a v e l o c i t y o f V r which was, i n r e a l i t y , r e l a t i v e t o t h e second a i r c r a f t . In a time i n t e r v a l , t h e f i r s t a i r c r a f t would move a d i s t a n c e o f V t , which was, a g a i n , r e l a t i v e to the second. T h i s meant t h a t a l l m o tion was con-15. s i d e r e d t o occur as a r e s u l t o f the f i r s t a i r c r a f t ' s movement a l o n e , s i n c e the second was c o n s i d e r e d as immovable. As the f i r s t a i r c r a f t moved w i t h v e l o c i t y V" , he deduced each p o i n t i n the Near M i s s Volume a l s o moved f o r w a r d a d i s t a n c e o f V . r t and so the t o t a l n e a r - m i s s volume swept out i n the time i n t e r -v a l t was 4M,M V . . h v r t FIGURE 1.3 E f f e c t i v e NMAC Volume May c o n c l u d e d t h a t i f the p r o b a b i l i t y o f the second a i r c r a f t b e i n g a t any p o i n t ( x , y, z) i n space a t any time was p ( x , y, z ) d x d y d z , t h e n the p r o b a b i l i t y o f an NMAC o c c u r -r i n g between the two a i r c r a f t i s : 16. p ( x , y , z ) d x d y d z where V o l = 4M,M V h i r Y a h e i F u j i i , w i t h Japanese M i n i s t r y o£ T r a n s p o r t ' s E l e c t r o n i c N a v i g a t i o n L a b o r a t o r y , and R e i j i r o S h i o b a r a , a member o f the Japanese A s s o c i a t i o n f o r P r e v e n t i n g Sea C a s u a l -t i e s , c r e a t e d a m a t h e m a t i c a l model which i s t h e o r e t i c a l l y s i m i l a r t o t h a t o f May's. In a paper "The A n a l y s i s o f T r a f f i c A c c i d e n t s " , ( V o l . 24, 1972) they d e s c r i b e t h e i r model which i s c a p a b l e o f c a l c u l a t i n g c o l l i s i o n r a t e s upon th e i n p u t o f t r a f f i c d a t a . They assumed two groups o f v e s s e l s o f the same s i z e L^ and L2 and the same v e l o c i t i e s V^ and V2 to be s a i l i n g i n random c o u r s e s . They proposed t h a t the number o f c o l l i s i o n s w i t h a s h i p b e l o n g i n g t o the f i r s t group i n u n i t time i s e q u a l to the number of v e s s e l s b e l o n g i n g t o the second group w i t h i n the a r e a swept out i n u n i t time by the f i g u r e e n c l o s e d by d o t t e d l i n e s w h i l e i t moves w i t h speed j ^ - ^ l * FIGURE 1.4 C o l l i s i o n E n c l o s u r e A r e a The number o f c o l l i s i o n s t hey t h e r e f o r e proposed was: D P 2 l V ^ I where p i s the t r a f f i c d e n s i t y and D i s the g e o m e t r i c a l c o l -l i s i o n d i a m e t e r . Hence, t h e y c o n j e c t u r e d the c o l l i s i o n number, N c o ^ , i n a time i n t e r v a l T to be: N c o l = P l P 2 D l V ^ 2 l S T where S i s the a r e a o f the waterway under c o n s i d e r a t i o n . S i n c e b o t h groups were assumed t o be s a i l i n g on r a n -dom c o u r s e s , F u j i i and S h i o b a r a next i n t r o d u c e d the concept o f p r o b a b i l i t y and r e w r o t e t h e i r e q u a t i o n f o r the more gen-e r a l case o f m groups o f v e s s e l s : where P i s the p r o b a b i l i t y f a c t o r . The term PD, d e f i n e d as the c o l l i s i o n d i a m e t e r , i s a f u n c t i o n o f the s i z e o f v e s s e l s ( p a r t i c u l a r l y l e n g t h ) and the a n g l e between c o u r s e s . The d e n s i t y p i s o b t a i n e d e i t h e r d i r e c t l y from r a d a r photos or from the t r a f f i c volume Q and v e l o c i t y V. 18. Q = \ " pVdx or a p p r o x i m a t e l y Q = pVW, where Oo W i s the w i d t h o f the waterway. The f o u r t h model t o be r e v i e w e d i s s i m i l a r t o Draper and B e n n e t t ' s a n a l o g model i n t h a t i t i s a l s o a p a r a l l e l p a t h encounter model. I t s development was m o t i v a t e d by the growing c o n c e r n o f a p o s s i b l e major o i l s p i l l i n the Puget Sound a r e a . The l i k e l i h o o d o f t h i s was i n c r e a s e d by the i n t r o d u c t i o n o f a d d i t i o n a l t a n k e r s , p a r t i c u l a r l y s u p e r t a n k e r s , t r a n s p o r t i n g A l a s k a n o i l t h r o u g h t h e s e w a t e r s . R e s e a r c h f o r the model was sponsored by the Honeywell M a r i n e Systems Center i n S e a t t l e , Washington, (hence the model w i l l h e r e a f t e r be r e f e r r e d t o as the Honeywell M o d e l ) , and the model was d e s i g n e d i n 1971 by D a v i d E. Wentzel o f Honeywell and by Dr. Dean L y t l e o f the U n i v e r s i t y o f Washington i n S e a t t l e . S i n c e the development of the computer s i m u l a t i o n model proposed i n t h i s paper r e l i e s to a l a r g e e x t e n t on the t h e o r y used i n d e v e l o p i n g t h e Honeywell model, i t s d e s c r i p t i o n " w i l l be s l i g h t l y more d e t a i l e d . The Honeywell P a r a l l e l - P a t h model r e p r e s e n t s a s h i p -p i n g c h a n n e l i n w h i c h v e s s e l p a t h s are e s s e n t i a l l y p a r a l l e l . Wentzel and L y t l e assumed t h a t s h i p s m a i n t a i n e d a c o u r s e p a r -a l l e l t o the c e n t e r l i n e o f the c h a n n e l and hence c o u l d be r e -p r e s e n t e d by a s i n g l e v a r i a b l e w h i c h was the d i s t a n c e from the c e n t e r l i n e . T h i s v a r i a b l e was c o n s i d e r e d t o be random and was sp e c i f i e d by a p r o b a b i l i t y density function. They also assumed a common density function, p , for a l l inbound ves-sels and p for a l l outbound ships. An inbound ship with path Xj and an outbound ship with path Y^ were considered to have created a c o l l i s i o n p o t e n t i a l , ( c o l l i s i o n potentials due to vessels being overtaken by faster ships were not con-sidered) , i f they were i n the channel simultaneously and i f : l* rY k|<c where c i s the necessary clearance. FIGURE 1.5 I 0 „ CEN1ERUNE I x-c CHANNEL Then assuming that X and Y were independent random variables, the p r o b a b i l i t y of a potential c o l l i s i o n would be w x+c q = p[|X.-Y k|<c] = C Z p x C x ) [ C P y (y)dy]dx ^x-c Wentzel and L y t l e then assumed t h a t X and Y were u n i f o r m l y d i s t r i b u t e d over the cha n n e l w i d t h W. Thus: p x ( x ) = ^ = p y ( y ) q = p l I X j - Y j ^ c ] W of r x + c w m ,X+c z '*-<= w w X+c dydx W' ' W w^  0 w 2c W Next they l o o k e d a t the number o f s h i p s i n the chan-n e l . They d e c i d e d t h a t g i v e n an average o f N/2 inbound and N/2 outbound s h i p s p e r u n i t o f t i m e , t h e y c o u l d assume t h a t the a r r i v a l times at the c h a n n e l e n t r a n c e s t o be independent P o i s s o n p r o c e s s e s . I f T, the t r a n s i t time i n the c h a n n e l , i s the same f o r each s h i p , t h e n they deduced t h a t the number o f s h i p s passed by each s h i p i n the ch a n n e l i s a P o i s s o n random v a r i a b l e w i t h parameter X=nT. Now the expected number of s h i p s t o be passed by any one s h i p t r a v e l l i n g i n the op-p o s i t e d i r e c t i o n i s : oo = nT 22 . Hence t h e r e are ^ i n b o u n d s s h i p s , each o f wh i c h passes an average o f u=NT outbound so t h a t the t o t a l number o f s h i p s passed i s : rN, _ N 2T Cj) (NT) = tLf 2 N T Each o f the —^— en c o u n t e r s has a p r o b a b i l i t y q o f b e i n g on a p o t e n t i a l c o l l i s i o n p a t h . Thus, the ex p e c t e d number o f p o t e n t i a l c o l l i s i o n s p e r y e a r i s : r _ r N 2 T . . . 1 _ N 2T n where C = expected number o f c o l l i s i o n s p e r y e a r N = number o f s h i p movements per y e a r W = c h a n n e l w i d t h i n n a u t i c a l m i l e s K = 8760 hours p e r y e a r But s i n c e T = L/V where L = c h a n n e l l e n g t h i n n a u t i c a l m i l e s V = s h i p v e l o c i t y Wentzel and L y t l e deduced t h a t : c = q 2KV W~ N 2 L c KVW They then used a f i g u r e f o r p ( p r o b a b i l i t y o f a c o l -l i s i o n ) d e v e l o p e d by the S p e r r y Piedmont Company u s i n g the t h e r e were 6700 p o t e n t i a l c o l l i s i o n s p e r a c t u a l c o l l i s i o n . Thus, the e x p e c t e d number o f c o l l i s i o n s p e r y e a r was c a l c u -l a t e d t o be: E[KJ = Cp = N z L c . _JL • KVW 6700 The model, when i n p u t t e d w i t h the a p p r o p r i a t e d a t a f o r Puget Sound waters over the t e n y e a r p e r i o d from 1960 t o 1970, c a l c u l a t e d the e xpected number o f c o l l i s i o n s per y e a r t o be 0.476, o r , i n o t h e r words, t h e r e s h o u l d have been 4.76 c o l l i s i o n s i n t h a t time p e r i o d . As a m a t t e r o f c o m p a r i s o n , r e s e a r c h v e r i f i e d t h a t f o u r c o l l i s i o n s had a c t u a l l y o c c u r r e d i n Puget Sound w a t e r s over t h e same time p e r i o d . E n g l i s h Channel i n a s i m i l a r c h a n n e l model. 12 In t h i s s t u d y 24. FOOTNOTES 1. Canadian H y d r o g r a p h i c S e r v i c e , B r i t i s h Columbia - Race  Rocks t o E a s t P o i n t , (Ottawa, 1973) , C h a r t #3449. 2. Canadian H y d r o g r a p h i c S e r v i c e , B r i t i s h Columbia - E a s t  P o i n t t o Sand Heads, (Ottawa, 1973), Chart #3450. 3. A. G. Dunne, C o l l i s i o n s and Groundings, J o u r n a l o f N a v i -g a t i o n , V o l . 25, No. 1, M. W. R i c h e y ^ ed., (London, Eng-l a n d : John Murray L t d . , 1972), p. 113. 4. F. W. F r i c k e r , R e g i o n a l I n c i d e n c e o f C o l l i s i o n , J o u r n a l o f N a v i g a t i o n , V o l . 18, No. 2, M. W. R i c h e y , ed., (London, England: John Murray L t d . , 1965), p. 163. 5. Roger A. P e t e r s o n , " O p e r a t i o n a l Hazards and t h e C o n t r o l o f O i l Tankers i n the V a l d e z - C h e r r y P o i n t Route", (un-p u b l i s h e d w o r k i n g paper f o r the C e n t e r o f T r a n s p o r t a t i o n S t u d i e s , U n i v e r s i t y o f B r i t i s h C olumbia, 1974), p. 1. 6. C. Grimes, A Survey o f M a r i n e A c c i d e n t s w i t h P a r t i c u l a r  R e f e r e n c e to~~Tankers, J o u r n a l o f N a v i g a t i o n , V o l . 25~, No. 4, M. W. R i c h e y , ed., (London, England: John Murray L t d . , 1972), p. 499. 7. The Vancouver Sun, A p r i l 9, 1974, S e c t . I , p. 2, c o l s . 4-9. 8. J . D r a p e r , C. B e n n e t t , M o d e l l i n g Encounter Rates i n Marine  T r a f f i c Flows w i t h P a r t i c u l a r A p p l i c a t i o n t o Dover S t r a i t , J o u r n a l o f N a v i g a t i o n , V o l . 25, No. 3, M..W. R i c h e y , ed., (London, England: John Murray L t d . , 1972), pp. 381-382. 9. A. S t r a t t o n , W. E. S i l v e r , O p e r a t i o n a l R e s e a r c h and Cost  B e n e f i t A n a l y s i s on N a v i g a t i o n w i t h P a r t i c u l a r R e f e r e n c e t o M a r i n e A c c i d e n c e , J o u r n a l o f N a v i g a t i o n , V o l . 23, No. 3, M. W. R i c h e y , ed. ("London, England: John Murray L t d . , 19 7 0 ) , pp. 325-340. | 10. R. B. Adams, A Shipowners' View o f T r a f f i c R e g u l a t i o n , J o u r n a l o f N a v i g a t i o n , V o l . 25, No. 4, M. W. R i c h e y , ed., (London, England: John Murray L t d . , 1972), pp. 467-482. 11. Draper and B e n n e t t , op. c i t . , p,. 382. 2 5 . 12. Sperry Piedmont Company, Final Report, Lookout Ass i s t  Device F e a s i b i l i t y Studies, Volumes I and II, Maritime Administration Contract M.A.-3374, 1965, c i t e d i n David E v Wentzel, Dean Lyt l e , PH.D., Automated Marine T r a f f i c  Advisory Systems, Their Needs and Implementation, 1971, Honeywell Marine Systems Center, Document 2330, p. 11. 26. CHAPTER I I THE MODEL DEVELOPMENT OF THE MODEL The a b i l i t y o f h i g h speed computers t o execute r e l a -t i v e l y s o p h i s t i c a t e d programmes t h a t a n a l y z e l a r g e volumes of d a t a has c o n t r i b u t e d t o the development o f models which enable a much more dynamic approach t o problem s o l v i n g . H i g h -l y complex problems i n v o l v i n g many v a r i a b l e s can be a n a l y z e d w i t h g r e a t e r ease and d i v e r s i t y . O f t e n i n " r e a l w o r l d " p r o -blem s o l v i n g , h i g h l y q u e s t i o n a b l e assumptions must be made i n o r d e r t o s a t i s f y c e r t a i n t h e o r e t i c a l c o n d i t i o n s which are n e c e s s a r y b e f o r e m a t h e m a t i c a l a n a l y s i s can be employed. Such assumptions can d e t r a c t from the v a l i d i t y o f a s o l u t i o n s i n c e t hey t e n d t o o v e r - s i m p l i f y t he problem. By s i m u l a t i n g " r e a l w o r l d " phenomena fewer assumptions need be made. Con-s e q u e n t l y ,computer s i m u l a t i o n models are o f t e n more f l e x i b l e and o f t e n a t t a i n a h i g h e r degree o f r e a l i s m r e s u l t i n g i n more g e n e r a l s o l u t i o n s w i t h g r e a t e r v a l i d i t y . The development o f the computer s i m u l a t i o n model t o be d e s c r i b e d i n t h i s c h a p t e r r e l i e s t o a l a r g e e x t e n t on the work o f Wentzel and L y t l e i n d e v e l o p i n g the Honeywell Model. U s i n g t r a f f i c f l o w d a t a , the computer model s i m u l a t e s v e s s e l s t r a v e l l i n g i n p a r a l l e l p a t h s t h r o u g h a c h a n n e l . The number o f head-on c o l l i s i o n s w h i c h can be e x p e c t e d t o o c c u r i n the c h a n n e l over a g i v e n time p e r i o d i s c a l c u l a t e d from the number of s i m u l a t e d s h i p e n c o u n t e r s . U n l i k e the Honeywell model, wh i c h o f f e r s o n l y an aggregate number o f expected c o l l i s i o n s , the s i m u l a t i o n model c a t e g o r i z e s the e n c o u n t e r s among v e s s e l t ypes so as t o y i e l d an e s t i m a t e on the e x p e c t e d number o f t a n k e r c o l l i s i o n s w hich i s more s e n s i t i v e t o the o b s e r v e d t r a f f i c p a t t e r n s . The Honeywell Model assumes t h a t i t s c h a n n e l , Puget Sound, has a u n i f o r m w i d t h a l o n g i t s e n t i r e l e n g t h . A b r i e f g l a n c e a t the map i n Chapter One w i l l i n d i c a t e t h a t t h i s i s g e n e r a l l y not t r u e . In the s i m u l a t i o n model, the p a r t i c u l a r s t r a i t or c h a n n e l i s d i v i d e d i n t o a f i n i t e number o f segments, depending upon topography. Each segment r e p r e s e n t s a p a r t i -t i o n o f the s t r a i t o r c h a n n e l which has a r e l a t i v e l y u n i f o r m w i d t h and i n which a v e s s e l can t r a v e l i n a s i n g l e n a v i g a t i o n a l c o u r s e or b e a r i n g . That i s t o say, no c h a n n e l i n the s i m u l a -t i o n model w i l l c o n t a i n a segment i n which a v e s s e l has t o make a s i g n i f i c a n t change i n i t s c o u r s e or b e a r i n g . Such p o i n t s i n the s t r a i t , c h a n n e l or p a s s , w i l l s i g n i f y the be-g i n n i n g o f a new segment i n the model. The Honeywell Model makes no p r o v i s i o n f o r v e s s e l s which t r a v e l t h r o u g h o n l y a p o r t i o n o f the c h a n n e l . Such v e s s e l s might e n t e r a t one end and d e p a r t b e f o r e r e a c h i n g the 28. o p p o s i t e end, or s i m i l a r l y , might e n t e r the c h a n n e l at some i n t e r m e d i a t e p o i n t . Such i s the case i n R o s a r i o S t r a i t , where t r a f f i c d e s t i n e d f o r B e l l i n g h a m must d e p a r t from the S t r a i t about m i d - p o i n t . T h i s poses no d i f f i c u l t y i n the s i -m u l a t i o n model s i n c e a v e s s e l need o n l y t r a v e l t h r o u g h the n e c e s s a r y number of segments i n o r d e r to r e a c h i t s ^ d e s t i n a t i o n ; o r , c o n v e r s e l y , e n t e r a segment o f the channel which l i e s mid-way between e i t h e r end. •The Honeywell Model a l s o assumes t h e r e i s , on an average, an e q u a l number o f inbound and outbound v e s s e l s i n the c h a n n e l per u n i t o f t i m e . S i n c e the number o f head-on v e s s e l e n c o u n t e r s i s p r o p o r t i o n a l t o the number o f v e s s e l s i n the c h a n n e l t r a v e l l i n g i n o p p o s i t e d i r e c t i o n s i n any g i v e n time u n i t , t h i s assumption i s q u e s t i o n a b l e . The Decca Radar s u r v e y v e r i f i e s t h a t t r a f f i c volume d e f i n i t e l y v a r i e s from hour to hour depending on the d i r e c t i o n . C o n s e q u e n t l y , i f no t r a f f i c appears i n a p a r t i c u l a r d i r e c t i o n over a f i x e d time p e r i o d , t h e r e w i l l be no head-on en c o u n t e r s (and hence no head-on c o l l i s i o n s ) , d u r i n g t h a t time p e r i o d r e g a r d l e s s of the volume o f t r a f f i c f l o w i n g i n the o p p o s i t e d i r e c t i o n . T h i s assumption need not be made i n the s i m u l a t i o n model. Data on i n t e r - a r r i v a l times and volume a r r i v a l r a t e s f o r the p a r t i c u l a r c h a n n e l can be programmed d i r e c t l y i n t o the model, a l l o w i n g i t to generate e n t r y o f v e s s e l s i n t o the c h a n n e l a t the a p p r o p r i a t e times so t h a t the a c t u a l t r a f f i c f l o w i s s i m u l a t e d . F u r t h e r , the Honeywell Model assumes t h a t T, the t r a n s i t time i n the c h a n n e l , i s the same f o r each v e s s e l . T h i s i s not t r u e . In p i l o t a g e w a t e r s , a c c o r d i n g t o the Department of T r a n s p o r t ' s M arine T r a f f i c C o n t r o l (Canada), t a n k e r s and f r e i g h t e r s t r a v e l a t speeds of a p p r o x i m a t e l y e i g h t t o t w e l v e k n o t s , depending on v i s i b i l i t y and c o n g e s t i o n , whereas tows t r a v e l at speeds r a n g i n g from t h r e e t o s i x k n o t s , depending on t h e s i z e o f the tow and the t i d e . S i n c e the number of v e s s e l s i n the c h a n n e l t r a v e l l i n g i n e i t h e r d i r e c -t i o n , a t any g i v e n t i m e , i s a f u n c t i o n o f v e s s e l t r a n s i t t i m e , w h i c h i n t u r n i s a f u n c t i o n o f v e s s e l v e l o c i t y , t h i s assump-t i o n tends to o v e r s i m p l i f y the a n a l y s i s by d i s r e g a r d i n g the v a r i a b i l i t y o f v e l o c i t i e s . However, the computer model r e -c o r d s the v e l o c i t y o f each v e s s e l e n t e r i n g the c h a n n e l e n a b l i n g the model t o s i m u l a t e the a c t u a l t r a n s i t time o f the v e s s e l i n the c h a n n e l . T h i s i s a c c o m p l i s h e d by a s s i g n i n g a v a l u e , which i n d i c a t e s the speed o f the v e s s e l , t o a s p e c i f i c p a r a -meter of each t r a n s a c t i o n i n the model. These t r a n s a c t i o n s g e n e r a t e d by the model s i m u l a t e the a c t u a l v e s s e l s i n the c h a n n e l . 30. THE SIMULATION LANGUAGE The computer language used to run the model was GPSS-V (General Purpose Simulation Systems V-IBM). The fea-tures of the language made i t an ideal choice. GPSS i s a transaction-oriented language. That i s , the special features of this language enable the analyst to describe d i r e c t l y the functional flow of items (vessels) through the system (the channel). In this respect the language i s quite d i f f e r e n t from a multipurpose language such as FORTRAN. In a FORTRAN simulation, the model i s usually written in a state-change form. The required changes ,are made into the values of v a r i -ables affected by the stage change. Flows of items (trans-actions) are not described d i r e c t l y by the language. An additional feature of the language which makes i t further compatible to a n a l y t i c a l models simulating flow pat-terns i s the a b i l i t y of the language to automatically maintain s t a t i s t i c s . This in t e r n a l feature of the language can greatly reduce programme size and complexity. The general p r i n c i p l e s of the GPSS-V have been ex-tracted from the IBM User's Manual and appear below: "Block diagrams or flow diagrams are widely used to describe the structure of systems. They consist of a series of blocks, each of which des-cribes., some step in the action of the system. Lines which j o i n the blocks i n d i c a t e the flow of t r a f f i c through the system, or describe the se-quence of events to be carried out. A l t e r n a t i v e courses of action that a r i s e in the system are represented by having more than one l i n e leaving a block. Conversely, one block may have several l i n e s entering i t to represent the fact that t h i s block i s a common step in two or more sequences of events. The choice of path, where ah alterna-time i s offered, may be a p r o b a b i l i s t i c event or a l o g i c a l choice, depending upon the state of the system at the time of the choice. Both of these methods of s e l e c t i o n can be used in the GPSS pro-gram. The units of t r a f f i c that move through the system depend upon the system being simulated. Units might be messages in a communication system, e l e c t r i c a l pulses in a d i g i t a l c i r c u i t , work items in a production l i n e , or any number of other units. These units upon which the system operates in the GPSS program w i l l be called "transactions". The GPSS program also has various other e n t i t i e s ( f a c i -l i t i e s , storages, queues, tables, etc.) whose at-t r i b u t e s are changed by the movement of transactions through the various block types. Although a block diagram i s a commonly used means of describing a system, the notation used in normal block diagrams depends upon the system and the person who i s describing the system. For the purpose of the GPSS program, certain conventions and systems concepts have been defined, each cor-responding to some basic action or condition that generally occurs in systems. S t a t i s t i c a l v a r i a t i o n s may be introduced in the block diagram, and many s t a t i s t i c a l sampling procedures are provided. Levels of p r i o r i t y may be assigned to transactions and com-plex l o g i c a l decisions may be made during the simu-l a t i o n . The GPSS program operates by moving tranactions from block to block of the simulation model in a manner s i m i l a r to the way in which the units of traf-f i c they represent progress in the real system. Each such movement i s an event that i s due to occur at some point in time. The GPSS program maintains a record of the times at which these events are due to_ occur,'- then proceeds by executing the event in t h e i r ' correct time sequence. When transactions are blocked and cannot move at the time they should, the program moves them as soon as the blocking con-d i t i o n or conditions change. In order to maintain the events in the cor-rect time sequence, the GPSS program simulates a clock that i s recording the instant of time that has been reached in the model of the real system. The number shown by t h i s clock at. any instant i s referred to as the "absolute clock time". Another clock time, the " r e l a t i v e clock time" i s one of the Standard Numerical A t t r i b u t e s which can be exter-n a l l y addressed by the analyst. A l l times in the simulation model are given as integral numbers. The unit of system time which i s represented by a unit change of clock time i s implied by the user3 who enters a l l data r e l a t i n g to times in terms of the time unit he has selected. Whatever unit of time i s chosen, such as millisecond or tenth of an hour, i t must be used c o n s i s t e n t l y throughout a simulation model. The GPSS program does not simulate the system at each successive i n t e r v a l of time. Instead, i t updates the absolute clock to the time at which the next most imminent event i s to occur. The control-l i n g factor in the amount of computing time that i s used by the program i s , therefore, the number of events to be simulated, not the length of real-sys-tem time over which the simulation i s being made".-. The time u n i t s o f the R o s a r i o S t r a i t s i m u l a t i o n model are m i n u t e s . The u n i t was used because o f t r a n s i t time o f v e s s e l s i n the system. For example, a t a n k e r t r a v e l l i n g a t 10 k n o t s would have t a k e n a p p r o x i m a t e l y 21 minutes t o t r a n s i t a c h a n n e l segment w h i c h was 3 1/2 n a u t i c a l m i l e s l o n g . DATA GATHERING Published data on the number of tanker, f r e i g h t e r , and large movements through Rosario S t r a i t , Haro S t r a i t , and Boundary Pass, i s non-existent. Although the U. S. Coast Guard Service offered estimates on the annual aggre-gate volume of t r a f f i c flowing through Rosario S t r a i t , they had no records of d a i l y movements. The Ports of Seattle and Bellingham only maintain records of port t r a f f i c and tonnage and could offer no information about Rosario S t r a i t . As a matter of fa c t , Bellingham Port Authorities suggested that estimates might be obtained from the l o c a l tow-boat companies. These companies, contacted by telephone, offered the following data: Rosario S t r a i t Through-movements: - 16 Cherry Point tankers per month (8 each way) 8 freighters per month (4 each way) Bellingham T r a f f i c : 4 freighters per month (2 each way) Barges: from Seattle, 3 per week in and out from Vancouver and V i c t o r i a - 4 per week in and out. These estimates appear to be r e l a t i v e l y accurate. In 1971, the U. S. Dept. of Commerce, Bureau of the Census, published that a t o t a l of 704 vessels entered and c l e a r e d B e l l i n g h a m Customs."' I f 2 f r e i g h t e r s e n t e r B e l l i n g -ham per month, then the number o f r e s u l t i n g Customs e n t r i e s and c l e a r a n c e s s h o u l d be a p p r o x i m a t e l y 50 per y e a r . S i m i -l a r l y , assuming t h a t most of the l a r g e t a n k e r s would a l s o be r e q u i r e d t o e n t e r and c l e a r t h r o u g h customs, t h i s would r e -s u l t i n an a d d i t i o n a l s t a t i s t i c o f a p p r o x i m a t e l y 700 per y e a r . A l t h o u g h the comparison between the suggested d a t a and the census f i g u r e s may not be t o t a l l y v a l i d , i t does i n d i c a t e t h a t the f i g u r e s on d a i l y movements are a c c e p t a b l e . Data on v e s s e l movements th r o u g h b o t h Haro S t r a i t and Boundary Pass was o b t a i n e d from the Department o f Trans-p o r t ' s (DOT) M a r i n e S e r v i c e s . S i n c e no p u b l i s h e d f i g u r e s on v e s s e l movements i n west c o a s t waters are y e t a v a i l a b l e , t h i s d a t a i s a l s o an e s t i m a t e . The head o f the DOT's r e c e n t l y formed M a r i n e T r a f f i c C o n t r o l i n Vancouver, C a p t a i n Johns, e s t i m a t e d t h a t 40 deep sea and c o a s t a l v e s s e l s pass t h r o u g h Haro S t r a i t and Boundary Pass d a i l y . He c o u l d o f f e r no break-down w i t h r e s p e c t to v e s s e l t y p e s . The N a t i o n a l Harbours Board was a l s o c o n t a c t e d . The Harbour M a s t e r ' s O f f i c e does m a i n t a i n r e c o r d s on t r a f f i c e n t e r i n g Vancouver Harbour. These are i n the form of raw d a t a e n t e r e d i n a d a i l y t r a f f i c s h e e t . The arduous t a s k o f c o l l a -t i n g t h i s d a t a was i n f e a s i b l e c o n s i d e r i n g t h a t no i n f o r m a t i o n on the v e s s e l s ' r o u t e s was a v a i l a b l e . 1. DESCRIPTION OF TRAFFIC FLOW R o s a r i o S t r a i t i s d i v i d e d i n t o s i x c h a n n e l segments, each h a v i n g a r e l a t i v e l y u n i f o r m w i d t h . "i TABLE 2.1 ROSARIO STRAIT Channel Segments Inbound D i r e c t i o n ( i . e . from Juan de Fuca t o G e o r g i a S t r a i t ) SEGMENT BEGIN END NAUTICAL MILES >J LENGTH WIDTH (mean) Cape S t . Mary B e l l Rocks 3.34 1.46 B e l l Rocks N o r t h Peapod Rock 9.17 0.56 N o r t h Peapod Rock Abeam Law-rence P t . 2.29 0.98 Abeam Lawrence P t . V i l l a g e P t . 2.78 1.39 V i l l a g e P t P t . M i g l e y Abeam P t . M i g l e y (Lum-n i I s l a n d ) 1.67 Ch e r r y P o i n t 7.08 1.49 1.60 B a s i c a l l y , the model o f R o s a r i o S t r a i t can be e n v i -s i o n e d as a s e r i e s o f s i x c o n s e c u t i v e c h a n n e l segments, each h a v i n g a u n i f o r m w i d t h and each c o n t a i n i n g v e s s e l s t r a v e l l i n g i n e i t h e r an inbound d i r e c t i o n o r an outbound d i r e c t i o n . I n -bound i n d i c a t e s t h a t the v e s s e l i s t r a v e l l i n g n o r t h , as i f from Juan De Fuca t o G e o r g i a S t r a i t . C o n v e r s e l y , outbound i n d i c a t e s the v e s s e l i s t r a v e l l i n g down R o s a r i o S t r a i t i n a s o u t h e r l y d i r e c t i o n . outbound d i r e c t i o n > inbound d i r e c t i o n As a v e s s e l p r o g r e s s i v e l y t r a n s i t s t h r o u g h the s y s -tem o f c h a n n e l segments, some method o f r e c o r d i n g i n which c h a n n e l the v e s s e l i s c u r r e n t l y l o c a t e d , i n what d i r e c t i o n the v e s s e l i s t r a v e l l i n g , and to what c l a s s i f i c a t i o n t he v e s s e l b e l o ngs ( t a n k e r , f r e i g h t e r , barge-tow, e t c . ) must be u t i l i z e d . T h i s i s a c c o m p l i s h e d i n the model by the use o f parameter v a l u e s . The model g e n e r a t e s what are c a l l e d t r a n s a c t i o n s and each t r a n s a c t i o n can be thought o f as r e p r e s e n t i n g one or more v e s s e l s o f a s p e c i f i c t y p e . Each t r a n s a c t i o n , has a t -t a c h e d t o i t s e v e r a l parameters and i t i s the v a l u e o f t h e s e parameters t h a t y i e l d coded i n f o r m a t i o n about the v e s s e l s i m u l a t e d by the t r a n s a c t i o n . For example, i f a v e s s e l i s e n t e r i n g the S t r a i t i n an inbound d i r e c t i o n , i t s parameter number seven w i l l be a s s i g n e d a v a l u e of one, and c o n v e r s e l y , i f the v e s s e l i s t o t r a v e l t h r o u g h the S t r a i t i n an outbound d i r e c t i o n , i t w i l l have a parameter seven v a l u e o f two. S i -m i l a r l y , the v a l u e of parameter one o f any t r a n s a c t i o n i n d i -c a t e s what type o f v e s s e l t h a t t r a n s a c t i o n r e p r e s e n t s . I f parameter number one has a v a l u e o f one, two, or t h r e e , t h e n the t r a n s a c t i o n i s t o be c o n s i d e r e d r e s p e c t i v e l y as e i t h e r a f r e i g h t e r , a t a n k e r , or a tow. P r e v i o u s l y mentioned was the f a c t t h a t not a l l v e s s e l s t r a v e l the e n t i r e l e n g t h o f R o s a r i o S t r a i t . Barge t r a f f i c , f o r example, o r i g i n a t i n g i n Vancouver and d e s t i n e d f o r B e l l i n g h a m , would e n t e r R o s a r i o abeam o f C h e r r y P o i n t and d e p a r t the s t r a i t abeam of Lawrence P o i n t . W i t h r e s p e c t t o the model, th e s e v e s s e l s would have c h a n n e l segment s i x as t h e i r e n t r y p o i n t i n t o the system and segment f o u r as t h e i r d e p a r t u r e p o i n t . S i n c e d a t a on the movement o f t r a f f i c t h r o u g h R o s a r i o was a v a i l a b l e , the o r i g i n and d e s t i n a t i o n o f each v e s s e l c o u l d be d e t e r m i n e d on a p e r c e n t a g e b a s i s . T h i s e n a b l e d the e n t r y and d e p a r t u r e p o i n t o f a v e s s e l i n the model 3 8 . to be predetermined. Consequently, the number of the f i r s t channel segment to be entered i n the system i s assigned as the value of parameter e i g h t and, s i m i l a r l y , the number of the l a s t channel segment through which the v e s s e l w i l l pass i n order to reach i t s d e s t i n a t i o n i s assigned as the value of parameter n i n e . Since the s t r a i t i s segmented i n t o s i x channels, the p o s i t i o n and d i r e c t i o n of each v e s s e l i n the system i s main-t a i n e d by r e c o r d i n g i n which channel and i n which d i r e c t i o n the v e s s e l i s t r a v e l l i n g at any u n i t of time. In order to complete i t s passage through the s t r a i t , a v e s s e l must t r a n s -i t K channel segments, where K < 6. T h i s i s simulated i n the model by having the v e s s e l s t r a n s i t the s u c c e s s i v e channel segments i n a l o o p i n g f a s h i o n . R e c a l l t h a t i f a v e s s e l i s to t r a n s i t the system i n an inbound d i r e c t i o n , then i t s r e s p e c t i v e t r a n s a c t i o n w i l l have a value of 1 f o r par ameter seven. This i n d i c a t e s that the v e s s e l i s to t r a n s i t the channel segments i n some conse-c u t i v e l y i n c r e a s i n g sequence, depending on the e n t r y and de-p a r t u r e p o i n t of the v e s s e l . I f , f o r any t r a n s a c t i o n , P. i s the v a l u e of parameter j , then upon the i n i t i a l e n t r y of an inbound v e s s e l i n t o the system, the f o l l o w i n g c o n d i t i o n h o l d s : 39. P8 < P9 where P8 = the # o f the c h a n n e l segment i n which the v e s s e l i s c u r r e n t l y l o c a t e d . P 9 = the # o f the l a s t c h a n n e l segment t h r o u g h which the v e s s e l w i l l p a s s . Each time the t r a n s a c t i o n s i m u l a t i n g the inbound v e s s e l passes t h r o u g h the l o g s , i t s v a l u e o f parameter e i g h t i s i n c r emented by one. C o n s e q u e n t l y , the v e s s e l w i l l not have completed i t s passage t h r o u g h the s t r a i t u n t i l i t s r e s -p e c t i v e t r a n s a c t i o n i n the model completes i t s l o o p and i s t e r m i n a t e d . T h i s o c c u r s when P8 > P9. The case o f a v e s s e l t r a n s i t i n g the system i n an outbound d i r e c t i o n i s h a n d l e d s i m i l a r l y . Parameter e i g h t i s i n s t e a d decremented and the r e s p e c t i v e t r a n s a c t i o n t e r m i n a t e s the l o o p o n l y when P8 < P9. A r r i v a l Rates The number o f s h i p s f o r each v e s s e l t y pe e n t e r i n g the s t r a i t was assumed t o have a P o i s s o n d i s t r i b u t i o n and assumed to be i n d e p e n d e n t l y d i s t r i b u t e d . Thus, the t o t a l number o f v e s s e l s a r r i v i n g i n any u n i t o f time was a l s o d i s t r i b u t e d s i m i l a r l y . Hence, the mean volume o f t r a f f i c by each v e s s e l type p e r time u n i t was d e t e r m i n e d i n the programme by t a k i n g a p r o p o r t i o n o f the t o t a l number of e n t r i e s p e r time u n i t , p a r t i c u l a r l y i n the case o f through-movements. T h i s , i n t u r n , was a s s i g n e d as the v a l u e o f parameter number 2 i n the 40. t r a n s a c t i o n s i m u l a t i n g the r e s p e c t i v e v e s s e l (or v e s s e l s ) . For example, a t r a n s a c t i o n having a parameter two value of 4, a parameter one value of 1 and a parameter seven value of 2 simulates four tankers t r a n s i t i n g the system i n the out-bound d i r e c t i o n . s e v e r a l v e s s e l s at the same time i s to reduce the number of tr a n s a c t i o n s i n the programme, thus reducing execution time and operating c o s t s . This loading method i s p a r t i c u l a r l y e f f e c t i v e when s i m u l a t i n g a channel having high t r a f f i c den-s i t y . T r a n s i t Time The t r a n s i t time i n each channel segment i s a f u n c t i o n of the channel length and the v e s s e l v e l o c i t y . Thus, i f t ^ ^ i s the mean t r a n s i t time i n segment j f o r a v e s s e l of type i , then: The purpose of having one t r a n s a c t i o n simulate t . . = channel length mean v e l o c i t y 1. l v. 3 where l = 1,2, 6 i s the index f o r the channel 3 = 1,2,3 i s the index f o r the v e s s e l type When a v e s s e l i s r e q u i r e d t o remain i n a c h a n n e l segment f o r some p e r i o d o f t i m e , thus s i m u l a t i n g i t s t r a n s i t time t h r o u g h t h a t segment, the model c a l l s the programmed f u n c t i o n ^TIME wh i c h i n t u r n , depending on the type o f v e s s e l , c a l l s ^ > o r ^ 3 ' w n i c h y i e l d s : t ^ . . Thus: V j ^ T I M E ™ %W = ^ CD S i n c e t r a n s i t time i s assumed to be 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 a c t o r s such as t i d e , weather, etc.)» the mean t r a n s i t time i s m o d i f i e d by the programmed e x p o n e n t i a l f u n c t i o n , ^gxPO* Hence, t r a n s i t time T ^ = t ^ j - ^"g^pg Encounters and C o l l i s i o n s i n the Model A v e s s e l encounter i n the model was d e f i n e d to have o c c u r r e d when two v e s s e l s passed w i t h i n 100 f e e t o f each o t h e r . S i m i l a r t o the Ho n e y w e l l Model, the s i m u l a t i o n model c o n s i d e r s o n l y head-on e n c o u n t e r s s i n c e the number o f c o l l i -s i o n s r e s u l t i n g from o v e r t a k i n g e n c o u n t e r s i s n e g l i g i b l e on west c o a s t w a t e r s . S i n c e d i f f e r e n t segments o f the chan-n e l have d i f f e r e n t w i d t h s , w^, i t i s i n t u i t i v e l y r e a s o n a b l e to assume t h a t the p r o b a b i l i t y o f a c o l l i s i o n o c c u r r i n g i n a g i v e n segment i s d i f f e r e n t from t h a t o f any o t h e r segment. R e c a l l t h a t an inbound v e s s e l w i t h p a t h X. and an outbound 3 v e s s e l w i t h p a t h Yj, w i l l c r e a t e a c o l l i s i o n p o t e n t i a l i f they are i n the c h a n n e l segment s i m u l t a n e o u s l y and i f | X . - Y k| < C where C i s the n e c e s s a r y c l e a r a n c e , e v a l u a t e d t o be 100 f e e t i n the model. S i n c e X and Y can be c o n s i d e r e d as random v a r i a b l e s , then: q. - P i L | X . - Y k| < C] wi/2 p X + 2 P x ' ( x ) [ \ P y ( y ) d y ] d x -wi/2 ^ X - 2 2C w. Thus, the ex p e c t e d number o f c o l l i s i o n p o t e n t i a l s , Crp, f o r the e n t i r e c h a n n e l i s : - £ EIC J = EIC.J 1 i = l 1 r 6 where E . i s the number o f v e s s e l e n c o u n t e r s t h a t have I o c c u r r e d i n c h a n n e l segment i d u r i n g the s i m u l a t i o n . The model was programmed t o r e c o r d the number o f enc o u n t e r s f o r each c h a n n e l segment i n a c o u n t e r . Each time two oncoming v e s s e l s i n the same cha n n e l passed each o t h e r , the c o u n t e r f o r t h a t segment was in c r e m e n t e d . R e c o r d i n g Encounters Each c h a n n e l segment o f the s t r a i t c o n t a i n s v e s s e l s t r a v e l l i n g i n b o t h d i r e c t i o n s . C o n s e q u e n t l y , each segment has a s s o c i a t e d w i t h i t two t r a n s i t s t o r a g e s ; one f o r v e s s e l s t r a v e l l i n g i n the inbound d i r e c t i o n and the o t h e r f o r ves-s e l s t r a v e l l i n g outbound. B e g i n n i n g w i t h the f i r s t c h a n n e l segment, t h e inbound s t o r a g e s were numbered from 1 t o 6 and a g a i n , b e g i n n i n g w i t h the f i r s t segment, the outbound s t o r a g e were numbered i n i n v e r s e o r d e r from 12 t o 7. FIGURE 2.1 TRANSIT STORAGES IN ROSARIO STRAIT — • inbound d i r e c t i o n outbound d i r e c t i o n > < • The programme a u t o m a t i c a l l y updates the c o n t e n t s o f each t r a n s i t s t o r a g e as t r a n s a c t i o n s e n t e r and d e p a r t . ( T h i s i s a b u i l t - i n f e a t u r e o f the s i m u l a t i o n l a n g u a g e ) . R e c a l l t h a t a t r a n s a c t i o n i n the programme s i m u l a t e s one or more v e s s e l s o f the same type i n the model. As each t r a n s a c t i o n e n t e r s the inbound s t o r a g e o f a p a r t i c u l a r c h a n n e l segment the programme i s caused t o scan the r e s p e c t i v e outbound s t o r a g e . Two v a l u e s are th e n a s s i g n e d t o parameters o f the t r a n s a c t i o n w h i c h t r i g g e r e d the s c a n . A l s o r e c a l l t h a t a v e s s e l e n t e r s the cha n n e l segment whose number i s e q u a l to the c u r r e n t v a l u e o f parameter 8 o f the t r a n s a c t i o n s i m u l a t i n g t h a t v e s s e l . Thus, i f a t r a n s a c t i o n has e n t e r e d t r a n s i t s t o r a g e P8 = i , (1 ^ i - 6 ) , then the c u r r e n t c o n t e n t s o f t r a n s i t s t o r a g e K, (where K = 13 - P8 i s the number o f the outbound s t o r a g e o f the same segment), i s a s s i g n e d as the v a l u e o f parameter 10 o f the t r a n s a c t i o n . The o t h e r v a l u e i s the t o t a l number o f v e s s e l s t o date h a v i n g e n t e r e d t r a n s i t s t o r a g e K, (the c o u n t e r p r o v i d i n g t h i s i s b u i l t i n t o the model). T h i s v a l u e i s a s s i g n e d t o parameter 11. The t r a n s a c t i o n then remained i n the inbound s t o r a g e f o r the a p p r o p r i a t e time p e r i o d , thus s i m u l a t i n g the t r a n s i t time o f the v e s s e l or v e s s e l s t h r o u g h the c h a n n e l segments. Immediately b e f o r e d e p a r t i n g the s t o r a g e , the t r a n s a c t i o n t r i g g e r e d a f u r t h e r scan i n which the updated t o t a l number of vessels having entered the respective segment in the out bound di r e c t i o n was assigned to parameter 12. From the values of parameters two, ten, eleven, and twelve, the pro-gramme calculates the number of oncoming vessel encounters re s u l t i n g from the simulation. This i s recorded in the accumulative counter for the respective channel segment. The transaction departing the inbound t r a n s i t stora w i l l have simulated E^ head-on vessel encounters: E h = P2 [P10 + (P12 - P l i ) ] where the value of the transaction parameters are: P 2 = number of inbound vessels the transaction simulated P10 = current number of outbound vessels i n channel segment at the time the inbound transaction entered P l i = t o t a l number of outbound vessels to date having entered the channel segment at the time the inbound transaction entered P12 = t o t a l number of outbound vessels to date having entered the channel segment at the time the inbound transaction departed. FIGURE 2.2 SYSTEM LOGIC 4 6 . FOR TRAFFIC FLOW ^GENERATE \VESSELS \ INTO ^SYSTEM/ ASSIGN INBOUND DIRECTION i . e . P7=l NO > CODE THE VESSEL AS A FREIGHTER i . e . ] Pl = 2 YES ^GENERATE ^VESSELS INTO ^SYSTEM/ ASSIGN OUTBOUND DIRECTION i . e . P7=2 CODE THE VESSEL AS P TANKER i'!e. P l = l YES TO" ENTER SEGMENT 3 i . e . P8=3 \ VESSE] DEPAR' SEGMEJ i . e . I , T O r vIT 1 '9 = 1 VESSEL TO ENTER SEGMENT 1 i . e . P8=l VESSEL TO DEPART SEGMENT 3 i . e . P9=3 NO ENTER CHANNEL VESSEL TO ENTER SEGMENT 6 i . e . P8=6 VESSEL TO DEPART SEGMENT 1 i . e . P9=l VESSE ENTER SEGME i . e . L TO NT 1 P8 = l \ VESSEL TO DEPART SEGMENT 6 i . e . P9=6 47 . ^GENERATE / i BARGE / TRAFFIC/ • CODE THE VESSELS AS BARGES i . e . Pl = 3 DESTINATION SEATTLE OR VICTORIA TO ENTER #3 i . e . P8=3 TO DEPART SEGMENT 1 i . e . P9=l OUTBOl DIREC i . e . I JND riON 37 = 2 DESTINATION [VANCOUVER TO ENTER SEGMENT 4 .e.P8=4 1 TO DEPART SEGMENT 6 i . e . P9=6 ORIGIN [VANCOUVER TO ENTER SEGMENT 6 i . e P8=6 ORIGIN SEATTLE OR VICTORIA TO| ENTER #1 DESTINATION BELLINGHAM TO DEPART SEGMENT 4 i . e . P9=4 INBOUND DIRECTION i . e . P7=l DESTINATION] BELLINGHAM TO DEPART SEGMENT 3 OUTBOUND DIRECTION i . e . P7=2 i . e . P8 = l i . e . P9 = 3 INBOUND DIRECTION i . e . P7=l ± ENTER VCHANNEL SYSTEM LOGIC FOR TRAFFIC FLOW P7=l INBOUND P7 = 2 "uUTBuUNir ENTER CHANNEL SEGMENT INBOUND ENTER THE CHANNEL SEGMENT WHOSE NUM-BER IS EQUAL TO THE TRANSACTION'S VALUE OF PARAMETER 8 ENTER CHANNEL SEGMENT OUTBOUND ADVANCE TIME "ADVANCE [TIME . I_ DEPART CHANNEL SEGMENT , Y _ DEPART CHANNEL SEGMENT PASSAGE COMPLETED VESSEL DEPARTS THE LOOP FIGURE 2.3 SYSTEM LOGIC FOR TRAFFIC FLOW P13 o ASSIGN VALUE TO PARAMETER 2 49 PARAMETER 2 INDICATES VOLUME OF TRAFFIC THE TRANSACTION SIMULATES (IN CASE OF MULTI-ARRIVALS) INBOUND VESSELS P7 = l ENTER TRANSIT STORAGE #P8 OUTBOUND VESSELS ASSIGN VALUE TO P6 ASSIGN TO PARAMETER 6 THE NUMBER OF THE OUT-BOUND TRANSIT STORAGE OF THE SAME CHANNEL SEGMENT i . e . P6=V-1 INITIALIZE" LOOPING PARAMETER P13 = 3 Jt 'INITIALIZE RESPECTIVE STORAGE i PARAMETER ASSIGN TO APPROPRIATE PARAMETER THE TOTAL . NUMBER OF VESSELS (WHOSE VALUE OF PI EQUALS VALUE OF P13) HAVING ENTERED STORAGE #P6, TO DATE DECREMENT VALUE OF P13 BY 1 P13 = 0 INITIALIZE P l l INITIALIZE PIO INITIALIZE LOOPING PARAMETER P13 = 3 ASSIGN TO PARAMETER 11 THE TOTAL # OF ALL VES-SELS HAVING ENTERED STORAGE #P6, TO DATE ASSIGN TO PARAMETER 10 THE CURRENT # OF ALL VESSELS IN STORAGE #P6 P7=2 ENTER TRANSIT STORAGE #V1 INCREMENT AGGREGATE COUNTER BY P2 I VI 13 P8 INCREMENT TYPE COUNTER BY P2 1 JOIN VESSEL GROUP ADVANCE TRANSIT TIME VESSEL REMOVED FROM GROUP f DEPART TRANSIT STORAGE ,#V1 \ r DECREMENT VALUE OF P8 BY 1 TOTAL # OF OUT-BOUND VESSELS TO DATE HAVING PASSED THROUGH SEGMENT P8 TOTAL # OF TOWS, TANKERS AND FREIGHTER HAVING PASSED THROUGH SEGMENT P8 VESSEL JOINS OUT-BOUND GROUP PI IN STORAGE P8 VESSEL TRANSITS THE CHANNEL SEGMENT VESSEL TRANSITS NEXT CHANNEL SEGMENT VESSEL DEPARTS THE SYSTEM (CHANNEL) so . INITIALIZE RESPECTIVE STORAGE , PARAMETERS' DECREMENT LOOPING PARAMETER BY 1 •P13>0 ^ TEST P13 P13=0 ADVANCE TRANSIT TIME INITIALIZE P12 I INCREMENT SEGMENT COUNTER BY V2 INITIALIZE LOOPING PARAMETER P13 = 3 INITIALIZE RESPECTIVE STORAGE PARAMETER INCREMENT COUNTER ASSIGN TO THE APPROPRIATE PARAMETER THE CURRENT NUMBER OF VESSELS (WHOSE VALUE OF PI EQUALS THE VALUE OF PI3) CONTAINED IN TRANSIT STORAGE #P6 (THIS IS OBTAINED FROM THE GROUP TYPES IN THE RESPECTIVE OUTBOUND STORAGES) VESSELS TRANSIT THE CHANNEL SEGMENT ASSIGN TO PARAMETER 12 THE UPDATED TOTAL NUMBER OF ALL VESSELS, TO DATE, HAVING ENTERED THE RESPECTIVE IN OUT-BOUND DIRECTION INCREMENT COUNTER FOR THE TOTAL NUMBER OF ONCOMING (HEAD-ON) VESSEL ENCOUNTERS TO DATE IN THE RESPECTIVE CHANNEL SEG-MENT V2 = P10 + (P12-P11) ASSIGN TO APPROPRIATE PARAMETER THE UPDATED TOTAL NUMBER OF VESSELS (WHOSE VALUE OF PI EQUALS VALUE OF PI 3) HAVING ENTERED STORAGE #P6, TO DATE INCREMENT COUNTER FOR HEAD-ON VESSEL ENCOUNTERS AMONG VESSELS WHOSE TYPE (VALUE OF PI) IS EQUAL TO VALUE OF P13 P13>0 DECREMENT LOOPING PARAMETER BY 1 SYSTEM LOGIC FOR TRAFFIC FLOW FIGURE 2.4 FIGURE 2.5 SYStEM LOGIC FOR TRAFFIC FLOW 0 DEPART T R A N S I T STORAGE #P8 t INCREMENT V A L U E OF P 8 BY 1 V E S S E L T R A N S I T S NEXT CHANNEL SEGMENT V E S S E L D E P A R T S THE S Y S T E M ( C H A N N E L ) FOOTNOTES 1. IBM User's Manual GPSS-V, #SH20-0851-1, IBM C o r p o r a t i o n T e c h n i c a l P u b l i c a t i o n Dept., 1971, pp. 8-10. 2. U. S. F o r e i g n Trade V e s s e l E n t r a n c e s and C l e a r a n c e s , 1970, U. S. Department o f Commerce, Bureau o f the Census, FT 975-70, August 25, 1971. CHAPTER I I I VALIDATION "Problems of v a l i d a t i o n are not unique to simulation models. A common method for v a l i d a t i n g i s to compare the output of the simulation model to h i s t o r i c a l data under s i -milar environmental conditions ( i . e . , under s i m i l a r exogenous and control values). If the output of the simulation i s close to the h i s t o r i c a l data, the simulation i s accepted as a r e a l i s t i c representation of the system. However, the ul-timate v a l i d a t i o n of any model i s how well i t predicts the future; a simulation model must at some point undergo such a test. V a l i d a t i o n o f the computer s i m u l a t i o n model was p e r -formed u s i n g d a t a a v a i l a b l e on marine t r a f f i c f l o w i n the E n g l i s h Channel. About 40% o f the w o r l d ' s marine t r a f f i c f l o w s t h r o u g h the t w e n t y - m i l e wide E n g l i s h C h a n n e l , r e s u l t i n g i n one o f t h e h i g h e s t i n c i d e n c e r a t e s o f c o l l i s i o n f o r any body o f water on the g l o b e . A p p r o x i m a t e l y 30 p e r cent o f a l l w o r l d - w i d e marine c o l l i s i o n s o c c u r i n the E n g l i s h Channel. In a d d i t i o n t o a h i g h t r a f f i c c o n c e n t r a t i o n , s h o a l s , r e e f s , and numerous sunken v e s s e l s i n the Varne a r e a r e n d e r e i g h t m i l e s o f the t w e n t y - m i l e w i d t h hazardous t o n a v i g a t i o n . C o n s e q u e n t l y , the E n g l i s h Channel has been the sub-j e c t o f much c o n c e r n . There has been an abundance o f d a t a c o l l e c t i o n and r e s e a r c h by b o t h government and p r i v a t e i n s -t i t u t i o n s . The a v a i l a b i l i t y o f such p u b l i s h e d s t a t i s t i c s made f e a s i b l e the use o f the r e s p e c t i v e d a t a on t h i s body o f water f o r the purpose o f v a l i d a t i n g t h e computer simu-l a t i o n model. The model was m o d i f i e d o n l y t o the e x t e n t o f i g n o r i n g t h e exogenous parameters o f v e s s e l t ype and c l a s s i f i c a t i o n . A l t h o u g h L l o y d s o f London and The L i v e r p o o l U n d e r w r i t e r ' s A s s o c i a t i o n make a v a i l a b l e s t a t i s t i c s on c a t e g o r i z e d v e s s e l c o l l i s i o n s , such d a t a w i t h r e s p e c t t o t r a f f i c f l o w i n the Channel i s not y e t a v a i l a b l e . However, t h i s e x c l u s i o n i n no way i m p a i r s o r d e t r a c t s from t h e v a l i d a t i o n s i n c e the p r i m a r y essence o f the model i s t o p r e d i c t the t o t a l number o f head-on c o l l i s i o n s v i a s i m u l a t i n g v e s s e l head-on e n c o u n t e r s . On t h i s p r e d i c a t i o n an e s t i m a t e o f c o l l i s i o n s among v e s s e l t y p e s i s made. F u r t h e r , i t was not n e c e s s a r y t o d i v i d e the Channel i n t o segments o f u n i f o r m w i d t h s i n c e the e s t a b l i s h e d steamer l a n e s are r e l a t i v e l y u n i f o r m i n w i d t h . Hence, i n v a l i d a t i n g the model, the assumption o f " u n i f o r m i t y " i s a c c e p t a b l e . 55. EN& LAND SMOBTTti if >«#^ ' / <</ ' [CAP SHI- nez i • / ) FRA NCE SI " A / 26' FIGURE 3.1 A r e a o f i n v e s t i g a t i o n showing t r a f f i c s e p a r a t i o n i n the Dover S t r a i t p r i o r t o 3 A p r i l , 1972 ... In 1971, Decca Radar L t d . , conducted a s u r v e y o f the n a r r o w e s t p a r t o f the D o v e r . S t r a i t , (the r e g i o n between F o l k -stone and Cap G r i s N e z ) . The purpose o f the s u r v e y was t o measure the f l o w o f marine t r a f f i c over t h e t w e n t y - f o u r hour p e r i o d from 12:00 S a t u r d a y , 13 March t o 12:00 Sunday, 14 March. T h i s was a f o l l o w - u p o f an e x p l o r a t o r y s u r v e y o f marine t r a f f i c o f t h e E n g l i s h s i d e o f the Dover S t r a i t o r -g a n i z e d and conducted i n F e b r u a r y o f the same y e a r by the N a t i o n a l P h y s i c a l L a b o r a t o r y o f t h e Department o f Trade and I n d u s t r y , (U.K.), i n w h i c h the b a s i c r a d a r s h i p count was FIGURE 3.2 Method of C o n d u c t i n g T r a f f i c Flow Survey (Decca Radar - 1971) performed by Decca Radar on b e h a l f o f N.P.L. Decca's s u r v e y was more e x t e n s i v e and d e r i v e d d a t a p r o v i d i n g i n f o r m a t i o n i n (a) Volume o f t r a f f i c ( s h i p s / h o u r and day) (b) Speed o f t r a f f i c (ground and s h i p ' s speed a f t e r a l l o w i n g f o r t i d a l stream) (c) D e n s i t y o f t r a f f i c ( s h i p s / s q u a r e m i l e ) (d) A r e a s e p a r a t i o n o f t r a f f i c (square m i l e s / s h i p ) (e) T r a f f i c s e p a r a t i o n ( f ) Route d i s c i p l i n e (g) N a v i g a t i o n o f v e s s e l s The f o l l o w i n g h i s t o g r a m s from J . J . B e a t t i e ' s a r t i c l e : on the r e s u l t s o f t h e Decca Survey p r o v i d e d the n e c e s s a r y i n -put d a t a f o r the computer model so t h a t a comparison c o u l d be made between the s i m u l a t e d r e s u l t s and the o f f i c i a l s t a t i s t i c o f t e n c o l l i s i o n s p e r y e a r i n the E n g l i s h C h a n n e l . ^ S i x o f . t h e s e c o l l i s i o n s are the r e s u l t o f head-on e n c o u n t e r s . ^ The Decca Survey a l s o r e v e a l e d t h a t a l a r g e number of s h i p s , h a v i n g e n t e r e d a t r a c k t o t r a v e l the l e n g t h o f the C hannel, do not remain i n t h a t t r a c k . T h i s i m p l i e s t h a t a l a r g e p r o p o r t i o n o f the v e s s e l s t r a v e l d i a g o n a l l y , a t l e a s t p a r t way t h r o u g h the C h a n n e l , thus e x p o s i n g a l a r g e c r o s s -s e c t i o n a l l e n g t h o f t h e i r h u l l to on-coming v e s s e l s . S i n c e s h i p s do not r e m a i n i n p a r a l l e l p a t h s , a s h i p c l e a r a n c e w i d t h 58 FIGURE 3.3 3 1 5 I t ir 1 3 12 4 1 1 1 0 9 .. 8 . 7 6 5 1 2 •• 1 + 0 S a t u r d a y 12:00 13 March Sunday 12:00 14 March ENGLISH SIDE NORTHBOUND H o u r l y T r a f f i c Volume o f f F o l k s t o n e / Cap G r i s Nez FIGURE 3.4 59. 1 5 1 "t 1 3 1 2 + 1 1 1 0 9 8 7 6 5 •• i» .. 3 2 • S a t u r d a y 12:00 13 March Sunday 12:00 14 March ENGLISH SIDE SOUTHBOUND H o u r l y T r a f f i c Volume o f f F o l k s t o n e / Cap G r i s Nez FIGURE 3.5 60. CO w CO CO m > ft o m pq 55 1 5 1 it.. 1 3 . . 1 2 . , 1 1 . , 10. 9-8. 7. 6-5., it-, 3 . . 2 ' • o L S a t u r d a y 12:00 13 March Sunday 12:00 14 March FRENCH SIDE NORTHBOUND H o u r l y T r a f f i c Volume o f f F o l k s t o n e / Cap G r i s Nez 61. FIGURE 3.6 1 5 1 k 1 3 1 2 1 1 1 0 9 4. 8 7 6 5 3 2 J 4-S a t u r d a y 12:00 13 March - i — i — i — i — i — » -Sunday 12:00 14 March FRENCH SIDE SOUTHBOUND H o u r l y T r a f f i c Volume o f f F o l k s t o n e / Cap G r i s Nez FIGURE 3.7 94% o f T r a f f i c Flow c o n t a i n e d i n segments A t o K and 12 t o 18 i n c l u s i v e 62 6 m i l e s 2 5,. 2 o 1 5 1 0 F o l k s 51 CO w CO CO w > o Pi w PQ S L J 1 0 1 5 2 0 2 5 3 0 3 5 1 >i <),• »t 5.. 5 0 one Insh o r e t r a f f i c zone NORTHBOUND 6 m i l e s S e p a r a t i o n j L i n e S e p a r a t i o n L i n e SOUTHBOUND ENGLISH SIDE Cap G r i s Nez FRENCH SIDE ( i / 2 m i l e b r a c k e t s ) N a u t i c a l M i l e s Track Route D i s c i p l i n e and T r a f f i c S e p a r a t i o n o f 392 V e s s e l s F o l k s t o n e / Cap G r i s Nez FIGURE 3.8 63. to +-> o to u o xi CD CD a CO 1 8 1 6 1 >S 1 2 1 S 8 6 •t 2 0 2 6 8 1 0 1 2 1 it 1 6 1 8 2 0 Inshore t r a f f i c zone NORTHBOUND S e p a r a t i o n L i n e n S e p a r a t i o n L i n e I n s h o r e t r a f f i c zone SOUTHBOUND ENGLISH SIDE FRENCH,SIDE I l i I—l—i i i l l l • — r — i — i — i — i i « i i i •—|—r-|—i—l—i—f—"— I ' I ' I—I I I—| X 6 c "D E P & H 1 Z K I M H 0 P Q RS T U a \Z H-'IS" U ' I? ' l& T r a c k s and Ranges o f f F o l k s t o n e / Cap G r i s Nez Average ground speed o f 376 v e s s e l s 13 March 71 - 14 March 71 r e q u i r e m e n t t h a t a l l o w e d f o r t h i s was n e c e s s a r y . The most obvio u s c h o i c e o f a c l e a r a n c e r e q u i r e m e n t was the mean over-a l l l e n g t h o f v e s s e l s . A s u r v e y o f marine a c c i d e n t s e s t i m a -t e d t h a t 22% o f c o l l i s i o n s i n N o r t h w e s t e r n European wat e r s i n v o l v e d t a n k e r s , which are u s u a l l y comparable i n l e n g t h t o f r e i g h t e r s . ^ Hence, the immediate a v a i l a b i l i t y o f d a t a on t a n k e r c o l l i s i o n s w i t h r e s p e c t t o c l a s s and s i z e r e n d e r e d u n n e c e s s a r y the arduous t a s k o f s e a r c h i n g the L l o y d s R e g i s t r y f o r s i m i l a r d a t a on f r e i g h t e r s . The same s u r v e y a l s o i n d i c a -t e d t h a t 95% o f a l l t a n k e r s i n v o l v e d i n c o l l i s i o n s are com-p r i s e d o f two groups - the l e s s than 20,000 dwt c l a s s and the 20,000 t o 50,000 dwt c l a s s . The w e i g h t e d mean l e n g t h o f the s e two c l a s s e s was e s t i m a t e d t o be 620 f e e t . T h i s f i g u r e was expanded by 30% t o account f o r the heavy c r o s s - c h a n n e l t r a f f i c , (a s i m i l a r e x p a n s i o n was made i n the Honeywell m a t h e m a t i c a l m o del), r e s u l t i n g i n a c l e a r a n c e r e q u i r e m e n t w i d t h o f 800 f e e t . T h i s a p p r o x i m a t i o n appears r e a s o n a b l e c o n s i d e r i n g t h a t the 'area o f e v a s i o n ' o f l a r g e v e s s e l s i n v o l v e s a ' t u r n i n g c i r c l e d i a m e t e r ' i n excess o f 2,000 f e e t and a ' c r a s h s t o p 7 r e a c h ' i n excess t o 4,000 f e e t . I t i s i n t e r e s t i n g t o note t h a t an a n a l o g model was d e s i g n e d t o i n v e s t i g a t e the number of o v e r t a k i n g or head-on e n c o u n t e r s which were d e f i n e d as the number o f approaches o f any two s h i p s w i t h i n 1/2 a n a u t i c a l g m i l e o f each o t h e r . The most s i g n i f i c a n t s i n g l e c i r c u m s t a n c e f o r c o l l i s i o n i n the E n g l i s h Channel i s poor v i s i b i l i t y . A p p r o x i m a t e l y 82% o f a l l c o l l i s i o n s i n the Channel o c c u r r e d i n v i s i b i l i t y 9 of l e s s t h a n two n a u t i c a l m i l e s . Because o f t h i s f a c t o r , the mean v e s s e l v e l o c i t i e s f o r b o t h the E n g l i s h and the F r e n c h s i d e o f the Channel i n b o t h d i r e c t i o n s ( n o r t h and south) were reduced by 20% to account f o r poor v i s i b i l i t y p e r i o d s which o c c u r about 10% o f the t i m e . As c i t e d i n the Honeywell model, the f i g u r e f o r the p r o b a b i l i t y of a c o l l i s i o n , g i v e n a p o t e n t i a l c o l l i s i o n was a c c e p t e d as: i p = 1/6700 = 1.49 x 10 ^ c o l l i s i o n s / p o t e n t i a l c o l l i s i o n s T h i s s t a t i s t i c was developed by the S p e f r y Piedmont Company u s i n g the E n g l i s h Channel i n a m a t h e m a t i c a l model s i m u l a t i n g v e s s e l e n c o u n t e r s . When u s i n g the Decca d a t a t o v a l i d a t e the computer model, the l e n g t h o f s i m u l a t e d time n e c e s s a r y f o r the system to s t a b i l i z e or r e a c h " s t e a d y s t a t e " was 525,600 time u n i t s . A time u n i t i n the model s i m u l a t e d one second o f r e a l time and so the p e r t u r b a t i o n s a s s o c i a t e d w i t h ! b r i n g i n g the system from an "unloaded" s t a t e t o normal o p e r a t i n g l e v e l s ( s h i p s i n c h e n n e l s converged t o an a c c e p t a b l e range i n a s i m u l a t e d time p e r i o d o f one y e a r . 66. TABLE 3.1 COMPARISON OF STATISTICS ON MARINE TRAFFIC FLOW IN ENGLISH CHANNEL S i m u l a t e d Observed Number o f v e s s e l movements d a i l y Number o f v e s s e l e n c o u n t e r s a n n u a l l y V e s s e l e n c o u n t e r s per hour per sq. n a u t i c a l m i l e Number of head-on c o l l i s i o n s A n n u a l l y 390 1760705 1.1 5.82 392-3.8' 6.2' T h e o r e t i c a l (Honeywell Model) 1692593 5.54 1. The Decca s u r v e y o b s e r v e d t h a t 243 and 149 v e s s e l s passed t h r o u g h the E n g l i s h s i d e and the F r e n c h s i d e o f Dover S t r a i t r e s p e c t i v e l y , over the 24 hour p e r i o d from 12:00 S a t u r d a y , 12 March t o 12:00 Sunday, 13 March. 2. The s t a t i s t i c o f 3.8 was the mean number o f v e s s e l e n c o u n t e r s per hour per n a u t i c a l m i l e f o r f i v e s e p a r a t e areas o f the Dover S t r a i t w hich were ob-s e r v e d by the N a t i o n a l P h y s i c a l L a b o r a t o r y o f the Dept. of Trade and I n d u s t r y o f the U.K. ( r e f . # 9 ) . "„ However, i t must be s t r e s s e d t h a t t h i s encounter r a t e a p p l i e s o n l y t o the p a r t i c u l a r a r e a s c o n s i d e r e d and not the whole s t r a i t . A l s o , the computer s i m u l a -t i o n model d e f i n e d an encounter t o be when two s h i p s passed w i t h i n a d i s t a n c e o f 800 f e e t o f each o t h e r , whereas the N.P.L. model used a d i s t a n c e o f 1/2 nau-t i c a l m i l e . Hence, t h i s comparison s h o u l d be c o n s i -dered o n l y as a p o i n t o f i n t e r e s t . 3. The s t a t i s t i c o b t a i n e d from the mean over of 6.2 head-on c o l l i s i o n s per y e a r was Hargreave's a r t i c l e (ref.#5) and was the t h r e e y e a r s from 1969 t o 1971. The error difference between the simulated and ob-served s t a t i s t i c s pertaining to the number of d a i l y vessel movements and the number of head-on c o l l i s i o n s annually were 5.2% and 6.1% respectively. These are well within the range of acceptance. Thus, i t may be concluded that the computer simulation model, as designed, does provide a r e a l i s t i c re-presentation of sa l i e n t aspects of the system of marine t r a f f i c flow i n a shipping channel. Consequently, for a limited period of time i n the future one would expect that the model loaded with the necessary input data, would y i e l d a r e l i a b l e s t a t i s t i c on the expected number of vessel c o l l i s i o n s (cate-gorized into vessel types i f the appropriate input data i s loaded). 68. FOOTNOTES 1. James R. Emshoff?and Roger L. S i s s o n , D e s ign and Use of Computer S i m u l a t i o n M odels, (New Yo r k , New Yo r k , The M a c m i l l a n Co., 1970), p. 57. 2. Robert P. Thompson ( C e l e s c o I n d u s t r i e s I n c . ) , E s t a b l i s h i n g  G l o b a l T r a f f i c F l o w s , The J o u r n a l o f N a v i g a t i o n , V o l . 25, 1973, p. 483. 3. J . H. B e a t t i e (Decca Radar L t d . ) , T r a f f i c Flow Measurements  i n t he Dover S t r a i t , The J o u r n a l o f N a v i g a t i o n , V o l . 24, 1971, p. 325. 4. I b i d . 5. E. R. H a r g r e a v e s , (Dept. o f Trade and I n d u s t r y , U.K.), S a f e t y o f N a v i g a t i o n i n the E n g l i s h C h a n n e l , The J o u r n a l o f N a v i g a t i o n , V o l . 26, 1973. 6. C. Grimes, A Survey o f M a r i n e A c c i d e n t s w i t h P a r t i c u l a r  R e f e r e n c e t o Tan k e r s , The J o u r n a l o f N a v i g a t i o n , V o l . 25, p. 497, 1973. 7. Roger A. P e t e r s o n , O p e r a t i o n a l Hazards and the C o n t r o l o f ; O i l Tankers i n the V a l d e z - C h e r r y P o i n t Route, Centre o f T r a n s p o r t S t u d i e s , U.B.C. Student Paper #8, p. 53. 8. J . Draper and C. B e n n e t t , M o d e l l i n g Encounter Rates i n  Ma r i n e T r a f f i c Flows w i t h P a r t i c u l a r A p p l i c a t i o n t o the Dover S t r a i t , The J o u r n a l o f N a v i g a t i o n , V o l . 25, 1973, p. 381. 9. J . H. W. Wheatley ( N a t i o n a l P h y s i c a l L a b o r a t o r y ) , C i r c u m s t a n c e s o f C o l l i s i o n s and S t r a n d i n g s , The J o u r n a l o f N a v i g a t i o n , V o l . 25, 1972, p. 92. CHAPTER IV EXPERIMENTS EXPERIMENT ONE The f i r s t experiment s i m u l a t e d t r a f f i c f l o w t h r o u g h R o s a r i o S t r a i t over a t e n - y e a r p e r i o d . Tankers d e s t i n e d f o r and d e p a r t i n g from C h e r r y P o i n t t r a n s i t e d R o s a r i o S t r a i t . An annual growth r a t e o f 41 f o r a l l t h r e e v e s s e l t y p e s was i n c o r -p o r a t e d i n t o the model t o determine the i n f l u e n c e o f t r a f f i c volume on encounter r a t e s and the number o f e x p e c t e d c o l l i -s i o n s . R e c a l l the s e g m e n t a t i o n o f R o s a r i o S t r a i t : TABLE 4.1 CHANNEL SEGMENT Length Width Number L o c a t i o n N a u t i c a l M i l e s 1 Cape S t . Mary - B e l l Rocks 3.34 1.46 2 B e l l Rocks - N. Peapod Rock 9.17 0.56 3 N. Peapod Rock - Lawrence P t . 2.29 0.98 4 Lawrence P t . - V i l l a g e P t . 2.78 1.39 5 V i l l a g e P t . - P t . M i g l e y 1.67 1.49 6 P t . M i g l e y - C h e r r y P t . 7.08 1.60 The t e n - y e a r computer s i m u l a t i o n produced the f o l l o w -i n g number o f v e s s e l e n c o u n t e r s i n the r e s p e c t i v e c h a n n e l segments: TABLE 4.2 - S i m u l a t e d V e s s e l E n c o u n t e r s Channel YEAR Segment 1 2 3 4 5 6 7 8 9 10 1 14 13 15 25 18 21 22 37 21 33 2 42 44 58 49 56 66 73 64 54 ;:83 3 9 14 20 11 19 13 14 34 15 19 4 5 8 16 17 14 4 11 19 13 16 5 2 4 2 7 8 5 11 6 5 4 6 15 17 26 36 29 23 41 45 34 42 Giv e n the number o f v e s s e l s t h a t t r a n s i t e d the seg-ments, the number o f v e s s e l e n c o u n t e r s t h a t s h o u l d have oc-c u r e d a c c o r d i n g t o the Honeywell Model a r e : Channel YEAR Segment 1 2 3 4 5 6 7 8 9 10 1 16 16 18 19 18 20 25 28 25 30 2 41 46 51 53 52 56 74 76 71 77 3 10 11 12 11 12 14 15 19 16 „ 19 4 7 7 10 10 10 10 12 14 13 12 5 4 4 6 6 6 6 7 8 8 8 6 21 19 27 27 26 29 32 36 34 34 TABLE 4.3 - T h e o r e t i c a l V e s s e l E n c o u n t e r s The type o f en c o u n t e r s t h a t o c c u r e d between v e s s e l s t r a v e l l i n g e i t h e r inbound or outbound i n the r e s p e c t i v e chan-n e l segments f o r y e a r 1 and y e a r 10 a r e ! YEAR 1 DIRECTION Channel Segment INBOUND OUTBOUND f r e i g h t e r t a n k e r tow f r e i g h t e r 0 0 1 1 t a n k e r 0 1 5 tow 1 2 4 f r e i g h t e r 1 2 2 2 t a n k e r 1 2 5 tow 3 8 18 f r e i g h t e r 1 0 1 3 t a n k e r 0 1 0 tow 1 3 2 f r e i g h t e r 1 0 1 4 t a n k e r 1 0 0 tow 0 1 1 f r e i g h t e r 0 1 0 5 t a n k e r 0 0 0 tow 0 0 1 f r e i g h t e r 0 0 3 6 t a n k e r 0 1 1 tow 0 2 8 TABLE 4.4 - Types o f Enc o u n t e r s - Year 1 YEAR 10 DIRECTION Channel OUTBOUND Segment INBOUND f r e i g h t e r t a n k e r tow f r e i g h t e r 1 1 4 1 t a n k e r 0 0 5 tow 1 3 18 f r e i g h t e r 1 2 3 2 t a n k e r 3 0 7 tow 8 7 40 f r e i g h t e r 0 1 1 3 t a n k e r 0 0 2 tow 1 4 10 f r e i g h t e r 0 1 1 4 t a n k e r 0 1 2 tow 3 3 5 f r e i g h t e r 0 1 0 5 t a n k e r 0 0 0 tow 1 1 1 : : f r e i g h t e r 1 1 1 6 t a n k e r 0 2 13 tow 2 6 16 TABLE 4.5 - Types o f En c o u n t e r s - Year 2 EXPECTED NUMBER OF COLLISIONS - E(K) Scale:xx:xxxxxE-04 C H A N N E L S E G M E N T TOTAL Pe r c e n t a g e 1 2 3 4 5 6 f t . t k . tw. 1 .47469 3 .7127 .45462 .17807 .06644 .46409 5.3507 16 20 63 2 .44078 3 .8895 .70710 .28491 .13289 .52597 5.9813 11 17 69 3 .50860 5 .1271 1.0102 .56982 .06644 .80440 8.0860 10 24 64 4 .84760 4 .3315 .55565 .60544 .23256 1.1138 7.6860 13 24 62 5 .61032 4 .9503 .95970 .49859 .26579 .89720 8.1820 6 31 62 6 .71200 5 .8343 .65660 .14245 .16611 .71160 8.2230 12 21 61 7 .74590 6 .4530 .70710 .39175 .36546 1.2685 9.9320 9 25 65 8 1.2545 5 .6575 1.7174 .67660 .19934 1.3922 10.897 11 22 65 9 .71200 4 .7735 .75770 .46298 .16611 1.0519 7.9224 8 19 72 10 1.1189 7 .3370 .95970 .56982 .13289 1.2994 11.418 12 21 65 MEAN .74253 5.20664 .84858 .43804 .17940 .95291 8.3678 11 22 65 TABLE 4.6 - EXPECTED NUMBER COLLISIONS - Experiment 1 E(K) FIGURE 4.1 YEAR SIMULATION FORECAST NUMBER OF EXPECTED COLLISIONS IN ROSARIO STRAIT Experiment one indicates that an annual growth of 4% in vessel t r a f f i c does increase the expected number of c o l l i -sions. In order to obtain a more accurate estimate of c o l l i -sion growth, experiment one was run three times, and the mean of the three runs was used to indicate c o l l i s i o n growth. This had the eff e c t of smoothing any deviations in the simulation forecast by de-emphasizing any pronounced or abnormal fluctua-tions in the forecast, should they occur. Each simulation run used a d i f f e r e n t random number sequence for the random number generator which was used to mod fy the vessel i n t e r - a r r i v a l rates and the vessel t r a n s i t times in the system; (see programme appendix). The resu l t i n g growth rates of c o l l i s i o n s for each of the three runs and the i r re-sult i n g mean are graphed i n Figure 4.1. The mean graph of the expected number of c o l l i s i o n s , E(K), for years one to ten inclusive suggests an exponential relationship between growth of vessel t r a f f i c and growth of c o l l i s i o n s . The exact rate of growth, however, i s evaluated in experiment two. 76. EXPERIMENT TWO The f l u c t u a t i o n s i n the e x p e c t e d number o f c o l l i s i o n s over the t e n - y e a r s i m u l a t i o n p e r i o d was smoothed by a moving average t h a t was b u i l t i n t o the s i m u l a t i o n model. The smooth-i n g e q u a t i o n i s : E ( K t ) = E C K ^ ) + o [ E ( K t ) - E C K ^ ) ] where a = 0.90 i s the w e i g h t i n g c o e f f i c i e n t . A v a l u e o f a = 0.9 was det e r m i n e d over s e v e r a l compu-t e t e r r u n s , a s 0.9 i s the v a l u e chosen t h a t smooths the i n t e r -mediate p o i n t s o f the growth curve w i t h o u t d i s t o r t i n g the v a l u e s of the end p o i n t s . Hence, the growth curve i s smoothed but the c o l l i s i o n f o r e c a s t s are not d i s t o r t e d by the smoothing t e c h n i q u e . T h i s i s one o f the methods o f smoothing s i m u l a t i o n r e s u l t s s uggested by M e i e r , N e w e l l , and Pazer i n " S i m u l a t i o n i n B u s i n e s s and Economics". The smoothed f o r e c a s t o f the e x p e c t e d number o f c o l l i -s i o n s E(K) over the t e n - y e a r p e r i o d i s graphed i n the f o l l o w i n g page. The graph i n d i c a t e s t h a t a 4% annual growth r a t e i n t r a f f i c causes an e x p o n e n t i a l growth i n E ( K ) . The p e r c e n t a g e breakdown among v e s s e l t ypes remained the same. The e x p o n e n t i a l r a t e o f growth was e v a l u a t e d u s i n g l i n -ear r e g r e s s i o n on the n a t u r a l l o g o f the c o l l i s i o n f o r e c a s t s ; (see Appendix I ) . The v a l u e o f the e x p o n e n t i a l growth r a t e was de-t e r m i n e d to be 6.75%. FIGURE 4.2 E(K) 0012 I L e a s t Squares E s t i m a t e o f E(K) ( r e g r e s s i o n a n a l y s i s on l o g [E Experiment 2 f o r e c a s t s smoothed 77 0011 1 0010 1 0009 + 0008 i 0007 1 0006 4 0005 i i • 4 > YEAR 6 10 SIMULATION FORECAST (EXPONENTIALLY SMOOTHED) NUMBER OF EXPECTED COLLISIONS E(K) ROSARIO STRAIT 78. EXPERIMENT THREE The v e s s e l e n c o u n t e r t a b l e o b t a i n e d from Experiment 1 i n d i c a t e s t h a t c h a n n e l segment #2, the segment o f R o s a r i o S t r a i t from B e l l Rocks t o N. Peapod Rock, has the h i g h e s t e n c o u n t e r r a t e . T h i s i s p r i m a r i l y because i t i s the l o n g e s t segment. One would i n t u i t i v e l y expect i t t o have the h i g h e s t i n c i d e n c e o f c o l l i s i o n s i n c e i t i s the segment h a v i n g the h i g h -e s t e n c o u n t e r r a t e and s i n c e i t i s o n l y 0.56 n a u t i c a l m i l e s wide; by f a r the na r r o w e s t p a r t o f R o s a r i o . S t r a i t . C o n s e q u e n t l y , i f o n l y one shore-based r a d a r marine t r a f f i c a d i v s o r y system were t o be p l a c e d anywhere i n R o s a r i o S t r a i t , t h i s segment o f t h e s t r a i t would appear t o be the o p t i m a l l o c a t i o n . The purpose o f experiment t h r e e i s t o determine the e f f e c t on c o l l i s i o n i n c i d e n c e o f i n s t a l l i n g such a system. I t was assumed t h a t such a system would have the e f f e c t o f r e d u c i n g the p r o b a b i l i t y o f a c o l l i s i o n by 20%. T h i s f i g u r e was a r b i t r a r i l y chosen s i n c e no d a t a e x i s t s on the e f f e c t s o f such systems i n r e d u c i n g the i n c i d e n c e o f c o l l i s i o n . Hence, p was changed from p = 1/6700 to p = 1/8375. The e f f e c t o f an a d v i s o r y system t h a t reduced the p r o b a b i l i t y o f a c o l l i s i o n by 20% anywhere i n R o s a r i o S t r a i t would be t o reduce the over-a l l i n c i d e n c e o f c o l l i s i o n by 20%. However, i f such a system c o v e r e d o n l y p a r t o f the s t r a i t ; t h e n , assuming i t a f f e c t e d o n l y c h a n n e l segment two i f i n s t a l l e d i n segment two, the o v e r a l l e f f e c t would be q u i t e d i f f e r e n t . TABLE 4.7 79. EXPECTED NUMBER OF COLLISIONS YEAR NO RADAR GUIDANCE RADAR GUIDANCE IN ALL SEGMENTS RADAR GUIDANCE IN SEGMENT #2 ONLY RADAR GUIDANCE IN ALL SEGMENTS BUT #2 1 5.3739 4.2991 4.6400 5.033 2 5.9206 4.7364 5.1471 5.551 3 7.8700 6.2960 6.8698 7.296 4 7.7050 6.1640 6.8253 7.043 5 8.1340 6.5070 7.1549 7.486 6 8.2140 6.5710 7.0659 7.719 7 9.7600 7.8080 8.4838 9.084 8 10.7840 8.5270 9.5380 9.773 9 8.2100 6.5680 7.2362 7.542 10 11.0970 8.8770 9 .6790 10.295 MEAN 8.3069 6.6454 7.2740 7:6822 s c a l e o f magnitude x.xxxxE-04 I n t r o d u c i n g a shore-based r a d a r marine t r a f f i c a d v i -s o r y system t h a t reduces the p r o b a b i l i t y o f a c o l l i s i o n by 20% i n c h a n n e l segment two, the segment o f R o s a r i o from B e l l Rocks to N o r t h Peapod Rock, has the e f f e c t o f r e d u c i n g the t o t a l 80. number o f e x p e c t e d c o l l i s i o n s i n R o s a r i o S t r a i t by 12.43%. T h i s i s s i g n i f i c a n t when one c o n s i d e r s t h a t g i v e n the assump-t i o n s o f a l i m i t e d r a d a r coverage and a p r o b a b i l i t y r e d u c t i o n o f 20% f o r each system, f u r t h e r i n s t a l l a t i o n s would reduce the i n c i d e n c e o f c o l l i s i o n by a t most 20% i n R o s a r i o S t r a i t . F u r t h e r , i f a guidance system were i n s t a l l e d i n e v e r y c h a n n e l segment except segment number two, the t o t a l number o f expect c o l l i s i o n s i n R o s a r i o S t r a i t would be reduced by 7.52%. T h i s i m p l i e s t h a t c h a n n e l segment two i s the o p t i m a l l o c a t i o n . 81. EXPERIMENT FOUR The purpose of experiments four, f i v e , and six was to determine i f routing tanker t r a f f i c through the San Juan Islands reduced the incidence of tanker c o l l i s i o n , and i f so, which route was the most e f f e c t i v e . The segment of Haro S t r a i t from Kelp Reefs to Turn Point on Stuart Island was segment number seven of the channel model. This segment has a length and width of approximately 8.88 and 1.67 nautical miles respectively. Channel segment number eight of the model consisted of the stretch of water from the east entrance of Prevost Passage, which i s due west of Stuart Island, to Alden Point on Patis Island, which i s the northerly entrance to Boundary Pass. This segment has a length and a mean width of approximately 13.32 and 1.11 nau-t i c a l miles respectively. Forty deep-sea or coastal vessels t r a n s i t these two segments d a i l y . Two large tankers per week tr a v e l through Haro and Boundary Pass enroute to Vancouver. Since no data existed i n the actual types of vessels, the t r a f f i c t r a n s i t i n g these two segments was assumed to be similar in composition to the Puget Sound t r a f f i c . Consequently, 50% of the t r a f f i c was assumed to be Barge or tow t r a f f i c , and the rest, other than the twojweekly larger tankers destined for and departing from Vancouver, was assumed to be fr e i g h t e r s - t r a f f i c . Again, 82. commercial f i s h b o a t s and p l e a s u r e c r a f t were i g n o r e d . Experiment f o u r s i m u l a t e d the marine t r a f f i c f l o w t h r o u g h R o s a r i o and Haro S t r a i t s and Boundary Pass over a t e n - y e a r p e r i o d . Tankers d e s t i n e d t o C h e r r y P o i n t were sim-u l a t e d t o t r a v e l enroute by way o f R o s a r i o S t r a i t and t a n k e r s d e p a r t i n g C h e r r y P o i n t were s i m u l a t e d t o a l s o t r a n s i t R o s a r i o S t r a i t . T a b l e s 4.8 and.4.9 g i v e the number o f v e s s e l encoun-t e r s f o r each c h a n n e l segment over the t e n - y e a r p e r i o d . N o t i c e t h a t the number o f v e s s e l e n c o u n t e r s f o r segment seven, which s i m u l a t e s Haro S t r a i t , and f o r segment e i g h t , which s i m u l a t e s Boundary P a s s , are much h i g h e r than the enc o u n t e r s which o c c u r r e d i n segments one to s i x . T h i s i s bacause c h a n n e l seg-ments one t o s i x s i m u l a t e R o s a r i o S t r a i t w hich has a much lower volume o f t r a f f i c than e i t h e r Haro S t r a i t or Boundary P a s s , and, c o n s e q u e n t l y , a much lower e n c o u n t e r r a t e . 83. TABLE 4.8 EXPERIMENT FOUR SIMULATED VESSEL ENCOUNTERS Channel YEAR Segment 1 2 3 4 5 6 7 8 9 10 1 11 18 14 25 24 29 20 27 25 30 2 36 47 42 57 56 61 65 77 76 78 3 8 12 12 11 15 14 13 22 22 19 4 6 7 14 12 8 19 11 11 13 20 5 8 6 10 11 6 9 12 10 8 12 6 13 16 26 23 31 31 34 27 32 32 7 16601 17832 20156 21502 23136 25594 26796 30349 32699 35527 8 25027 27123 30211 32092 34653 38403 40724 45746 48207 53504 TABLE 4.9 THEORETICAL NUMBER OF ENCOUNTERS (HONEYWELL MODEL) 1 13 15 15 20 21 23 21 25 29 29 2 41 50 45 53 58 58 58 67 77 87 3 10 10 10 12 14 13 13 16 18 21 4 7 8 9 10 10 12 12 12 14 16 5 4 5 5 6 6 7 8 7 8 10 6 17 22 24 25 28 31 32 29 37 46 7 16653 17906 20103 21608 23222 25507 26966 30320 32349 35396 8 25049 27098 29899 32254 34686 38224 40724 45746 48372 53736 TABLE 4.10 EXPERIMENT FOUR EXPECTED NUMBER OF COLLISIONS E(K) S c a l e of magnitude: xxxx.xxxxxEO-4 C H A N N E L S E G M E N T YEAR 1 2 3 4 5 6 7 8 TOTAL 1 .38484 3.2637 .39956 .21510 .25549 .42573 491.04 1112.0 1608 .0 2 .58777 4.0656 .58550 .24588 .20495 .48810 524.83 1199.8 1730.8 3 .48600 3.7480 .60410 .47332 .31951 . 77280 590.21 1332.6 1929.2 4 .81140 4.9097 .56049 .43196 .36086 .71770 632.60 1421.3 2061.8 5 .81350 4.9463 .73790 .29961 .21549 .93490 680.50 1533.0 2221.4 6 .96630 5.3477 .71020 .63890 .29066 .95670 750.80 1694.7 2454.5 7 .70690 5.7061 .66200 .41647 .38788 1.04240 789.90 1804.0 2602.9 8 .89460 6.6960 1.06630 .39422 .33780 .85600 888.60 2016.5 2915.4 9 .85230 6.7160 1.10680 .45610 .27299 .97660 961.20 2136.5 3108.2 10 1.00070 6.8770 .97440 .68660 .38611 .98870 1043.90 2361.2 3416.0 MEAN .746787 5.22761 .740725 .425816 .303174 .815963 735.358 1660.86 2404.82 85. The mean pe r c e n t a g e o f f r e i g h t e r s , t a n k e r s , and tows i n v o l v e d i n c o l l i s i o n s over the t e n - y e a r s i m u l a t i o n p e r i o d i s : f r e i g h t e r s : 40.7% t a n k e r s : 1.0% tows: 57.3% Hence, i f t a n k e r s d e s t i n e d f o r and d e p a r t i n g from C h e r r y P o i n t t r a n s i t R o s a r i o S t r a i t b o t h inbound and outbound, then the mean e x p e c t e d number o f head-on c o l l i s i o n s per v e s s e l type over the t e n - y e a r p e r i o d s i m u l a t e d i s : Mean Number o f Ex p e c t e d C o l l i s i o n s E(K) f r e i g h t e r s : 0.0988 t a n k e r s : 0.0024 tows: 0.1391 TOTAL: 0.2404 Experiment f o u r i n d i c a t e d t h a t d u r i n g the next t e n y e a r s , r o u t i n g inbound and outbound C h e r r y P o i n t t a n k e r s t h r o u g h Ros-a r i o S t r a i t w i l l r e s u l t i n 2.404 head-on c o l l i s i o n s i n R o s a r i o S t r a i t , Boundary P a s s , and the a r e a o f Haro S t r a i t n o r t h o f K e l p Reef. Of the s e c o l l i s i o n s , 0.024 w i l l i n v o l v e t a n k e r s . A c o n c l u s i o n on the most e f f e c t i v e r o u t i n g s t r a t e g y cannot be made a t t h i s p o i n t . These r e s u l t s must f i r s t be compared t o the r e s u l t s of the two a l t e r n a t i v e r o u t e s s i m u l a t e d , r e s p e c t i v e l y , i n the f o l l o w i n g two e x p e r i m e n t s . 86. EXPERIMENT FIVE The purpose of experiment f i v e was to determine the effect of one-way Cherry Point tanker t r a f f i c through Rosario S t r a i t . Consequently, in experiment f i v e , tankers destined for Cherry Point were simulated to t r a n s i t Rosario S t r a i t i n -bound while tankers departing Cherry Point were simulated to tr a n s i t outbound v i a Boundary Pass and Haro S t r a i t . TABLE 4.11 EXPERIMENT FIVE Simulated Vessel Encounters YEAR C H A N N E L S E G M E N T 1 2 3 4 5 6 7 8 1 18 24 9 7 2 17 16599 24684 2 15 33 9 9 4 19 18326 27555 3 17 40 6 7 2 23 20476 30244 4 25 56 6 7 6 24 21897 32305 5 16 43 12 5 6 20 24292 36875 6 18 47 8 5 7 20 25314 37571 7 ' 15 60 17 10 5 19 27727 41252 8 18 62 14 10 Z6 28 .30067 45375 9 23 72 19 8 13 29 33231 49660 10 25 68 21 13 7 30 35730 53512 103. Letting E(K ) = £(t) for t = 1, 2, 10 we have: Y t = l o g e E(K t) = c + r t for t = 1, 2, ..., 10 The regression equation for the least squares estimators of Y t is : Y t = a + 8t Thus, a denotes c and, s i m i l a r l y , 3 denotes the expo-nentia l rate of growth, r. Hence, we can use the li n e a r regression 8 to evaluate the growth rate r. Thus: Sim i l a r l y : TABLE 4.12 EXPERIMENT FIVE EXPECTED NUMBER OF COLLISIONS E(K) S c a l e o f magnitude: xxxx.xxxxxEO-4 C H A N N E L S E G M E N T YEAR 1 2 3 4 5 6 7 8 TOTAL 1 . 588 28. 2.19.31 .43442 .23256 .06345 .53433 490.96 1101.4 1596.4 2 .51656 " 2.8447 .45260 .31173 .12595 .58250 538.01 1216.1 1758 .9 3 .57042 3.4668 .31803 .25554 .07239 .69870 600.07 1335.5 1941.0 4 .81990 4.8020 .30457 .24992 .18664 .73810 644.10 1430.2 2081.5 5 .57025 3.9012 .57600 .18525 .19807 .63070 712.40 1623.1 2341.6 6 .60631 4.1294 .42130 .17878 .22911 .61998 746.50 1670.3 2423.1 7 . 51837 5.1865 .81490 .33840 .17241 .59106 814.30 1822.8 2644.8 8 .60112 5.4513 .71790 .35436 .19665 .83870 883.50 2003.5 2895.2 9 .76190 6.2730 .93550 .29185 .40838 .89140 974.9 2193.6 3178.0 10 . 83900 6.0373 1.04820 .44587 .25014 .92450 1050.70 2367.2 3427.4 MEAN .63921 4.4285 .61134 .28443 .19042 .70499 745.54 1676.37 2428.79 88. The mean p e r c e n t a g e o f f r e i g h t e r s , t a n k e r s , and tows i n v o l v e d i n c o l l i s i o n s over the t e n - y e a r s i m u l a t i o n p e r i o d i s : 3 f r e i g h t e r s : 40.6% t a n k e r s : 1.0% tows: 57.3% Hence, i f t a n k e r s d e s t i n e d f o r C h e r r y P o i n t t r a v e l i n -bound v i a R o s a r i o S t r a i t and i f t a n k e r s d e p a r t i n g C h e r r y P o i n t t r a v e l outbound v i a Boundary Pass and Haro S t r a i t , t hen the f o r e c a s t e d mean e x p e c t e d number o f head-on c o l l i s i o n s p e r ves-s e l type over the t e n - y e a r s i m u l a t e d p e r i o d i s : Mean Number o f E x p e c t e d C o l l i s i o n s E(K) f r e i g h t e r s : 0.0996 t a n k e r s : 0.0025 tows: 0.1407 TOTAL: 0.2428 Experiment f i v e i n d i c a t e d t h a t C h e r r y P o i n t t a n k e r s t r a v e l l i n g inbound v i a R o s a r i o S t r a i t and outbound v i a Boundary Pass and Haro S t r a i t w i l l r e s u l t i n 2.428 head-on c o l l i s i o n s '• the next t e n y e a r s . Of the s e c o l l i s i o n s , 0.025 w i l l i n v o l v e t a n k e r s . Thus, t h i s r o u t i n g s t r a t e g y y i e l d s a h i g h e r o v e r a l l c o l l i s i o n i n c i d e n c e and a h i g h e r t a n k e r c o l l i s i o n i n c i d e n c e than r e s t r i c t i n g inbound and outbound C h e r r y P o i n t t a n k e r s t o R o s a r i o S t r a i t . 89. EXPERIMENT SIX The purpose of experiment six was also to determine the effect of one-way Cherry Point tanker t r a f f i c . However, in experiment six, tankers destined for Cherry Point were simulated to t r a n s i t inbound v i a Haro S t r a i t and Boundary Pass while tankers departing Cherry Point were simulated to tran-s i t outbound v i a Rosario S t r a i t . This was the converse of the routing strategy simulated i n experiment f i v e . TABLE 4.13 EXPERIMENT SIX Simulated Vessel Encounters C H A N N E L S E G M E N T YEAR 1 2 3 4 5 6 .7 . . . 8 1 14 26 3 6 3 13 16747 24984 2 21 43 8 11 1 18 18329 27610 3 17 41 15 7 5 16 19772 28456 4 22 58 . 15 10 7 17 21298 32190 5 17 46 15 11 1 17 23987 35695 6 11 49 9 10 9 32 . 25398 37228 7 26 80 12 8 8 21 27792 41276 8 28 64 16 7 8 26 30495 45485 9 28 57 15 11 6 30 32295 48074 10 24 69 14 11 6 31 35023 51464 TABLE 4.14 EXPERIMENT SIX EXPECTED NUMBER OF COLLISIONS E(K) S c a l e o f magnitude: xxxx.xxxxxEO-4 C H A N N E L S E G M E N T YEAR 1 2 3 4 5 6 7 8 TOTAL 1 .47265 2.4460 .18942 .21154 .09933 .40593 497.69 1115.8 1617.3 2 .68810 3.6656 .38264 .37373 .039835 .54181 538.76 1219.7 1764.2 3 .58758 3.6285 . 720.20 .26174 .15349 .49971 581.36 1264.1 1851.3 4 .73010 4.9773 .75390 .34670 .22466 .52335 626.30 1418.4 2052.3 5 .59178 4.1574 .75730 .38725 .052367 .52571 702.50 1574.5 2283 .6 6 .39485 4.3141 .48489 .35925 .27435 .94360 747.80 1651.7 2406.3 7 .83290 6.7960 .59404 .20234 .26664 .67910 816.20 1821.9 2647.6 8 .93770 5.7714 .78680 .25360 .26587 .79190 895.10 2007.8 2911.8 9 .94820 5.1120 .76060 .37794 .20599 .91450 951.10 2130.3 3089.8 10 .82720 6.0008 .71250 .39037 .20000 .95460 1029.4 2278.7 3317.2 MEAN .701106 4.68691 .614229 .325446 .1782532 .678021 738 .621 1648.29 2394.14 The mean p e r c e n t a g e o f f r e i g h t e r s , t a n k e r s and tows i n v o l v e d i n c o l l i s i o n s over the t e n - y e a r s i m u l a t i o n p e r i o d i s : f r e i g h t e r s : 40% t a n k e r s : 2% tows: 57% Hence, i f t a n k e r s d e s t i n e d f o r C h e r r y P o i n t t r a v e l inbound v i a Haro S t r a i t and Boundary Pass and i f t a n k e r s de-p a r t i n g C h e r r y P o i n t t r a v e l outbound v i a R o s a r i o S t r a i t , the f o r e c a s t e d mean ex p e c t e d number o f head-on c o l l i s i o n s per . v e s s e l type over the t e n - y e a r s i m u l a t i o n p e r i o d i s : .Mean Number of Ex p e c t e d C o l l i s i o n s E(K) f r e i g h t e r s : 0.0967 t a n k e r s : 0.0048 tows: 0.1378 TOTAL: 0.2394 Experiment s i x i n d i c a t e d t h a t C h e r r y P o i n t t a n k e r s t r a v e l l i n g inbound v i a Haro S t r a i t and Boundary Pass and out-bound v i a R o s a r i o S t r a i t w i l l r e s u l t i n 2.394 c o l l i s i o n s over the n e x t t e n y e a r s . Of the s e c o l l i s i o n s , 0.048 w i l l i n v o l v e t a n k e r s . T h i s r o u t i n g s t r a t e g y w i l l r e s u l t i n the h i g h e s t i n c i d e n c e o f t a n k e r c o l l i s i o n s . However, i t w i l l y i e l d an o v e r a l l i n c i d e n c e o f c o l l i s i o n w h i c h i s s l i g h t l y l o wer t h a n e i t h e r r e s t r i c t i n g t a n k e r t r a f f i c t o R o s a r i o S t r a i t or r o u t i n g 92". inbound tankers t r a f f i c to Rosario and r o u t i n g outbound t a n k e r . : t r a f f i c through Boundary Pass and Haro S t r a i t . Although the three r o u t i n g s t r a t e g i e s produced s l i g h t d i f f e r e n c e s i n c o l l i s i o n i n c i d e n c e s , these d i f f e r e n c e s cannot be considered s i g n i f i c a n t . CHAPTER V CONCLUSIONS In p r e s e n t i n g the c o n c l u s i o n s o f t h i s t h e s i s , Chapter V w i l l be concerned w i t h f i v e a r e a s : 1. The c o n c l u s i o n s on the ex p e c t e d growth r a t e o f c o l l i s i o n s i n R o s a r i o S t r a i t over the next t e n y e a r s , i . e . 1974 t o 1984. 2. The c o n c l u s i o n s on the " o p t i m a l " l o c a t i o n o f a shore-based r a d a r marine guidance system i n R o s a r i o S t r a i t . 3. The c o n c l u s i o n o f the system's a n a l y s i s o f t a n k e r t r a f f i c r o u t i n g and s e p a r a t i o n . 4. The f o r e c a s t o f the number o f c o l l i s i o n s t o be ex p e c t e d i n the next t e n y e a r s . 5. The p r o p o s a l o f f u t u r e areas o f r e s e a r c h i n marine t r a f f i c s i m u l a t i o n models. 1. GROWTH RATE OF COLLISION The graph o f the smoothed s i m u l a t i o n f o r e c a s t s (see page 78.) o f the ex p e c t e d number o f c o l l i s i o n s , E ( K ) , i n R o s a r i o S t r a i t s u g g ests t h a t a 4% a n n u a l ; i n c r e a s e i n v e s s e l t r a f f i c w i l l cause an e x p o n e n t i a l growth i n the i n c i d e n c e o f c o l l i s i o n over the nex t t e n y e a r s . The e x a c t r a t e r o f the e x p o n e n t i a l growth i n E(K) i s e v a l u a t e d i n Appendix I . The v a l u e o f r i s a p p r o x i m a t e l y 0.0675. In o t h e r , w o r d s , a 4% annual i n c r e a s e f o r marine t r a f f i c i n R o s a r i o S t r a i t w i l l cause an e x p o n e n t i a l i n c r e a s e i n the i n c i d e n c e o f c o l l i s i o n a t the r a t e o f 6.75%. T h i s compares f a v o u r a b l y t o the approximate growth r a t e o f 6.05% o b t a i n e d from the Honeywell model. 2. RADAR MARINE GUIDANCE SYSTEMS The model can be used as a q u a n t i t a t i v e t o o l i n de-c i d i n g the o p t i m a l l o c a t i o n o f a shore-based r a d a r marine g u i -dance system. S i n c e the model y i e l d s the ex p e c t e d number o f c o l l i s i o n s f o r each segment o f the c h a n n e l , the e f f e c t o f i n s t a l l i n g a guidance system i n any p a r t i c u l a r c h a n n e l segment can be s i m u l a t e d . The f o r e c a s t o f the ex p e c t e d number.of c o l -l i s i o n s r e s u l t i n g from one i n s t a l l a t i o n l o c a t i o n can th e n be compared to r e s u l t s o f o t h e r l o c a t i o n s . I n t h i s way the model can be used i n d e t e r m i n i n g the i n s t a l l a t i o n l o c a t i o n most e f -f e c t i v e i n r e d u c i n g the o v e r a l l c o l l i s i o n i n c i d e n c e . These l o c a t i o n s can then be a n a l y z e d f o r c o n s i d e r a t i o n s such as the a c c e s s i b i l i t y o f the l o c a t i o n t o p e r s o n n e l i n s t a l l i n g , main-t a i n i n g , or r e p a i r i n g the r a d a r base as w e l l as the numerous economic c o n s t r a i n t s i n v o l v e d i n such a system. A c c o r d i n g t o the model, the l o c a t i o n most e f f e c t i v e i n r e d u c i n g the e x p e c t e d number o f c o l l i s i o n s i n R o s a r i o S t r a i t i s segment two w h i c h i s the segment between B e l l Rocks and N o r t h Peapod Rock. 3. ROUTING T r a f f i c s e p a r a t i o n and one-way r o u t i n g has s i g n i f i -c a n t l y reduced the i n c i d e n c e o f marine c o l l i s i o n s i n the E n g l i s h Channel. However, the l a s t t h r e e e x p e r i m e n t s i n d i c a -t e d t h a t t h e r e would be no s i g n i f i c a n t d i f f e r e n c e i n the over-a l l mean number o f c o l l i o n s , ( c o l l i s i o n s i n v o l v i n g o n l y f r e i g h t e r s and/or tows as w e l l as t a n k e r s ) , r e s u l t i n g from the t h r e e a l t e r n a t i v e r o u t i n g s t r a t e g i e s . The r e s u l t s o f the l a s t t h r e e experiments d i d , however, i n d i c a t e t h a t the r o u t i n g scheme most e f f e c t i v e i n r e d u c i n g the number o f head-on c o l l i -s i o n s i n v o l v i n g t a n k e r s was t o r e s t r i c t b o t h inbound and out-bound C h e r r y P o i n t t a n k e r t r a f f i c t o R o s a r i o S t r a i t . E xperiment number f o u r , which s i m u l a t e d t h i s r o u t i n g d i s c i p l i n e , f o r e c a s t e d t h a t 2.4 head-on c o l l i s i o n s c o u l d be e x p e c t e d t o o c c u r d u r i n g the t e n - y e a r p e r i o d f o r a l l marine t r a f f i c i n Haro S t r a i t , Boundary P a s s , and R o s a r i o S t r a i t . ( T h i s experiment a l s o s i m u l a t e d a 4% annual growth i n v e s s e l p o p u l a t i o n ) . , Of t h i s , the e x p e c t e d number o f t a n k e r c o l l i s i o n s was 0.02. 4. FORECAST A p p r o x i m a t e l y 40 v e s s e l s p e r day t r a n s i t the segment of Haro S t r a i t and Boundary Pass from K e l p Reef to A l d e n P o i n t . T h i s passage i s about twenty m i l e s l o n g . I f t a n k e r t r a f f i c d e s t i n e d t o and d e p a r t i n g from C h e r r y P o i n t i s r e s t r i c t e d t o R o s a r i o S t r a i t , the model f o r e c a s t s t h a t 2.402 head-on c o l l i -s i o n s w i l l o c c u r i n t h i s segment o f water d u r i n g the nex t t e n y e a r s , t h a t i s , from 1974 t o 1984. I f R o s a r i o S t r a i t t r a f f i c i s i n c l u d e d , the f o r e c a s t i s then i n c r e a s e d t o 2.404 c o l l i s i o n s . T h i s f o r e c a s t can be approximated as 2 v e s s e l c o l l i s i o n s r e -s u l t i n g from head-on e n c o u n t e r s over the next e i g h t y e a r s . I t i s i n t e r e s t i n g t o compare t h i s e i g h t y e a r f o r e c a s t w i t h h i s t o r i c a l d a t a on c o l l i s i o n s . A c c o r d i n g t o u n p u b l i s h e d s t a t i s t i c s c o m p i l e d by the Ma r i n e S e r v i c e s D i v i s i o n o f the Department o f T r a n s p o r t (Canada), e x a c t l y two c o l l i s i o n s and two groundings o c c u r r e d i n Haro S t r a i t d u r i n g the t w e n t y - t h r e e y e a r p e r i o d from J a n u a r y 1950 t o June 1973. A l l f o u r mishaps were c l a s s i f i e d as major s i n c e they i n v o l v e d v e s s e l s o f over 1000 g r o s s tons i n s i z e . The c o l l i s i o n s , u n f o r t u n a t e l y , were not c l a s s i f i e d as t o whether they were caused by head-on, ove r -t a k i n g , or c r o s s i n g e n c o u n t e r s . One gro u n d i n g o c c u r r e d o f f K e l p Reef and the o t h e r o f f T u r n ' P o i n t . One c o l l i s i o n o c c u r r e d abeam o f Hanbury P o i n t on San Juan I s l a n d and the o t h e r o c c u r r e d o f f o f Cowland P o i n t on South Pender I s l a n d . I n e s s e n c e , a l l f o u r mishaps o c c u r r e d i n the segment o f Haro S t r a i t and Boundary Pass s i m u l a t e d by the model and f o r which the model f o r e c a s t s 2 major c o l l i s i o n s i n a p p r o x i m a t e l y the nex t e i g h t y e a r s . 9 7 . 5. AREAS OF FUTURE RESEARCH The computer s i m u l a t i o n model developed i n t h i s t h e s i s c o n s i d e r s o n l y those c o l l i s i o n s r e s u l t i n g from head-on v e s s e l e n c o u n t e r s . The model c o u l d be expanded t o encompass the f o l l o w i n g : 1) A s i m u l a t i o n o f v e s s e l s o v e r t a k i n g o t h e r v e s s e l s i n a c h a n n e l and c a l c u l a t i o n o f c o l l i s i o n s r e -s u l t i n g from such e n c o u n t e r s . 2) A s i m u l a t i o n o f v e s s e l s i n v o l v e d i n c r o s s - c h a n n e l e n c o u n t e r s and a c a l c u l a t i o n o f c o l l i s i o n s r e s u l t -i n g from such e n c o u n t e r s . 3 ) A s i m u l a t i o n o f a shore-based marine guidance system t h a t d e t e r s and d e t a i n s v e s s e l s from e n t e r i n g chan-n e l segments d u r i n g hours o f h i g h c o n g e s t i o n o r when p a r t i c u l a r l y l a r g e v e s s e l s are t r a n s i t i n g the c h a n n e l . i 98. BIBLIOGRAPHY ADAMS, R. B., A Shipowners' View o f T r a f f i c R e g u l a t i o n , J o u r n a l o f N a v i g a t i o n , V o l . 25, No. 4, M. W. R i c h e y , ed., (London, England: John Murray L t d . , 1972). BEATTIE, J . H., T r a f f i c Flow Measurements.in the Dover S t r a i t , J o u r n a l o f N a v i g a t i o n , V o l . 25, No. 4, M. W. R i c h e y , ed., (London, E n g l a n d : John Murray L t d . , 1971). CANADIAN HYDROGRAPHIC SERVICE, B r i t i s h Columbia - Race Rocks  to E a s t P o i n t , (Ottawa, 1973), C h a r t #3449. CANADIAN HYDROGRAPHIC SERVICE, B r i t i s h Columbia - E a s t P o i n t  t o Sand Heads, (Ottawa, 1973), C h a r t #3450. DRAPER, J . , BENNET, C , M o d e l l i n g E n c o u nter Rates i n M a r i n e T r a f f i c Flows w i t h P a r t i c u l a r A p p l i c a t i o n t o Dover S t r a i t , J o u r n a l o f N a v i g a t i o n , V o l . 25, No. 3, M. W. R i c h e y , ed., (London, E n g l a n d : John Murray L t d . , 1972). DUNNE, A. G., C o l l i s i o n s and Groundings, J o u r n a l o f N a v i g a t i o n , V o l . , 25, No. 1, M. W. R i c h e y , ed., (London, E n g l a n d : John Murray L t d . , 1972). EMSHOFF, J . R., SISSON, R. L., De s i g n and Use o f Computer Simu- l a t i o n models, (New Yo r k , New York, the M a c m i l l a n Co., 1970). FRICKER, F. W., R e g i o n a l I n c i d e n c e o f C o l l i s i o n , J o u r n a l o f N a v i g a t i o n 7 V o l . 18, No. 2, M. W. R i c h e y , ed., (London, England: John Murray L t d . , 1965). F U J I I , Y a h e i , YAMANOUCHI, H a r o y u k i , The D i s t r i b u t i o n o f C o l l i s i o n s  i n Japan and Methods of E s t i m a t i n g C o l l i s i o n Damage, J o u r n a l o f N a v i g a t i o n , V o l 26, No. 1, M. W. R i c h e y , ed., (London, England: John Murray L t d . , 1973). F U J I I , Y a h e i ; SHIOBARA, R e i j i r o , The A n a l y s i s o f T r a f f i c A c c i -d ents , J o u r n a l o f N a v i g a t i o n , V o l . 24v No. 4, M. W. R i c h e y , ed., (London, E n g l a n d : John Murray L t d . , 1971). GORDON, G e o f f r e y , System S i m u l a t i o n , Englewoods C l i f f s , New J e r s e y : P r e n t i c e H a l l , I n c . , 1969. GRIMES, C., A Survey o f A c c i d e n t s w i t h P a r t i c u l a r R e f e r e n c e s  t o T a n k e r s , J o u r n a l o f N a v i g a t i o n , V o l . 25, No. 4, M. W. R i c h e y , ed., (London, England: John Murray L t d . , 1972). HARGREAVES, E. R., S a f e t y o f N a v i g a t i o n i n The E n g l i s h Channel, J o u r n a l o f N a v i g a t i o n , V o l . 26, M. W. R i c h e y , ed., (London, England: John Murray Ltd:-, 1973). IBM APPLICATION PROGRAM, G e n e r a l Purpose S i m u l a t i o n Systems V, User's Manual, #SH20-0851-1, I.B.M. C o r p o r a t i o n T e c h n i c a l P u b l i c a t i o n Dept., 1971. MAY, G., A Method f o r P r e d i c t i n g the Number o f Near M i d - A i r C o l l i s i o n s i n a D e f i n e d A i r s p a c e , O p e r a t i o n a l R esearch Q u a r t e r l y , V o l 22, No. 3 MEIR, R. C , NEWELL, W. T., PAZER, H. L., S i m u l a t i o n i n B u s i n e s s  and Economics, (Englewood C l i f f s , New J e r s e y : P r e n t i c e H a l l I n c . , 1969). NAYLOR, Thomas H., BALINTFY, Joseph L., BURDICK, Donald S., KONG CHU, Computer S i m u l a t i o n T e c h n i q u e s , New Y o r k , New York: John W i l e y § Sons, I n c . , 1966. STRATTEN, A., SILVER, W.. E., O p e r a t i o n a l R esearch and Cost . c B e n e f i t A n a l y s i s i n N a v i g a t i o n w i t h P a r t i c u l a r R e f e r e n c e t o M a r i n e A c c i d e n t s , J o u r n a l o f N a v i g a t i o n , V o l 23, No. 3, M. W. R i c h e y , ed., (London, E n g l a n d : John Murray L t d . , 1970). THOMPSON, R. P., E s t a b l i s h i n g G l o b a l T r a f f i c F l o w s , J o u r n a l o f N a v i g a t i o n , V o l . 25, M. W. R i c h e y , ed., (Tondon, E n g l a n d , John Murray L t d . , 1970). U. S. F o r e i g n Trade V e s s e l E n t r a n c e s and C l e a r a n c e s , 1970, : W. S. Department o f Commerce, Bureau o f the Census, FT975-70, 1971. The VANCOUVER SUN, newspaper a r t i c l e , A p r i l 9.; 1974, S e c t . 1, p. 2, c o l s . 4-9. WENTZEL, E., LYTLE, P., Automated M a r i n e T r a f f i c A d v i s o r y Sys-tems, T h e i r Needs and I m p l e m e n t a t i o n , Honeywell M a r i n e Systems C e n t e r , Document 2330, 1971. WHEATLEY, J . H. W..., C i r c u m s t a n c e s o f C o l l i s i o n s and S t r a n d i n g s , J o u r n a l o f N a v i g a t i o n , V o l . 25, M. W. R i c h e y , ed., (London, E n g l a n d : John Murray L t d . , 1972). 100. WONNACOTT, R. J . , WONNACOTT, T. H., E c o n o m e t r i c s , (New Yo r k , New York: John W i l e y t} Sons, I n c . , 1970). APPENDIX I EVALUATION OF EXPONENTIAL GROWTH RATE 102. APPENDIX I Let f ( t ) denote the e x p e c t e d number o f c o l l i s i o n s a t time t where t - 1, 2, " • , 10 y e a r s Continuous growth i m p l i e s t h a t at ev e r y i n s t a n t o f time t , the expected number o f c o l l i s i o n s f ( t ) = E ( K t ) i s a c c u m u l a t i n g a t the r a t e o f r % . Thus, the i n s t a n t a n e o u s r a t e o f i n c r e a s e a t time t i s r f ( t ) . Hence, by d e f i n i t i o n : ^ ( f ( t ) ) = f ( t ) = r f ( t ) > f ' ( t ) - r > S ^ f a t = S r d t = > l n f ( t ) = l o g f ( t ) = r t + c i 6 ^ JTY*-> r t + c i , r t = > f,(t) = e = ce •10*K where n = 10 y e a r s X V = t f o r t = 1, 2, ... , 10 x = X - X t t Y t denotes the s i m u l a t e d v a l u e o f EfK^] from experiment two. The v a l u e o f r was e v a l u a t e d as 0.0675 u s i n g the f o l l o w i n g WATFIV programme. A N G S xxxxxxxxxxxxxx'xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx R F S N O , 1 1 7 5 0 2 U N I V E R S I T Y OF B C C O M P U T I N G C E N T R E M T S ( U L 1 8 4 ) 1 S I 2 2 I 3 6 T H U A U G 1 5 / 7 « SHUTDOWN W I L L BE AT 2 2 | 0 0 S U N D A Y S AND 2 3 | 3 0 W E E K D A Y S T E M P O R A R I L Y - S E E OPS N O T I C E S S I G S H I P * * L A S T S I G N O N WASJ 1 5 I H I I U 8 S S S S S S S S S S HH HH I I I I I I I I I I ppppppppppp S S S S S S S S S S S 3 HH HH I I I I I 1 1 I I I pppppppppppp ss ss HH HH I I P P P P ss HH HH I I P P P P sss HH HH I I P P P P sssssssss H H H H H H H H H H H H I I pppppppppppp sssssssss H H H H H H H H H H H H I I P P P P P P P P P P P sss HH HH I I P P ss HH HH I I P P S S S 3 HH HH I I P P S S S S S S S S S S S S HH HH I I I I I I I I I I P P S S S S S S S S S S HH HH I I I I I I I I I I P P A A A A A A A A A A NN NN G G G G G G G G G G S S S S S S S S S S A A A A A A A A A A A A NNN NN G G G G G G G G G G G G S S S S S S S S S S S S AA AA NNNN NN GG GG ss ss AA AA NN NN NN GG ss AA AA NN NN ' NN GG sss , A A A A A A A A A A A A NN NN NN GG sssssssss / A A A A A A A A A A A A NN NN NN GG GGGGG sssssssss AA A A NN NN NN GG GGGGG sss AA AA NN NNNN GG GG ss AA AA NN NNN GG GG ss ss AA AA NN NN G G G G G G G G G G G G S S S S S S S S S S S S AA AA NN N G G G G G G G G G G S S S S S S S S S S U S E R " S H I P " S I G N E D ON AT 1 5 l 2 2 l 3 6 ON THU AUG 1 5 / 7 « F I L E " B B A N | S I G F I L E " D O E S NOT E X I S T , S I G F I L E U N A V A I L A B L E 1 R U N * W A T F I V E X E C U T I O N B E G I N S C 5 C • . fc C C A L C U L A T I N G THE T H E O R E T I C A L E X P O N E N T I A L GROWTH C U R V E 7 C FOR T H E E X P E C T E D NUMBER OF C O L L I S I O N S B C U S I N G L I N E A R R E G R E S S I O N ON THE N A T U R A L L O G 9 C OF T H E S I M U L A T E D C O L L I S I O N F O R C A S T S 10 C 11 c ia 1 R E A L K ( 1 0 0 ) , L N C 1 0 0 ) , Y ( 1 0 0 ) 13 2 I N T E G E R T ( 1 0 0 ) 1U 3 A A = 0 , 9 15 « 3 U M X = S U M Y = 0 . 0 16 • E X T E N S I O N * O T H E R C O M P I L E R S MAY NOT A L L O W M U L T I P L E A S S I G N M E N T S T A T E M E N T S 5 R E A 0 , T ( 1 ) » Y ( 1 ) 17 6 K ( l ) a y ( i ) 1 8 7 P R I N T 1 7 , K ( 1 ) 19 8 17 F O R M A T C ' 1 ' , ' E X P E C T E D tt C O L L I S I O N S FOR Y E A R I I S I . F l t t . B ) 20 9 S U M X = 3 U M X + T ( t ) 21 10 S U M Y = S U M Y + A L 0 G C K C 1 ) ) 2 2 11 UsZ 2 5 12 8 R E A 0 ( 5 , * , E N D = 7 ) T ( N ) , Y ( N ) 2 a I J K ( N ) = K ( N - l ) + A A * < r ( N ) - K ( N M > > 2 5 Itt P R I N T 1 8 , N , K ( N ) 2 6 15 I B F O H M A T t ' O ' , ' E X P E C T E D tt C O L L I S I O N S FOR Y E A R » , 2 X , 1 2 , 2 X , ' I S ' , F 1 U , 6 ) 27 16 S U M X = S U M X + T ( N ) , 28 17 S U M Y = S U M Y * A L O G ( K ( N > ) 29 18 N = N+1 JO 19 GO TO 8 J l 2 0 7 N o N » l 3 2 21 A = S U M Y/N J J 2 2 X B A R = S U M X / N JO 2 J S U M X 2 = 3 U M Y X = 0 , 0 3 5 • E X T E N S I O N * OTHER C O M P I L E R S MAY NOT ALLOW M U L T I P L E A S S I G N M E N T S T A T E M E N T S 2tt DO 9 1 = 1 , N 36 2 5 S U M X 2 = S U M X 2 * ( T C I ) « X B A R ) * * 2 37 2 6 9 S U M Y X = 3 U M Y X + A L 0 G ( K ( I ) ) « ( T ( I ) « X B A R ) J 8 2 7 B E T A = S U M Y X / S U M X 2 39 2 8 Al.PH» = A - R E T A * X B A R 00 2 9 P R I N T 1 , A L P H A , B E T A ttl 3 0 1 F O R M A K ' 1 ' Y = ' . F l O . t t , t t ' , F 1 2 ' . 6 , ' X ' , / , ' « • ' , ' L E A S T S Q U A R E S E S T I M A T E 0 2 1 0 F L O G TO THE B A S E E OF THE E X P E C T E D * OF C O L L I S I O N S FOR THE R E S P E 0 3 2 C T I V F Y E A R S A R E AS F O L L O W S I ' ) 00 J l DO 10 1=1,H as 3 2 L N ( I ) = A L P H A + B E T A * T ( I ) > « 6 J J 10 P R I N T ? , I , L N ( I ) 07 Jtt 2 F O R M A T C ' 0 ' , ' L N ( E ( K ) ) FOR Y E A R ' , I J , ' I S « ' , F 1 0 , 8 ) a s J 5 P R I N T 3 . B E T A 0 9 J 6 3 F O R M A T C 't ' « ' E X P O N E N T I A L GROWTH R A T E OF THE E X P E C T E D tt OF C O L L I S I O N 50 I S I S l ' , F 1 2 , 6 , / , ' - ' , ' T H E L E A S T S Q U A R E S E S T I M A T E OF E ( K ) FOR THE R E S 51 2 P E C T I V E Y E A R S A R E A S F O L L O W S I ' ) 5 2 J 7 DO I S 1 = 1 , N 5 J J 8 1 5 P R l N T O , I , E X P ( L N U ) ) 5 « • E X T E N S I O N * O T H E R C O M P I L E R S MAY NOT ALLOW E X P R E S S I O N S I N O U T P U T L I S T S J 9 0 F O R M A T C ' C ' E C K ) FOR Y E A R • » 1 3 , ' I S | ' , F 1 « , 8 ) 5 5 ttO P R I N T S 56 01 5 F 0 R M A T C ' 1 ' , 5 9 X , ' E N D OP P R O G R A M M E ' ) 57 0 2 S T O P 5 8 aj E N D 5 9 S O A T A E X P E C T E D * C O L L I S I O N S FOR E X P E C T E D * C O L L I S I O N S FOR E X P E C T E D « C O L L I S I O N S FOR E X P E C T E D * C O L L I S I O N S FOR E X P E C T E D « C O L L I S I O N S FOR E X P E C T E D « C O L L I S I O N S FOR E X P E C T E D * C O L L I S I O N S FOR E X P E C T E D » C O L L I S I O N S FOR E X P E C T E D * C O L L I S I O N S FOR E X P E C T E D * C O L L I S I O N S FOR Y E A R 1 I S 5 , 3 5 0 7 0 0 0 0 Y E A R 2 I S 5 . 9 1 8 2 5 9 0 0 Y E A R 3 I S 7 , 8 b 9 2 2 3 0 0 Y E A R a I S 7 , 7 0 ( 1 3 2 1 0 0 Y E A R 5 I S 8 , 1 3 0 2 3 1 0 0 Y E A R 6 I S 8 . 2 1 A 1 2 1 0 0 Y E A R 7 I S 9 , 7 6 0 2 1 1 0 0 Y E A R 8 I S 1 0 , 7 8 3 3 2 0 0 0 Y E A R 9 I S 8 , 2 0 8 0 9 3 0 0 Y E A R 10 I S 1 1 , 0 9 7 0 4 0 0 0 r» 1 , 7 2 1 1 * 0 . 0 6 7 5 7 0 X L E A S T S Q U A R E S E S T I M A T E OF L O G TO THE B A S E E OF THE E X P E C T E D * OF: C O L L I S I O N S ( r 0 R T H E R E S P E C T I V E Y E A R S A R E AS F O L L O W S I L N ( E C K ) ) FOR Y E A R 1 1 s t 1 , 7 8 8 9 2 7 0 0 L N C E ( K ) ) FOR Y E A R 2 I S l 1 , 8 5 6 5 0 0 0 0 L N C E ( K ) ) FOR Y E A R 3 I S I 1 , 9 2 0 0 7 0 0 0 L N C E C l O ) FOR Y E A R 0 I S l 1 , 9 9 1 6 0 7 0 0 L N ( E f K ) ) FOR Y E A R 5 I S l 2 , 0 5 9 2 2 1 0 0 L N C E C K ) ) FOR Y E A R 6 I S l 2 , 1 2 6 7 9 0 0 0 L N f E ( K ) ) FOR Y E A R 7 I S l 2 , 1 9 0 3 6 8 0 0 L N ( E ( K ) ) F O R Y E A R 8 I S 1 2 , 2 6 1 9 0 1 0 0 L N C E C K ) ) FOR Y E A R 9 I S l 2 , 3 2 9 5 1 5 0 0 L N ( E ( K ) ) FOR Y E A R 10 I S l 2 , 3 9 7 0 8 9 0 0 E X P O N E N T I A L GROWTH R A T E OF THE E X P E C T E D » OF C O L L I S I O N S I S l 0 , 0 6 7 5 7 a THE L E A S T S Q U A R E S E S T I M A T E OF E ( K ) FOR THE R E S P E C T I V E Y E A R S A R E AS F O L L O W S I E C K ) FOR Y E A R 1 I S l 5 , 9 6 3 0 2 9 0 0 E ( K ) FOR Y E A R 2 I S l 6 . 4 0 1 2 9 6 0 0 E C K ) FOR Y E A R 3 I S l 6 , 6 4 8 8 0 4 0 0 E C K ) FOR Y E A R 4 I S l 7 , 3 2 7 5 9 7 0 0 E C K ) FOR Y E A R 5 I S l 7 , 8 3 9 8 6 1 0 0 E C K ) FOR Y E A R 6 I S l 8 , 3 8 7 9 3 8 0 0 E C K ) FOR Y E A R 7 I S l 8 , 9 7 4 3 2 9 0 0 E C K ) FOR Y E A R S I S l 9 , 6 0 1 7 1 6 0 0 E C K ) FOR Y E A R 9 I S l 1 0 , 2 7 2 9 6 0 0 0 E C K ) FOR Y E A R 10 I S l 1 0 , 9 9 1 1 3 0 0 0 110. APPENDIX I I FLOWCHARTS OF SIMULATION MODEL K T R L l V34oo ,F^fe<po,„ ,2S 7, KI TANKER OR FREIGHTER INTO THE SVST5M 1 IHKKATES INBouNb V £ S S 5 i S \l INDICATES 0UT80UN0 V £ S S £ i S (FREIT) ( ) 1 IMC/cATES FREIGHTER 1 INDICATES A TANKER > {THRU) (BELL) IN&OVNb # OOTI2,0UNO THRO TRAFFIC FREIGHTER TRAFFIC OfST/wf O To EGLLIN&HAM ORIG-CORIG-) 4 > -f?os/o v 8> KI AJ • • ' A 7> A -N ) FREIGHTER. TRAFFIC ORICr/NATIAld- /N BELLIN6-HAM 8, K 3 A-N ' % K» A •N A ) ASSIST TO PARAMETER # S THE NUMBER OF THE CHANNEL SEGMENT THE VESSEL WILL IN IT/ALLY ENTER ASS'fi/N/ TO PARAMETER rf °[ THE NUMBER OF THE LA%T CHANN6L SEG-MENT THRU VsimcH THE V5SS5Z W/AL KTRL3 G-V»60, FrtSexPo, B A R G E TRAFFIC TO HELLtNGHAM FROM VANCOUVER ( 3 PER WE£H) P B I S T H E # O P T H C CHANNEL SEGMENT TUB VESSEL VJILL /NI7/ALI V ENTER P<^  I-J THE # OF THE iAST CHANNEL SEGMENT THRU \NHICH THE VESSEL VI ILL PASS P~? INDICATES /A/ WHAT blRECJION (/NQoVNb OR OUTBovNb) THE VESSEL THE VE£S£L WILL T/?/fAJS,r THE CHANNEL OR STRAIT BAK&£ TRAFFIC TO BELL/NG-NAM FKoM SEATTLE A/J{> VICTORIA C 4- PER WEEK) p-) = [ i INDICATES /NgOUNt) Z INDICATES OUTBOUhJb 8AR6 5 TRAFFIC ORIGINATING-IN Q.ELL/NG-HAM C 7 PEI? W 5 £ « ) I5ARG-E TRAFFIC FROM &ELLINGHAM TQ SEATTLE OR TO VICTORIA C 4- PER WE EH) (MAN) BARGE TRAFFIC FROM BEL L INGHAM TO VANCOUVER ( 3 PER WEEK) o PARAMETER 1 HAMl/VG- A VALUE OF 3 INDICATES THE VESSEL TRANSACT/OA/ 'S /t BARG-E TYPE-ENTRY POINT OF TANKER A WO FREIGHTER TRANSACTIONS INTO THE PROGRAM FL OVA/ PARAMETER *2 INDICATES THE VOLUME OF TRAFFIC THE TRANSACTION REPRESENTS C IN CASE OF MULT/ - ARRIVALS) P8 15 T H 6 L O O P I M G - P A R A M E T E R W . R. T. T H E NUMBER OF THE CHANNEL STORAGE SEG-MEN T PS IS THE NUMBER OF THE CHANNEL STORAGE SEGMENT THE VESSEL /NIT/AL L. Y ENTERED 1 1 3 O U T DETERMINE? IF THE VESSEL IS /NBOUNO COOT) PI c c INBoUND VESSELS ENTER THE RESPECTIVE CHANNEL SEGMENTS <S, Vi A-N 1 13, K3 A-N CBAK) ASSIGN TO PARAMETER *C THE NUMBER OF THE OUTBOUND LANE OF THE SAME CHANNEL SEGMENT Pl3> IS LO0PIN& PARAMETER. 1 3 Loop BAK ASSI6N THE ACCUMULATED NUMBER OF T O W S ; TANKER^ ANb FREIGHTERS, RESPECTIVELY) HAVING ENTERED THIS CHANNEL SEGMENT TKAVE/L/NG IN THE OPPOSITE CIKECTION. TO THE THE RESPECTIVE PARAMETERS  C F THIS VESS E L TdA H'S A C TIO OUlBouNO VESSELS, ENTER TNE RESPECTIVE CHANNEL S EG-ME NTS INCREMENT ACCUMULATIVE COUNTERS FOR l TOTAL NUMRER OF OUT/2 ou/UD VESSELS PASS/NG THRU RESPECTIVE CHANNEL SEGMENTS TOTAL NUMBER OP To IMS. TANKERS j AND FREIGHTERS HAVING PASS ED THROUGH VESSELS 70/N THE APPROPRIATE GROUP (VJ.R.T. VESSEL TypC) IN THE RES PEC Ti V£ CHANNEL SEGMENTS A-E FN&TIHE, FNkEY.Po ASS.I6- N TOTAL # HAVING SESMENT IN DlZEC TION TO PARAMETER II THE OP VESSELS TO DATE PASSED THRU 77//S THE OUTBOUND VESSEL TRANSITS THE CHANNEL S£GMENT> TRAMS I T TIME BE/NG A FUNCTICAJ OF Born CHANNEL SEGMENT LENGTH ANO VELOCITY OF VESSEL VESSELS REMOVED FRO PI THE & ROUPS VJHICH THEY JotNE& AS,S'6N TO PAR A MB TER IO THE #0E \IESSELS CURRENTLY /N THIS SEgML'MT THAT ARE TRAM ELL IN 6r IN /IN 00 TROUND DIRECTION HIS IS LOOPING- PARAMETER L-E PI C8AG) c A-N- ) A iS 16 N THE HVM&ER; OF TovJS, TANITERS ) A NO FREIGHTERS ' RESPECTIVELY, CURRENTLY'/N THIS SE6NENT TRAVEL L IN&-IN QO7&OVNL> DIRECTION, TO THE RESPECTIVE PARAMETERS OF THIS VESSEL TRANSACTION "VESSELS DEPART THE RESPECTIVE CHANNEL SEGMENT NEXT TEST To DETERMINE IF VESSEL HAS TRANS/TIED THE APPROR/ATE NUMBER OF CHANNEL SEGMENTS BEFORE IT DEPARTS THE CHANNEL VESSEL DEPARTS THE S ys TEA? (C//A AlNEL) .114. A-E FN$.7IME, FfJ 3_ ( ) (BACK) c /4 -A/ V f s A-N VESSEL TRANSITS THE RES Pieri^E , CHANNEL SEGMENT ^EKPO C/NBouND DIRECT/ON) ASSIGN To PI2 THE UP DA TEC TOTAL * o^ " VESSELS HAM/N& ENTERED THE RESPECTIVE SE&MENT IN OUT80UND) DlREc 7/0 A/ INCREMENT COUNTER FOR THE TOZAi. NUMBER OF ONCOMING- C HEAD-ON) VESSEL ENCOUNTERS TO t>A TE /N THE RESPECTIVE CHAllHEL ZECrMENTS PI2 IS LOOPING-PARAMETER A" N ASSI6M UPDATED VS. MXl\(pR Pl~>\ ACCUMULATIVE TO\NS, TANKERS, y FREIGHTERS HAVlklG-ENTERED RESPECTIVE N SEGMENT, TT> APPROPRIATE £ ) TRANSACTION" PARAMETERS INCREMENT COUNTER FOR HE Ad ~ OA) VESSB ENCOUNTERS AMON VESSEL TYF>E£ VESSEL DEPARTS THE RESPECTIVE OH AH HE L SEGMENT \ TEST TO DETERMINE IF THE VESSEL HAS TgANS/TEb A L L THE CHANNEL 2>£@MEAITS\ NECESSARY To ARR/t/E AT ITS bESr/NN TIOAJ. SIMULATE TH£ SiSTEpi Fon ONE YEAR. AND THEN" RECORO ALL TRAFFIC FLOVJ STATISTICS FOR TH£r S£GM£AJT£ OF THE CHANNEL VESSEL DEPARTS THE SYSTEM APPENDIX I I I PROGRAM LISTINGS AND SAMPLE OUTPUT ANGS xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx R F S N O . 1 3 9 5 3 3 U N I V E R S I T Y O f B C C O M P U T I N G C E N T R E M T S C P R 1 8 4 ) 1 1 1 4 1 ( 1 8 THU J U N 2 0 / 7 4 * * A L L S P E C I A L FORMS & T N O U T P U T W I L L B E D E L A Y E D U N T I L F U R T H E R N O T I C E * * " " S S I G S H I P T = 1 2 0 P = 5 0 * * L A S T S I G N O N WAS« 1 1 : 3 0 1 1 0 3 S S S S S S S S S S HH HH I I I I I I I I I I P P P P P P P P P P P S S S S S S S S S S S 3 HH HH I I I I I I I I I I P P P P P P P P P P P P S S 3 3 HH HH I I P P P P o S S HH . HH I I P P P P S S S HH HH I I P P P P S S S S S S S S S H H H H H H H h H H H H I I P P P P P P P P P P P P . . . c S S S S S S S S S H H H H H H H H H H H H I I p p p p p p p p p p p S S S HH HH I I P P S S HH HH I I P P S S S S HH HH I I P P S S S 3 S S S S S S S S HH HH I I I I I I I I I I P P S S S S S S S S S S HH HH I I I I I I I I I I P P A A A A A A A A A A NN NN G G G G G G G G G G S S S S S S S S S S A A A A A A A A A A A A NNN NN G G G G G G G G G G G G S S S S S S S S S S S S AA AA NNNN NN GG GG S 3 S S AA AA NN NN NN GG SS AA AA NN NN NN GG S S S A A A A A A A A A A A A NN NN MN GG S S S S S S S S S A A A A A A A A A A A A NN NN NN GG GGGGG S S S S S S S S S AA AA NN NN NN GG GGGGG S S S AA A A NN NNNN GG GG SS AA AA NN NNN GG GG S S S S AA AA NN NN G G G G G G G G G G G G S S S S S S S S S S S S AA AA NN N G G G G G G G G G G S S S S S S S S S S U S E R " S H I P " S I G N E D ON AT 11S 4 1 : 18 ON THU J U N 2 0 / 7 4 F I L E " B B A N j S I G F I L E " D O E S NOT E X I S T , i S I G F I L E U N A V A I L A B L E S R U N * G P S S V P A R = S I Z E o C ' E X E C U T I O N B E G I N S * * * G P S S V - M T S V E R S I O N * * * * * I B M P R O G R A M P R O D U C T 5 7 3 4 - X S 2 C V 1 M 2 ) * * * FOR U P - T O - D A T E I N F O R M A T I O N R E G A R D I N G * G P S S V ' S L I S T N E W S S G P S S V B L O C K ' S T A T E M E N T So' NUMBER * L 0 C O P E R A T I O N A , B , C , D , E , F , G , H , I C O M M E N T S NUMBER S I M U L A T E 1 * ' 2 v'H-1 * ~ 3 oy * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 4 • ' * * * S . J. ' * * V A L I D A T I O N U S I N G E N G L I S H C H A N N E L DATA * b \ * * ' * - 7 t-* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 8 > * 9 * 1 0 kli * 11 ff» P o o 'a •9 117, ^ w . ^ ^ ^ ^ ^ ^ r u n j r u r v j n j n j n i r \ j ( \ i i \ i r o r o > o r t =j c i i n i n t r » i n L f > t n i n i n i r > i n - o - o ^ o ^ o - ^ > - C N O ' X ) - c -£> r~ r>-» rvi OJ OJ \ •— un r o i £ * . * o r o cn *-H V. W tt v ro 3 =j ^  o w » X *• ro t i l v . x r o i • • ro n o - o • i n o • cr- o> > cr • i • \ • v ro » ro » r • i n • ev ^ ^ » i n "i cr- o-1 • t v . • J to c J DO O-•-». • • ro u =1 13 — t> 00 • OJ O O ^ w o » o o o o o o n a *. oj rvi * C J T J ^ r ^ iT rvj =r o —• «-• o o «• » r\j ». » » » » » *. o * rvj ^ cj =r * •» » ». « <-\ *. » o - " * r t 3 i / i - o r - a 3 t > t \ i « » - M f \ i w - * * •>• r - «. ^ ^ . ^ x — w ^ ^ ^ T - « - . x - « x w x X - ^ ' - ' w ^ w w w ^ x ^ ^ x X X X X X X - v X O X N , . X ^ w ^ ^ X X ^ ^ \ \ 0 3 % v \ \ \ > v > v \ o N V . . - . N > . . 0 V . X X X X X X X X = J - O • O h t > - £ N ' « « ) ru » o x x r x ^ - v x ; * : ^ \ ^ \ \ A J C I \ \ ^ ^ ^ ^ « ^ ^ ^ ^ ^ ^ - x ^ ^ . K l * - » r O ^ r - i n c r - — » . - « o ^ r O f O * r > ^ f r f " ' " l p ^ r o r O r O r o r O *• ro * s - x * . * * . * . . * . * . * . * . . * * o j * . A J * r o ^ ^ « " " ^ ^ " 0 - i ^ « i a i n -o N £ o ~ o j r o I M * r O r o r o r o r O r o r o r o w r - t w ^ . ^ . r * ^ i ^ t » - i ^ n J ( \ J « - ' n j v ^ — . w w w * ^ w w w * - . x : x x x x x x x x x x x x . x x I r i T , r t ^ - - . ^ « 3 . z \ i i ' z i i r J : i v r \ X X X . X X X X X X * v . \ — ^ ^ • V N . N . ^ - N ^ ' V S . - J ^ ' S . O N . x x x x x x z s r i n w H M M n i / i O ' W ^ s M ^ o - H \ fc „, » » * •«. » » »» » «» «. ». n j TO CO —• -3 lOI\l^ *-ir.^ -n-i*ii-»n,j-ir.A^ r^tr» » » *. *. » < f c n j n j n j f \ j . - \ j r u r \ i r v j r \ i n j ( \ : n i n j n j r \ i nj^ *->«^-.--.-r>^^ * * * * v * . •» * » - * «. * i \ i r \ j r \ j n j A j r v j i \ i n j o - - » r \ i r o = j i n x M C O o ^ f t j c i q —. «. % » * ^ * . n j r c n j r v i r u x — — — x x x x x x x x x x x x x x x x x x x x x x x x x x X X X X X X x x x x x x x N . X X X X X X X X X N i ' v > v \ X L N l \ > v \ ^ , V > v X L N . • * X X X X X X X X X X I X X X X J X X X X X X X X c x x x x x x x x x x x x x x x x x x x x x x x x a : r - r - f ~ t — i— r— >~ t— r- r - r- t -•CO C -K * J O O ; o o ) o o [ co CO * o o » sO o • ^ w f\J « a> to -o ' + :^ • w * * v . i u •-* ro M X X U i n o r o X. XL * \ ru ^ o-co \ n j + ^ i t o U N CL ^ X O -« * * —• * * UJ UJ UJ IU U i U J _ l _ ) _ J J j J U i _ i _ J J J E D CD -a < < CD CD < < •d >-\ r-i -a. «i t-i t-* ca t r a M MQ: t r < > > > < < > > > U - U . U ^ > > U . U . — i r u r o ^ u i ^ s t o ('• ('i ('". • o (i {""i C") o o 0 o (J u u (j U 118. »o o o o o O Q . x x i -Z L i O U_ >— CO O K1 M in i x y rvj r\j nj • - nj > rvj > X- * * CL X CO » X * X *. y-. CJ- d - J • H IM 7 ^ *-» w co O «> cj ^  J J rvj » «. v «. ». tn -o r» x. x x x : o x x x : —« x x \ • * cn o r x — . X . X SL / CT X . X < - 0 3 X X SL r X. X . x - * - • — « — • x x x x x x *x £ SL X X X .-O "X. V . X , X , X . »• CI •© o • ro m ro ro • r\j ro cy m 4 5 M O O • • c in -c i X — — 3: x x x V . 31 SL SL 4} X X X ». nj ro cc X X X SL X X X X X ' X X X I x x x £ X X X X X X . X X X X SL —• X X . X X . X . ' ^ r- o> in in o r\i a. i~ r\j CL • . w o . «. -•-I M W I L I V O ' nj t\j ru .it 43 nj O J r\j r~- x> O o «-* (\j fy A J nj fu (\j nj ro in -o r-x x x x x X x X. X X X «-> 3 ifl I V I X X X X X X x x x x x x X X X . X X . X M O « ^ f \ i O o —• x x x x O 43 X •O O -O X < f\J tO 7 N CO m x > * . a a > > > > > m « N a ^ M ^ rv ^ c * X X X X X X X X X X X X X X X X X x x r x x x x x x x x x x x x x . x x Ui 3 • -»— U: _l < < a i : z u 2 < ^ tr »- tr (J> i t i i i u o z o > iu M ^ H H M H t - U J l L I H H < H l U > X ^ _ i t o c o c o c o f ~ u . c o c o > t o > < . 3 : uj a. cn co iu iu z 3 C O C O O C O < I J J U J L D C O < < f - h - U J £ D 4 < < < W _ J | -<1 t_> 2 f t > 2 a J M U ; U) < > X t- > > < i Z 4 C UJ UJ aJ tO - i _ J t-U l U l UJ UJ UJ U i UJ UJ 3 r 3 !J 3 D H t~ _* i i —i —i i < x z < < <r < -i - i ^ c t o o > > > > > » - * > -u j i - . t - . u j c x u j u j u i u j L U X or j r c o c o j » - o > > > > > a t < . UJ CO CO i ' Q < < - t < « i a l h 0 < < 0 ) _ 1 0 ) t f ) ( O C O O T H 00 ru X < t < J < l < < l H « l -- J <t z z Z Z Z Z Z Z Z Z Z Z Z Z 2 o o o I N I T I A L M H 1 C 1 8 , 1 ) , 1 / M H 1 ( 1 8 , 2 ) , 3 / M H l C 1 8 , 3 ) , 6 / M H 1 ( 1 8 , 4 ) , 0 1 3 2 I N I T I A L M H 1 ( I 9 , l ) , 3 / M h l ( 1 9 , 2 ) , 4 / M H l ( 1 9 , 3 ) , 7 / M K 1 ( 1 9 , 4 ) , 2 1 3 3 I N I T I A L , M H 1 ( 2 0 , 1 ) , 2 / M H l ( 2 0 , 2 ) , 4 / M H l ( 2 0 , 3 ) , 1 0 / M H i ( 2 0 , 4 ) , 0 134 I N I T I A L M H 1 ( 2 1 , 1 ) , 1 / M H 1 ( 2 1 , 2 ) , 3 / M H l ( 2 l , 3 ) , 8 / M H l ( 2 1 , 4 5 , 2 1 3 5 I N I T I A L f.Hl (22, 1 ) , 3/MHl (22,2) , 1 5 / N H l (22 , 3 ) , 1 O / H H 1 ( 2 2 , 4 ) , 2 136 1 M 1 I AL M h l ( 2 3 , 1 ) , 1 / M M 1 ( 2 3 , 2 ) , 9 / M H l ( 2 3 , 3 ) , 2 / M H l ( 2 3 , 4 ) , 2 137 c I N I T I A L MM I ( 2 4 , I ) , 3 / M H l ( 2 4 , 2 ) , 1 0 / M H 1 ( 2 4 , 3 ) , 6 / M H 1 ( 2 4 , 4 ) , 1 138 S T A R T 1 139 * 140 R E P O R T 141 E J E C T 142 CIO T I T L E . S I M U L A T I O N T I M E ( C L O C K ) S T A T I S T I C S 1 4 3 c S P A C E 5 144 B L O T I T L E , V E S S E L T R A F F I C I N THE S I M U L A T I O N MODEL 1 4 5 E J E C T 1 4 6 c STO T I T L E ( E N G L I S H C H A N N E L ( D O V E R S T R A I T ) V E S S E L S T A T I S T I C S • 147 S P A C E 2 148 5 T E X T V O L U M E Or N O R T H B O U N D V E S S E L S I N D I C A T E D BY S T O R A G E 1 149 S P A C E 2 / 150 5 TE<T V O L U M E OF S O U T H B O U N D V E S S E L S I N D I C A T E D BY S T O R A G E 2 151 S P A C E 2 152 5 T E X T A P P R O X , 1 2 0 , 0 0 0 V E S S E L T H R U - M O V E M E N T S P E R - Y E A R 1 5 3 S P A C E 1 154 5 T E X T B A L A N C E C O N S I S T S OF L O C A L AND C R O S S - C H A N N E L T R A F F I C 1 5 5 E J E C T 1 5 6 E J E C T 157 G R A P h X H , 1 , 2 4 158 O R I G I N 5 0 , 6 159 X , 3 , 2 , , , , N 0 1 160 Y 0 , 1 , 2 4 , 2 161 7 S T A T E M E N T 5 1 , 1 2 4 , S A T U R D A Y 1 1 6 2 1 1 6 3 S U N D A Y 164 9 S T A T E M E N T 5 2 , 1 2 2 , 1 2 : 0 0 1 1 6 5 1 166 2 : 0 0 167 7 S T A T E M E N T 5 3 , 1 2 5 , 1 3 M A R C H 1 168 1 169 0 M A R C H 170 3 8 S T A T E M E N T 5 5 , 4 8 , H O U R L Y T R A F F I C V O L U M E OFF F O L K S T O N E / C A P G R I S N E I 171 Z 172 3 8 S T A T E M E N T 5 7 , 4 8 , D I U R N A L / N O C T U R N A L FLOW - N O R T H B O U N D / E N G L I S H S I D 1 1 7 3 e 174 E N D G R A P H . i 1 7 5 E J E C T 1 7 6 G R A P H X H , 2 5 , 4 8 •177 O R I G I N 5 0 , 8 1 7 8 X , 3 , 2 , , , , N 0 . . . . 179 Y 0 , 1 , 2 4 , 2 180 7 S T A T E M E N T 5 1 , 1 2 4 , S A T U R D A Y 1 181 1 1 8 2 S U N D A Y 1 8 3 9 S T A T E M E N T 5 2 , 1 2 2 , 1 2 : 0 0 ; 1 184 1 8 5 2 : 0 0 186 7 S T A T E M E N T 5 3 , 1 2 5 , 1 3 M A R C H 1 187 * 1 188 U M A R C H 189 38 S T A T E M E N T 5 5 , 4 8 , H O U R L Y T R A F F I C V O L U M E OFF F O L K S T O N E / C A P G R I S N E 1 190 Z 191 38 S T A T E M E N T 5 7 » 4 7 , D I U R N A L / N O C T U R N A L FLOW - N O R T H B O U N D / F R E N C H S I D E E N D G R A P H E J E C T G R A P H X H , 4 9 , 7 2 O R I G I N S O , 8 X , 3 , 2 , , , , N 0 Y 0 , 1 , 2 1 , 2 7 S T A T E M E N T 5 1 , 1 2 4 , S A T U R D A Y 1 S U N D A Y 9 S T A T E M E N T 5 2 , 1 2 2 , ! 2 : ' 0 0 ' 1 2 : o o 7 S T A T E M E N T 5 3 , 1 2 5 , 1 3 • M A R C H 1 U M A R C H 3 8 S T A T E M E N T 5 5 , 4 8 , H O U R L Y T R A F F I C V O L U M E O F F F O L K S T O N E / C A P G R I S NE1 Z 3 8 S T A T E M E N T 5 7 , 4 8 , D I U R N A L / N O C T U R N A L FLOW - S O U T H B O U N D / E N G L I S H S I O l E E N D G R A P H E J E C T G R A P H X h , 7 3 , 9 6 O R I G I N 5 0 , f i X , 3 , 2 , , , , N 0 Y 0 , 1 , 2 4 , 2 7 S T A T E M E N T 51 , 1 2 4 , S A T U R D A Y 1 S U N D A Y > 9 S T A T E M E N T 5 2 , 1 2 2 , 1 2 : 0 0 1 2 ( 0 0 7 S T A T E M E N T 5 3 , 1 2 5 , 1 3 M A R C H 1 a M A R C H 3 8 S T A T E M E N T 5 5 , 4 8 , H O U R L Y T R A F F I C V O L U M E O F F F O L K S T O N E / C A P G R I S NE 1 z 3 8 S T A T E M E N T 5 7 , 4 7 , D I U R N A L / N O C T U R N A L FLOW - S O U T H B O U N O / F R E N C H S I D E E N O G R A P H E J E C T L S V T I T L E , N U M B E R OF S I M U L A T E D D A I L Y V E S S E L M O V E M E N T S ( E N G L I S H I C H A N N E L ) L S V I N C L U D E , L X 3 S P A C E 5 | S A V T I T L E , N U M B E R OF S I M U L A T E D V E S S E L E N C O U N T E R S A N N U A L L Y S A V I N C L U D E , X 1 S P A C E 5 S A V T I T L E / T H E O R E T I C A L NUMBER OF V E S S E L E N C O U N T E R S S A V I N C L U D E , X 3 S P A C E 5 L S V T I T L E , N U M B E R OF S I M U L A T E D . V E S S E L E N C O U N T E R S / H O U R / S Q U A R E NA1 U T I C A L M I L E L S V I N C L U D E , X L 4 ' E J E C T L S V T I T L E . S I M U L A T E D NUMBER OF P R E D I C T E D H E A D - O N C O L L I S I O N S I N 1 T H E E N G L I S H C H A N N E L A N N U A L L Y L S V I N C L U D E , X L 1 S P A C E 5 L S V T I T L E . T H E O R E T I C A L NUMBER OF P R E D I C T E D H E A D - O N C O L L I S I O N S 11 N T H E E N G L I S H C H A N N E L A N N U A L L Y 192 193 194 195 196 197 198 199 200 r 201 202 203 204 205 206 r~' 207 208 209 <~-\ \J 210 211 212 213 214 215 c 216 217 218 219 220 221 222 223 c 224 225 226 227 w 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 ro 245 '< o 246 247 248 249 250 251 > \ L S V I N C L U D E , X L 2 S P A C E 5 5 T E X T T H E M E A N A N N U A L NUMBER OF H E A D - O N C O L L I S I O N S I N T H E . E l N G L I S H C H A N N E L FOR T H E Y E A R S 1 9 6 9 - 1 9 7 1 WAS 6 , 2 E J E C T E N D 2 5 2 2 5 3 2 5 4 2 5 5 2 5 6 2 5 7 ah C R O S S - R E F E R E N C E B L O C K S S Y M B O L NUMBER R E F E R E N C E S B A K K 2 3 1 0 4 J U M P 3 7 6 — K T R L 1 1 ' -K T R L 2 21 S O U T H 16 80 TERM 15 7 9 C R O S S - R E F E R E N C E F U N C T I O N S o S Y M B O L N U M B E R R E F E R E N C E S C O L L 3 2 3 1 0 3 c E X P O 4 27 8 5 94 HOUR 1 14 7 8 1 0 3 T I H E 2 19 8 5 94 ' . . . . * * * * A S S E M B L Y T I M E * ' . 0 1 M I N U T E S * * * * S I M U L A T E * * * i t * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * V A L I D A T I O N U S I N G E N G L I S H C H A N N E L DATA * * * * It It * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1 F U N C T I O N P 7 , 0 2 4 0 24 1 1 2 2 1 3 3 4 4 5 S I 6 6 7 7 8 B 1 9 9 10 10 11 11 1 12 12 13 13 14 14 1 15 15 16 16 17 17 1 18 18 19 19 2 0 20 1 21 it 21 2 2 2 2 2 3 2 3 1 * 2 F U N C T I O N P I , D 4 1 8 3 2 1 1 4 3 7 5 1 a * 1 1 4 1 * 3 F U N C T I O N P 6 , 0 4 2 4 1 48 2 7 2 3 I 9 6 it * 4 1 4 F U N C T I O N f » N l , C 2 f l 0 0 . 1 . 1 0 4 . 2 . 2 2 2 1 . 3 . 3 5 5 . 5 0 9 , 5 , 6 9 1 . 6 . . 9 1 5 . 7 1 . 2 . 7 5 1 . 3 8 1 . 8 1 , 6 . 8 4 1 . 8 3 . 8 8 2 . 1 2 1 . 9 2 . 3 . 9 2 2 . 5 2 . 9 4 2 . 8 1 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 I , 9 9 8 it 6 . 2 . 9 9 9 7 . 9 9 9 8 8 | 1 it 1 • M A T R I X H , 2 « , 4 I N I T I A L MH1 C 1 , 1 ) , 1 2 / M H 1 ( 1 , 2 ) , 6 / M H l ( 1 , 3 ) , 1 0 / M H 1 ( 1 , 4 ) , 0 I N I T I A L M H i ( 2 , 1 ) , U / i - H l ( 2 , 2 ) , 2 / M H 1 ( 2 , 3 ) , 7 / M H 1 C 2 , 4 ) , 0 I N I T I A L M H 1 C 3 , 1 ) , 5 / M h l ( 3 , 2 ) , 3 / M H l ( 3 , 3 ) , 5 / M H l ( 3 , 4 ) , 1 I N I T I A L M H I ( 4 , t ) , 2 / M H 1 ( 4 , 25 , 8 / M H l ( 4 , 3 ) , 9 / M H l ( 4 , 4 ) , 1 I N I T I A L MHI ( 5 , 1 ) , 5 / M H 1 ( 5 , 2 ) , 1 / M H l ( 5 , 3 ) , 7 / M H l ( 5 , 4 ) , 0 I N I T I A L M H I ( 6 , 1 ) , 7 / M H 1 ( 6 , 2 ) , « / M H l ( 6 , 3 ) , 1 2 / M H l ( 6 , 4 ) , l I N I T I A L M H 1 ( 7 , 1 ) , 6 / M H 1 ( 7 , 2 ) , 3 / M H l ( 7 , 3 ) , 1 4 / M H l ( 7 , 4 ) , l I N I T I A L M H I ( 8 , 1 ) , 3 / M H 1 ( 8 , 2 ) , 2 / M H l C 8 , 3 ) , 9 / M H 1 ( 8 , 4 ) , 1 I N I T I A L M H I ( 9 , 1 ) , 1 / M H I ( 9 , 2 ) , 1 / M H l ( 9 , 3 ) , 4 / M H l ( 9 , 4 ) , 0 I N I T I A L MHI ( 1 0 , 1 ) , 3 / M H l C 1 0 , 2 ) , 5 / M H l ( 1 0 , 3 ) , 4 / M H l ( 1 0 , 4 ) , 1 I N I T I A L MHI ( 1 1 , 1 ) , 1 / M H l ( 1 1 , 2 ) , 3 / M H l ( 1 1 , 3 ) , 6 / M H l ( 1 1 , 4 ) , 0 I N I T I A L M H I ( 1 2 , 1 ) , 3 / M H l ( 1 2 , 2 ) , 1 1 / M H l ( 1 2 , 3 ) , 8 / M H l ( 1 2 , 4 ) , 0 I N I T I A L M H I ( 1 3 , 1 ) , 0 / M H l ( 1 3 , 2 ) , 7 / M H l ( 1 3 , 3 ) , 3 / M H l ( 1 3 , 4 ) , 0 I N I T I A L MH1 ( 1 4 , 1) , 1 / M r i l ( 1 4 , 2 ) , 9 / M H l ( 1 4 , 3 ) , 4 / M H l ( 1 4 , 4 ) , 0 I N I T I A L M H 1 ( 1 5 , 1 ) , 1 / M H 1 ( 1 5 , 2 ) , 5 / M H l ( 1 5 , 3 ) , 6 / M H l ( 1 5 , 4 ) , 0 I N I T I A L M H 1 ( 1 6 , 1 ) , 2 / M H l ( 1 6 , 2 ) , 5 / M H 1 ( 1 6 , 3 ) , 7 / M H l ( 1 6 , 4 ) , 0 O I N I T I A L M H 1 ( 1 7 , 1 ) , 0 / M H t ( 1 7 , 2 ) , 9 / M H I ( 1 7 , 3 ) , 9 / M H 1 ( 1 7 , 4 ) , 0 I N I T I A L M H 1 ( 1 8 , 1 ) , 1 / M H 1 ( 1 8 , 2 ) , 3 / M H l ( 1 8 , 3 ) , 6 / M H 1 ( 1 8 , 4 ) , 0 I N I T I A L M H 1 ( 1 9 , 1 ) , 3 / M H 1 ( 1 9 , 2 ) , 4 / M H 1 ( 1 9 , 3 ) , 7 / M H 1 ( 1 9 , 4 ) , 2 • O I N I T I A L M H 1 ( 2 0 , 1 ) , 2 / M H l ( 2 0 , 2 ) , 4 / M H l ( 2 0 , 3 ) , 1 0 / M H 1 ( 2 0 , 4 ) , 0 • I N I T I A L M H 1 ( 2 1 , 1 ) , 1 / M H 1 ( 2 1 , 2 ) , 3 / M H l ( 2 1 , 3 ) , 8 / M H l ( 2 1 , 4 ) , 2 I N I T I A L M H 1 ( 2 2 , 1 ) , 3 / M H l ( 2 2 , 2 ) , 1 5 / M H l ( 2 2 , 3 ) , 1 0 / M H 1 ( 2 2 , 4 ) , Z I N I T I A L M h l ( 2 3 , 1 ) , 1 / M H 1 ( 2 3 , 2 ) , 9 / M H l ( 2 3 , 3 ) , 2 / M H 1 ( 2 3 , 4 ) , 2 * I N I T I A L H H i C 2 4 , l ; , 3 / n H i ( 2 4 , 2 ) , i 0 / r - i H i ( 2 4 , 3 ) , 6 / M H i C 2 4 , 4 ; , i c * 1 V A R I A B L E ( P 5 + ( P 6 - P 4 ) ) » P 2 O 2 F V A R I A B L E ( S C 1 + S C 2 ) * ( S C 1 * S T 1 + S C 2 * S T 2 ) / C 1 / K 2 o 3 F V A R I A B L E (X 1 * K 8 0 0 ) / ( K 6 0 8 0 * K 6 7 0 0 * K 6 ) a F V A R I A B L E ( X 3 * K 8 0 0 ) / ( K 6 0 8 0 * K 6 7 0 0 * K 6 ) o 5 V A R I A B L E ( C 1 / K 6 0 ) » K 2 4 6 V A R I A B L E P 6 C K 2 4 • 7 F V A R I A B L E ( S C 1 + S C 2 ) / K 3 6 5 S * F V A R I A B L E X 1 / C 1 / K 1 9 2 * K 6 0 * * S T O R A G E S S l - S 2 , 2 0 0 —' * * 1 G E N E R A T E 6 0 , , 6 0 , , , , F 1 2 S P L I T 3 , 3 , 1 3 A S S I G N 7 , V 5 4 A S S I G N 2 , M H 1 ( F N 1 , P 1 ) ~> 5 T E S T G P 2 , K 0 , 1 5 6 T E S T L P 1 , K 3 , 1 6 7 E N T E R 1 , P 2 8 B U F F E R 9 A S S I G N 4 , X 2 10 A S S I G N 5 , S 2 11 A D V A N C E F N 2 , F N 4 12 A S S I G N 6 , X 2 13 S A V E V A L U E l + . V l 10 L E A V E 1 , P 2 15 * T E R M I N A T E 0 * 16 E N T E R 2 , P 2 17 S A V E V A L U E 2 + , P 2 18 A D V A N C E F N 2 , F N 4 19 L E A V E 2 , P 2 20 it T E R M I N A T E 0 tt « '• ro 21 G E N E R A T E 5 2 5 6 0 0 , , , , , , F _ 2 2 A S S I G N 6 , K 9 f c • 2 3 A S S I G N 7 , V 6 24 S A V E V A L U E P 6 , M H 1 ( F N 1 , F N 3 ) , H 2 5 L O O P 6 , 2 3 26 S A V E V A L U E 3 , V 2 2 7 S A V E V A L U E 1 , V 3 , X L 2 8 S A V E V A L U E 2 , V « , X L 2 9 S A V E V A L U E 3 , V 7 , X L 3 0 S A V E V A L U E « , V 8 , X L 31 T E R M I N A T E 1 S T A R T 1 SIMULATION TIME (CLOCK) S T A T I S T I C S R E L A T I V E CLOCK 5 2 5 6 0 0 ABSOLUTE CLOCK 5 2 5 6 0 0 VESSEL T R A F F I C I N THE SIMULATION MODEL BLOCK COUNTS BLOCK CURRENT TOT«L 1 0 8 7 5 9 2 0 35036 3 0 35036 4 0 3 5 0 3 6 5 0 3 5 0 3 6 6 0 29561 7 0 16788 8 0 16788 9 0 16788 10 0 16788 BLULK UUKKLN I 11 1 12 0 13 0 14 0 15 0 16 0 17 0 18 2 19 0 20 0 TUTAL 16788. 16787 16767 16787 2 2 2 6 2 12773 12773 12773 12771 12771 B L O C K CURRENT 21 0 22 0 23 0 24 0 25 0 26 0 27 0 28 0 29 0 30 0 \ T O T A L B L O C K C U R R t N T T O T A L B L O C K C U R R E N T T O T A L 1 31 0 1 1 96 96 96 O ro ON IS?:*' E N G L I S H C H A N N E L ( D O V E R S T R A I T ) V E S S E L S T A T I S T I C S - A V E R A G E U T I L I Z A T I O N D U R I N G -S T O R A G E C A P A C I T Y A V E R A G E E N T R I E S A V E R A G E T O T A L . A V A I L . U N A V A I L . C U R R E N T P E R C E N T C U R R E N T M A X I M U M C O N T E N T S T I M E / U N I T T I M E T I M E T I M E S T A T U S A V A I L A B I L I T Y C O N T E N T S C O N T E N T S 1 2 0 0 1 3 . 9 6 4 7 3 7 1 7 9 9 , 5 6 3 , 0 6 9 1 0 0 , 0 3 60 2 2 0 0 9 , 8 2 0 6 8 6 1 3 7 5 . 2 2 5 , 0 4 9 1 0 0 . 0 12 4 9 V O L U M E OF N O R T H B O U N D V E S S E L S I N D I C A T E D BY S T O R A G E 1 V O L U M E OF S O U T H B O U N D V E S S E L S I N D I C A T E D BY S T O R A G E 2 A P P R O X , 1 2 0 / 0 0 0 V E S S E L T H R U - M O V E M E N T S P E R Y E A R B A L A N C E C O N S I S T S OF L O C A L AND C R O S S - C H A N N E L T R A F F I C \ -2 4 * * 2 3 * * 2 2 * * 21 * 20 * * 19 « * 18 * 17 « * 16 * 15 * 1 « * * 13 * * 1 2 * 11 * * 10 » 9 * 8 * 7 * 6 * 5 * * 3 * * 2 * 1 * 0 *** *** * * * * * * * * * ******************* ****** S A T U R D A Y 1 2 : 0 0 13 M A R C H *** 1 S U N 0 A Y 1 2 : 0 0 14 M A R C H H O U R L Y T R A F F I C V O L U M E O F F F O L K S T O N E / C A P G R I S NEZ D I U R N A L / N O C T U R N A L FLOW - N O R T H B O U N D / E N G L I S H S I D E 24 * * 23 * * 21 * . * 20 * * 19 * * 16 * * 17 * 16 * . . * ' 15 * *** * * * 14 * * * * _ . . . . * * 13 * * * * * * 12 * * * * * * 11 * 1 *** * * * . _ * * . * » 1 0 * * * * * * * * * * 9 * * * *** *** * * a 7 6 5 4 3 2 1 * * * * * * * * * *** * * 0 **************************************************************************************************************************** • SATURDAY 1SUNDAY 12:oo 12:00 13 MARCH 14 MARCH , 'x£> • ** * * * * * * *** * * * * * * * * * * * * * * * * " * * * * * * * * *** * * * * * * * * * * *** * * * • * * * * * * * *  *  *  *  * * * * * * * • * * •* * * * * * * * * * * * * * * _ * * * * * * * * * * * * * * * * * * * * * * *** * * * * * * * * * * * * * * •. * * * * * * * * * * * * * * * * * * * * • * * * * * . * * * * * * * * * * * * *** * * * * * * *** *** * * * * . * * * * * * * * * * * * * * * * * * * * * * * * ** * * * •* * * * * * * * * * * * *** *** * * * * * * * * * * * * * ft * * * * * * * * * * * * * * * * * * * * *** * * *** * * * * * * * * * * * * *** * * * * *** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * HOURLY TRAFFIC VOLUME OFF FOLKSTONE/CAP GRIS NEZ DIURNAL/NOCTURNAL FLOW - NORTHBOUNO/FRENCH SIDE P: I O 2 4 2 3 2 2 21 2 0 19 18 17 16 1 5 14 13 1 2 11 10 9 8 7 6 5 4 3 2 1 0 A A A A A A A A A A A A A A A A A A A A A A A A AAA A A A * * A A A A A A A A * * A A A A A A A A A A A A A A A A A * * A A A A A A A A A A A A A A A * A A A A A A A A A A A A A A A A A A A A * * A A A A A A A A A A A A A A A A A A * It A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A It It It It A A A A A A it A A A A A A A A A A A A A A A A A * * A * A A * A A A A A A A A A A A A A A A A A A' A A A A A A A A A A A A A A A It It * It A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A It * * * A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A * * It It It A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A * It " It * It * A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A It * * * * * A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A It It It * It A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A It It * It It A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A * It * * It A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A * It It * It A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A It It It It It A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A * It It * A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A S A T U R D A Y 1 2 1 0 0 13 M A R C H t A A 1 S U N D A Y 1 2 ( 0 0 14 M A R C H H O U R L Y T R A F F I C V O L U M E O F F F O L K S T O N E / C A P G R I S N E Z D I U R N A L / N O C T U R N A L FLOW - S O U T H B O U N D / E N G L I S H S I D E zn * * 2 3 * . . . c • 2 2 * \ : * 21 * . C | * i 20 * ; * >.. 19 * * i is * C ! * } 17 * . ! * . . . . W I 16 * * " '• ! is * ' c ; 14 * 13 * " - ! * 12 * . . . ... C : * n * ' | * C. ' 10 . * 9 * * 8 * * . . .... .. . ' . ' C I 7 * * 6 * ; * 5 * 4 * * i 3 * . . . . . ' * * 2 * *** *** *** *** j * * * * * * * * * r,, s i * *** *** *** *** *** *** ** * * * * * * *** * * * * * * * * * * * * * * * * * * * * * * * o * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * S A T U R D A Y 1 S U N D A Y " ' 1 2 t 00 1 2 : 00 13 M A R C H 14 M A R C H f VJJ I - * H O U R L Y T R A F F I C V O L U M E O F F F O L K S T O N E / C A P G R I S N E Z * D I U R N A L / N O C T U R N A L FLOW - S O U T H B O U N D / F R E N C H S I D E NUMBER OF S I M U L A T E D D A I L Y V E S S E L M O V E M E N T S ( E N G L I S H C H A N N E L ) NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER • C O N T E N T S NUMBER . C O N T E N T S NUMBER - C O N T E N T S 3 3 6 9 , 9 1 5 0 6 . . . NUMBER OF S I M U L A T E D V E S S E L E N C O U N T E R S A N N U A L L Y NUMBER - C O N T E N T S NUMBER • C O N T E N T S NUMBER - C O N T E N T S NUMBER -• C O N T E N T S ' NUMBER - C O N T E N T S NUMBER - C O N T E N T S 1 1 7 6 0 7 0 5 T H E O R E T I C A L NUMBER OF V E S S E L E N C O U N T E R S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER « C O N T E N T S 3 1 6 9 2 5 9 3 NUMBER OF S I M U L A T E D V E S S E L E N C O U N T E R S / H O U R / S Q U A R E N A U T I C A L M I L E NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER » ' C O N T E N T S NUMBER - C O N T E N T S NUMBER • C O N T E N T S 4 1 , 0 4 6 8 4 . . . . S I M U L A T E D NUMBER OF P R E D I C T E D H E A D - O N C O L L I S I O N S I N T H E E N G L I S H C H A N N E L A N N U A L L Y O N U M B E R - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER » C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S 1 5 , 7 6 2 9 7 T H E O R E T I C A L NUMBER OF P R E D I C T E D H E A D - O N C O L L I S I O N S I N THE E N G L I S H C H A N N E L A N N U A L L Y • „ NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S 2 5 . 5 4 0 0 3 T H E M E A N A N N U A L NUMBER OF H E A D - O N C O L L I S I O N S I N T H E E N G L I S H C H A N N E L FOR THE Y E A R S 1 9 6 9 - 1 9 7 1 WAS 6 , 2 C L E A R M A T R I X I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L I N I T I A L S T A R T H , 2 4 , 4 M H l ( l , n , M H 1 ( 2 , 1 ) , M H 1 ( 3 , 1 ) , MH1 ( 4 , 1 ) , MH1 ( 5 , 1 ) , M H 1 ( 6 , 1 ) , M H 1 ( 7 , 1 ) , M H 1 ( 6 , 1 ) , M H 1 ( 9 , 1 ) , M H 1 ( 1 0 , 1 ) M H 1 ( 1 1 , 1 ) M H 1 ( 1 2 , 1 ) MH1 ( 1 3 , 1 ) MH1 ( 1 4 , 1 ) M H 1 ( 1 5 , 1 ) MH 1 ( 1 6 , 1 ) M H 1 ( 1 7 , 1 ) . M H 1 ( 1 8 , 1 ) M H 1 ( 1 9 , 1 ) M H 1 ( 2 0 , 1 ) M H 1 ( 2 1 , 1 ) M H 1 ( 2 2 , 1 ) M H 1 ( 2 3 , 1 ) M H 1 ( 2 4 , 1 ) 1 1 2 / M H 1 ( 1 , 2 ) , 6 / M H l ( 1 , 3 ) 4 / M H l ( 2 , 2 ) , 2 / M H l ( 2 , 3 ) , 5 / M H l ( 3 , 2 ) , 3 / M H l ( 3 , 3 ) , 2 / M H l ( 4 , 2 ) , 8 / M H l ( 4 , 3 ) , 5 / M H l ( 5 , 2 ) , l / M H l ( 5 , 3 ) , 7 / M H l ( 6 , 2 ) , 4 / M H l ( 6 , 3 ) , 6 / M H 1 ( 7 , 2 ) , 3 / M H l ( 7 , 3 ) , 3 / M H 1 ( 8 , 2 ) , 2 / M H l ( 8 , 3 ) , 1 / M H 1 ( 9 , 2 ) , ! / M H 1 ( 9 , 3 ) , , 3 / M H l ( 1 0 , 2 ) , 5 / M H l ( 1 0 , , 1 / M H 1 ( 1 1 , 2 ) , 3 / M H l ( 1 1 , , 3 / M H l ( 1 2 , 2 ) , 1 1 / M H 1 ( 1 2 , 0 / M H l ( 1 3 , 2 ) , 7 / M H l ( 1 3 , , 1 / M H 1 ( 1 4 , 2 ) , 9 / M H 1 ( 1 4 , , 1 / M H 1 ( 1 5 , 2 ) , 5 / M H I ( 1 5 , , 2 / M H l ( 1 6 , 2 ) , 5 / M H l ( 1 6 , , 0 / M H l ( 1 7 , 2 ) , 9 / M H 1 ( 1 7 , , 1 / M H 1 ( 1 8 , 2 ) , 3 / M H l ( 1 8 , , 3 / M H l ( 1 9 , 2 ) , 4 / M H l ( 1 9 , , 2 / M H l ( 2 0 , 2 ) , 4 / M H l ( 2 0 , , 1 / M H 1 ( 2 1 , 2 ) , 3 / M H 1 ( 2 1 , , 3 / M H l ( 2 2 , 2 ) , 1 5 / M H l ( 2 2 , 1 / M H 1 ( 2 3 , 2 ) , 9 / M H 1 ( 2 3 , , 3 / M H l ( 2 4 , 2 ) , 1 0 / M H l ( 2 4 , 1 0 / M H l ( 1 , 4 ) , 0 7 / M H l ( 2 , 4 ) , 0 5 / M H 1 ( 3 , 4 ) , 1 9 / M H l ( 4 , 4 ) , l 7 / M H l ( 5 , « ) , 0 1 2 / M H 1 ( 6 , 4 ) , 1 1 4 / M H 1 ( 7 , 4 ) , 1 9 / M H 1 ( 8 , 4 ) , 1 4 / M H 1 ( 9 , 4 ) , 0 3 ) , 4 / M H l ( 1 0 , 4 ) , 1 3 ) , 6 / M H l ( l l , 4 ) , 0 , 3 ) , 8 / M H l ( 1 2 , 4 ) , 0 3 ) , 3 / M H l ( 1 3 , 4 ) , 0 3 ) , 4 / M H l ( 1 4 , 4 ) , 0 3 ) , 6 / M H l ( 1 5 , 4 ) , 0 3 ) , 7 / M H l ( 1 6 , 4 ) , 0 3 ) , 9 / M H l ( 1 7 , 4 ) , 0 3 ) , 6 / M H l ( 1 3 , 4 ) , 0 3 ) , 7 / M H l ( 1 9 , 4 ) , 2 3 ) , 1 0 / M H 1 ( 2 0 , 4 ) , 0 3 ) , 8 / M H l ( 2 1 , 4 ) , 2 , 3 ) , 1 0 / M H 1 ( 2 2 , 4 ) , 2 3 ) , 2 / M H l ( 2 3 , 4 ) , 2 , 3 ) , 6 / M H l ( 2 4 , 4 ) , i U) S I M U L A T I O N T I M E ( C L O C K ) S T A T I S T I C S R E L A T I V E C L O C K 5 2 5 6 0 0 A B S O L U T E C L O C K 5 2 5 6 0 0 V E S S E L T R A F F I C I N THE S I M U L A T I O N K O O E L B L O C K C O U N T S n. K i i n n r i i T -r n w t • n l rt r U r i i n n C M T T r t T i l Dt f\T U f I I • D C" ki T DL.U U r\ u u n n c ' * t | l u t » U • L i ' K " »»wiMifcn i i u i ^ u wtawwi^ v v i>" " ' 1 0 8 7 5 9 11 1 1 6 7 8 8 21 " 0 2 0 3 5 0 3 6 12 0 1 6 7 6 7 2 2 0 3 0 3 5 0 3 6 13 0 1 6 7 8 7 2 3 0 0 3 5 0 3 6 14 0 1 6 7 8 7 24 0 5 0 3 5 0 3 6 I S 0 2 2 2 6 2 2 5 0 6 0 2 9 5 6 1 16 0 1 2 7 7 3 26 0 7 0 1 6 7 6 8 17 0 1 2 7 7 3 2 7 0 8 0 1 6 7 6 8 18 1 1 2 7 7 3 28 0 9 0 1 6 7 8 8 19 0 1 2 7 7 2 2 9 0 10 0 1 6 7 8 8 20 0 1 2 7 7 2 30 0 T O T A L B L O C K C U R R E N T T O T A L B L O C K C U R R E N T T O T A L 1 31 0 I C 1 9 6 9 6 e 9 6 1 i c i i i •~1 i :• \ - • . ' _ . E N G L I S H C H A N N E L ( D O V E R S T R A I T ) V E S S E L S T A T I S T I C S - A V E R A G E U T I L I Z A T I O N D U R I N G -S T O R A G E C A P A C I T Y A V E R A G E E N T R I E S A V E R A G E T O T A L A V A I L , U N A V A I L , C U R R E N T P E R C E N T C U R R E N T M A X I M U M C O N T E N T S ' T I M E / U N I T " T I M E - T I M E T I M E S T A T U S A V A I L A B I L I T Y C O N T E N T S C O N T E N T S 1 2 0 0 1 0 , 2 7 9 7 3 7 1 7 1 0 1 . 8 0 9 . 0 7 1 1 0 0 . 0 2 6 3 2 2 0 0 9 , 6 7 8 6 8 6 1 3 7 4 , 1 4 4 . 0 4 8 1 0 0 , 0 2 4 8 V O L U M E OF N O R T H B O U N D V E S S E L S I N D I C A T E D BY S T O R A G E 1 V O L U M E OF S O U T H B O U N D V E S S E L S I N D I C A T E D BY S T O R A G E 2 A P P R O X , 1 2 0 , 0 0 0 V E S S E L T H R U - M O V E M E N T S P E R Y E A R B A L A N C E C O N S I S T S OF L O C A L AND C R O S S - C H A N N E L T R A F F I C G I I - 1 A A 2 3 2 2 2 1 19 * * 18 * 17 * * 16 * * I S * 14 * 1 3 12 11 10 9 8 7 6 S 4 3 2 1 0 AAA A A A A AAA A A A A *** *** A A A A * * * A A A A A *** * * A A A A A A • * * * A A A A A j * * * * * A A A A A AAA AAA AAA AAA AAA AAA * * * * * A A A A A A A A A A A A A A A A A * * * * AAA * A A A A A A A A A A A AAA A A AAA A A A A * * * * * * * A A A A A A A A A A A A A A A A A A A A A * * * * * * * A A A A A A A AAA A A AAA A A AAA AAA A A AAA A A A A AAA A A AAA A A * * * * * * * A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A S A T U R D A Y 1 2 : 0 0 1 3 M A R C H 1 S U N D A Y 1 2 1 0 0 14 M A R C H V-O: H O U R L Y T R A F F I C V O L U M E O F F F O L K S T O N E / C A P G R I S NEZ D I U R N A L / N O C T U R N A L FLOW - N O R T H B O U N D / E N G L I S H S I D E : \ -o 2 4 * * 2 3 * * 2 2 * * 21 * * 2 0 * * 19 * * 18 * * 17 * * 16 • * 15 * * 14 * * 13 * * 12 * * 11 * * 10 * 9 * * 8 • * 7 * * 6 * * 5 * * 3 * * 2 * * 1 * 0 *** ' * * *** * * O * * * * * * * * * * * * *** * * * * * * * * * * * * It It * * * * * * * * * • * * It It * * *** * * * * * * * * * * It It * * * * '• * * * * * * * * * * *** It It * * * * * * * * * * * * * * * * It It * * * * * * * * * * * * * * * * * * *** * * * * * * *** *«* * * * * * * * * * * It It * * * * * * * * * * * * * * * * * * * * * * It It I t * * * * * •* * * * * * * * * * * *** *** * * * * * * • * It It * * 1 * * * * * * * * * * * * * * * * * * * * * * * * * * *** * It * * *** * * *** * *' * * * * * * * * * * *** * * * * *** * * * * * * * * * * It It * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *«* * * * It * * * * *** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * « It It * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * It * *** * * * * * * *** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * » It It It * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * **************************************************************************************************************************** S A T U R D A Y 1 S U N D A Y 1 2 1 0 0 1 2 1 0 0 13 M A R C H . . . . . . 1 " M A R C H H O U R L Y T R A F F I C V O L U M E O F F F O L K S T O N E / C A P G R I S N E Z D I U R N A L / N O C T U R N A L FLOW - N O R T H B O U N D / F R E N C H S I D E I P -\ 2 4 2 3 2 2 21 2 0 19 18 17 16 15 I t 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Ik Ik Ik Ik * * Ik * * Ik * Ik « * * ik * < *** * * ik Ik *** *** * ik * * * * * * * * *** ik * Ik ik I k i k i k *** * * * * * • * Ik * Ik * * Ik * * * * * * * * * * * Ik * * Ik ik * *** * * * * *** * * * * * * * Ik Ik Ik Ik * Ik * * * * * * * * * * * *** Ik * *** Ik * Ik Ik Ik ik Ik Ik I k * * * * *** * * * * * * * * Ik * Ik Ik Ik Ik Ik ik Ik Ik * Ik * Ik * * * * * * * * * * * * * * ik * * * Ik Ik Ik * * Ik * Ik *** Ik * Ik Ik Ik * * * * *** * * * * * * * * *** * * Ik * Ik ik Ik Ik * * Ik * * * * Ik * Ik * Ik * * * * * * * * * * * * * * * * * * * * *** * Ik * Ik * •k Ik * * Ik * * Ik •* Ik * * * * * * * * * * * • * * * * * * * * Ik Ik Ik * Ik * * ik *. * Ik * * * * ik Ik * * * * * * * * * * * * * * * * * * * Ik * * * * ik * * * * Ik * * * * *** Ik ik ik ik Ik Ik *** Ik * * * * * * * * * * * * * * * * * * Ik Ik Ik Ik * Ik * Ik * * * * * ik Ik * Ik Ik * * •k .* Ik Ik Ik * Ik * * * * * * * * * * * * * * * * * * * * * * * * * Ik ik * ik Ik * Ik * Ik Ik Ik Ik Ik * * *** Ik * . * * * * * * * * * * * * * * * * * * * * * * * ik Ik * * * * Ik * * * * Ik * * * Ik Ik Ik * Ik Ik Ik * ik * * * * * * * * * * * * '* * * * * * ik * Ik Ik Ik * * Ik * Ik * * Ik Ik Ik Ik Ik Ik Ik * ik * » * * * * * Ik * * * * * * * * * * * * * * *** * * * * Ik Ik ik Ik Ik ik * Ik * * * Ik * Ik Ik * Ik * * Ik Ik Ik * * Ik * * * * * * * * * * * * * * * * • * * • • Ik Ik * ik Ik ik * ik * * * * * Ik * ik Ik ik ik Ik Ik * Ik Ik * * Ik Ik * ik * * * * * * * * * * * * * * * * * * * * * ik * ik * Ik * * * * * * * Ik •k * ik Ik Ik ik Ik * * Ik ik Ik Ik * * * * * * * * * * * * * * *' * * * * ********** S A T U R D A Y 1 2 1 0 0 13 M A R C H k * * * * * * * * * * * * * 1 S U N D A Y 1 2 ( 0 0 14 M A R C H .VJJ 00 H O U R L Y T R A F F I C V O L U M E O F F F O L K S T O N E / C A P G R I S N E Z D I U R N A L / N O C T U R N A L FLOW - S O U T H B O U N D / E N G L I S H S I D E 2 « * * 2 3 * 2 2 * * 21 * * 20 * 19 * 18 * * 17 * » 16 * 15 * 1<I * * 13 * * 12 * 11 * * 10 * * 9 * * 8 * * 7 * * * 5 * •k Ii * * 3 * * 2 * * 1 * S A T U R D A Y 1 2 1 0 0 1 3 M A R C H *** . * * *** * *» *** *** * * Ik * * Ik • Ik *** *** *** t k * * Ik Ik * * Ik * Ik * *** * * * * * * * * ik ik • * * Ik * * * * k * * * 1 S U N D A Y 1 2 : 0 0 t « M A R C H H O U R L Y T R A F F I C V O L U M E O F F F O L K S T O N E / C A P G R I S N E Z D I U R N A L / N O C T U R N A L FLOW - S O U T H B O U N D / F R E N C H S I D E ^ f 0», NUMBER OF S I M U L A T E D D A I L Y V E S S E L M O V E M E N T S ( E N G L I S H C H A N N E L ) N U M B E R • C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER • C O N T E N T S NUMBER - C O N T E N T S 3 3 8 9 , 9 4 5 0 6 N U M B E R OF S I M U L A T E D V E S S E L E N C O U N T E R S A N N U A L L Y N U M B E R - C O N T E N T S NUMBER » C O N T E N T S N U M B E R - C O N T E N T S NUMBER - C O N T E N T S NUMBER • C O N T E N T S NUMBER - C O N T E N T S 1 1 7 7 7 1 4 7 T H E O R E T I C A L NUMBER OF V E S S E L E N C O U N T E R S N U M B E R - C O N T E N T S NUMBER - C O N T E N T S NUMBER — C O N T E N T S NUMBER - C O N T E N T S NUMBER • C O N T E N T S NUMBER - C O N T E N T S 3 1 7 0 4 9 7 3 N U M B E R OF S I M U L A T E D V E S S E L E N C O U N T E R S / H O U R / S Q U A R E N A U T I C A L M I L E N U M B E R - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER »> C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S 4 1 , 0 5 6 7 9 i o S I M U L A T E D NUMBER OF P R E D I C T E D H E A D - O N C O L L I S I O N S I N T H E E N G L I S H C H A N N E L A N N U A L L Y NUMBER » C O N T E N T S NUMBER - C O N T E N T S NUMBER • C O N T E N T S NUMBER • C O N T E N T S NUMBER - C O N T E N T S NUMBER « C O N T E N T S 1 5 , 8 1 7 7 7 _. . .. • _ T H E O R E T I C A L NUMBER OF P R E D I C T E D H E A D - O N C O L L I S I O N S I N THE E N G L I S H C H A N N E L A N N U A L L Y NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S 2 5 , 5 6 0 5 5 T H E M E A N A N N U A L NUMBER OF H E A D - O N C O L L I S I O N S I N T H E E N G L I S H C H A N N E L FOR THE Y E A R S 1 9 6 9 - 1 9 7 1 WAS 6 , 2 END * * * * * T O T A L RUN T I M E ( I N C L U D I N G A S S E M B L Y ) a 1 , 1 6 M I N U T E S * * * * * E X E C U T I O N T E R M I N A T E D J S I G H c I A N G S xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx—7 R P S N O i 1 3 9 5 3 3 U N I V E R S I T Y O F B C C O M P U T I N G C E N T R E M T S C P R 1 8 4 ) I U 4 1 I 1 8 T H U J U N 2 0 / 7 4 O o U S E R : S H I P D E P A R T M E N T I COMM * * * * ON AT 1 1 : 4 1 1 1 8 . * * . O F F AT l l : 4 4 | 0 7 * * * * E L A P S E D T I M E * * * * C P U T I M E U S E D * * * * C P U STOR V M I * * * * WAIT STOR V M I * * * » C A R D S R E A D * * * * L I N E S P R I N T E D » « * * P A G E S P R I N T E D * * * * DRUM R E A D S THU J U N 2 0 / 7 4 THU J U N 2 0 / 7 4 2 . 8 M I N , 7 0 . 3 7 S E C , $ 1 9 , 5 4 1 1 3 . 8 6 8 P A G E - M I N , S 9 . 4 8 2 , 6 5 1 P A G E - H R , $ . 2 6 2 6 3 $ . 5 3 1 1 1 8 3 8 $ 1 , 5 2 121 * * * * A P P R O X . COST OF T H I S RUN I S $ 3 1 , 2 9 0 1 , 0 * * * * D I S K S T O R A G E 1 3 P A G E - H R , * * * * A P P R O X , R E M A I N I N G B A L A N C E J $ 5 4 3 , 2 3 * * L A S T S I G N O N W A S S 1 1 : 3 0 : 1 0 T H U J U N 2 0 / 7 4 iP1 ro ANGS x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x R F S N O . 1 1 7 1 3 9 U N I V E R S I T Y O F 8 C C O M P U T I N G C E N T R E M T S ( U L 1 8 4 ) 0 1 l t 2 | 4 0 T H U J U L 2 5 / 7 4 $ S I G C A S H P R I O = L F O R M = 8 L A N K T = 6 0 0 P = 3 0 0 * * L A S T S I G N O N WAS t 2 2 : 5 1 : 1 3 WEO J U L 2 4 / 7 4 C C C C C C C C C C C C C C C C C C C C C C C C cc cc cc cc cc cc cc cc cc C C C C C C C C C C C C C C C C C C C C C C AAAAAAAAAA A A A A A A A A A A A A AA AA AA AA AA AA AAAAAAAAAAAA AAAAAAAAAAAA AA AA AA AA AA AA AA AA AA AA S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S sss ss ss ss S S S S S S S S S S S S S S S S S S S S S S nn H H H H H H H H n n H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H HH H H HH H H H H H H H H H H A A A A A A A A A A N N NN G G G G G G G G G G S S S S S S S S S S A A A A A A A A A A A A N N N NN G G G G G G G G G G G G S S S S S S S S S S S S A A A A N N N N NN G G G G S S S S A A A A NN N N NN G G S S A A A A NN N N NN G G S S S A A A A A A A A A A A A N N N N NM G G S S S S S S S S S A A A A A A A A A A A A NN N N N N G G G G G G G S S S S S S S S S A A A A NN NN NN G G G G G G G S S S A A A A NN N N N N G G G G S S A A A A NN N N N G G G G S S S S AA A A NN NN G G G G G G G G G G G G S S S S S S S S S S S S A A A A NN N G G G G G G G G G G S S S S S S S S S S U S E R " C A S H " S I G N E D O N A T 0 1 : 1 2 1 4 0 O N T H U JUL 2 5 / 7 4 $ R U N * G P S S V P A R = S I Z E s C E X E C U T I O N B E G I N S * * * • G P S S V - M T S V E R S I O N * * *** I B M P R O G R A M P R O D U C T 5 7 3 4 - X S 2 ( V 1 M 2 ) *** F O R U P - T O - D A T E I N F O R M A T I O N R E G A R D I N G * G P S S V ' I L I S T N E W S l G P S S V B L O C K N U M B E R * L O C O P E R A T I O N A , B , C , D , E , F , G , H , I C O M M E N T S ******* * * R O S A R I O S T R A I T S I M U L A T I O N M O D E L ************************************** S T A T E M E N T N U M B E R 1 2 3 4 5 6 7 8 9 1 0 11 1 2 1 3 1 4 S I M U L A T I O N T I M E ( C L O C K ) S T A T I S T I C S R E L A T I V E C L O C K 512640 A B S O L U T E C L O C K 512640 V E S S E L T R A F F I C I N T H E S I M U L A T I O N MODEL B L O C K C O U N T S B L O C K C U R R E N T T O T A L B L O C K C U R R E N T T O T A L B L O C K C U R R E N T 1 0 2 1 6 11 0 1 9 5 21 0 2 0 2 1 6 12 0 2 5 5 2 2 0 3 0 2 1 6 13 0 2 5 5 2 3 0 a 0 1 5 6 14 0 4 3 24 0 5 0 1 5 6 15 0 2 6 2 5 0 6 0 3 6 8 16 0 2 6 2 6 0 7 0 3 6 8 17 0 2 6 27 0 e 0 3 6 8 18 0 2 6 2 8 0 9 0 1 9 5 19 0 17 2 9 0 10 0 1 9 5 20 0 17 30 0 B L O C K C U R R E N T T O T A L B L O C K C U R R E N T T O T A L B L O C K C U R R E N T 51 0 7 8 3 9 61 0 2 6 1 3 71 0 5 2 0 7 8 3 9 6 2 0 2 6 1 3 7 2 0 53 0 2 6 1 3 6 3 0 7 8 3 9 7 3 0 54 0 2 6 1 3 6 4 0 7 8 3 9 74 0 5 5 0 2 6 1 3 6 5 0 > 7 8 3 9 7 5 0 56 0 2 6 1 3 6 6 0 2 6 1 3 7 6 0 57 0 7 8 3 9 67 0 2 6 1 3 7 7 0 58 0 7 8 3 9 68 0 2 6 1 3 78 0 59 0 2613 69 0 6 7 5 79 0 60 0 2613 7 0 0 2 6 2 2 80 0 B L O C K C U R R E N T T O T A L B L O C K C U R R E N T T O T A L B L O C K C U R R E N T 101 0 1 102 0 1 Output For Simulation Of Year Ten T O T A L B L O C K C U R R E N T T O T A L BLOCK C U R R E N T T O T A L 17 31 0 2 6 9 11 0 1 3 7 7 17 3 2 0 2 6 9 12 0 1 8 4 2 1 3 3 3 0 4 6 4 1 3 0 184 2 1 3 34 0 4 6 4 41 0 184 2 1 3 3 5 0 3 0 0 4 5 0 184 2 1 3 36 0 3 0 0 46 0 1 3 7 7 2 1 3 37 0 3 0 0 47 0 5 2 3 5 2 6 9 38 0 3 0 0 18 0 2 6 1 3 2 6 9 3 9 0 9 6 6 49 0 2 6 1 3 2 6 9 40 0 1 3 7 7 50 0 2 6 1 3 T O T A L B L O C K C U R R E N T T O T A L BLOCK C U R R E N T T O T A L 2 6 2 2 81 0 1 91 0 1 2 6 2 2 6 2 0 1 9 2 0 3 2 6 2 2 8 3 0 6 9 3 0 18 2 6 2 2 84 0 6 94 0 5 4 2 6 2 2 8 5 0 6 9 5 0 51 2 6 2 2 8 6 0 6 9 6 0 18 2 6 2 2 87 0 1 97 0 3 2 6 2 2 8 8 0 6 98 0 3 1 3 7 7 8 9 0 6 99 0 1 1 90 0 6 100 .0 1 T O T A L B L O C K C U R R E N T T O T A L B L O C K C U R R E N T T O T A L C H A N N E L S E G M E N T V E S S E L S T A T I S T I C S S T O R A G E C A P A C I T Y A V E R A G E C O N T E N T S t 10 , 0 2 6 2 10 , 0 7 9 3 10 . 0 1 9 « 10 , 0 1 5 5 10 , 0 1 0 f> 10 , 0 4 2 7 10 , 0 4 6 8 10 , 0 1 0 9 10 , 0 1 6 10 10 , 0 2 0 11 10 , 0 7 9 1 2 10 , 0 3 2 • A V E R A G E E N T R I E S A V E R A G E T O T A L T I M E / U N I T T I M E 4 9 1 3 0 , 2 1 7 . 0 0 2 4 9 1 . 8 2 , 8 8 3 , 0 0 7 49 * 20,336 n A * a w v 4 3 8 0 2 1 , 2 0 2 , 0 0 1 3 8 0 1 3 . 6 7 3 , 0 0 1 3 8 0 5 7 , 5 4 9 . 0 0 4 3 8 5 6 1 , 6 5 4 , 0 0 4 3 8 5 1 4 , 6 2 8 . 0 0 1 3 8 5 2 1 , 7 1 6 , 0 0 1 4 8 9 2 1 , 3 9 0 , 0 0 2 4 8 9 8 3 , 3 6 6 . 0 0 7 4 8 9 3 3 , 9 2 0 . 0 0 3 U T I L I Z A T I O N D U R I N G " A V A I L , U N A V A I L . C U R R E N T T I M E T I M E S T A T U S P E R C E N T C U R R E N T M A X I M U M A V A I L A B I L I T Y C O N T E N T S C O N T E N T S 1 0 0 . 0 2 1 0 0 , 0 3 i O O . O 2 1 0 0 . 0 2 1 0 0 . 0 2 1 0 0 , 0 3 1 0 0 . 0 3 1 0 0 , 0 2 1 0 0 , 0 2 1 0 0 , 0 2 1 0 0 . 0 3 1 0 0 . 0 2 N U M B E R OF V E S S E L E N C O U N T E R S I N R E S P E C T I V E C H A N N E L S E G M E N T S ' N U M B E R • C O N T E N T S NUMBER <• C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER - C O N T E N T S NUMBER . C O N T E N T S 1 3 3 2 8 3 3 19 « 16 5 4 6 4 2 THE N U M B E R OP V E S S E L E N C O U N T E R S T H A T S H O U L D T H E O R E T I C A L L Y OCCUR I N THE R E S P E C T I V E C H A N N E L S E G M E N T S N U M B E R » C O N T E N T S NUMBER - C O N T E N T S NUMBER • C O N T E N T S NUMBER - C O N T E N T S NUMBER • C O N T E N T S NUMBER - C O N T E N T S 1 30 2 7 7 3 19 4 12 5 8 6 3 4 A C C U M U L A T E D N U M B E R OF V E S 3 E L 8 TO D A T E T R A V E L L I N G I N OUTBOUND D I R E C T I O N OF R E S P E C T I V E C H A N N E L S E G M E N T S N U M B E R - C O N T E N T S NUMBER - C O N T E N T S NUMBER » C O N T E N T S NUMBER - C O N T E N T S NUMBER . C O N T E N T S NUMBER . C O N T E N T S 7 3 8 5 8 3 8 5 9 3 8 5 10 4 8 9 11 4 8 9 12 4 8 9 A C C U M U L A T E D * OF V E S S E L S P E R T Y P E I N R E S P E C T I V E C H A N N E L S E G M E N T S T R A V E L L I N G I N OUTBOUND D I R E C T I O N P U L L W O R D M A T R I X 7 1^6. KI O O O KI CI K I O O O * 4 * 4 KI KI m ru r\i ru AJ KI KI Kt KI KI Kl n j rvj o j n j o j n j ••« - o « <c t r o> a - O X « ^ 5» TYPE OF VESSEL ENCOUNTERS IN CHANNEL SEGMENT ONE: rULLWORO MATRIX 1 ROW/COLUMN 1 2 3 1 1 1 4 2 0 0 5 3 1 3 18 COLUMNS INDICATE VESSEL TYPES IN OUTBOUND DIRECTION ROWS INDICATE VESSEL TYPES IN INBOUND DIRECTION TYPE OF VESSEL ENCOUNTERS IN CHANNEL SEGMENT TWO rULLWORD MATRIX 2 ROW/COLUMN 1 2 3 1 3 0 7 2 0 4 14 3 8 7 40 COLUMNS INDICATE VESSEL^ TYPES IN OUTBOUND DIRECTION ROWS INDICATE VESSEL TYPES IN INBOUND DIRECTION TYPE' OF VESSEL ENCOUNTERS IN CHANNEL SEGMENT THREE . FULLWORO MATRIX 3 ROW/COLUMN t 2 3 1 0 1 1 2 0 0 2 3 1 4 10 COLUMNS INDICATE VESSEL TYPES IN OUTBOUND DIRECTION ROWS INDICATE VESSEL TYPES IN INBOUND DIRECTION . TYPE OF VESSEL ENCOUNTERS IN CHANNEL SEGMENT FOUR FULLWORD MATRIX 4 ROW/COLUMN 1 2 3 1 0 ' 1 1 2 0 1 2 3 3 3 5 COLUMNS INDICATE VESSEL TYPES IN OUTBOUND DIRECTION ROWS INDICATE VESSEL TYPES IN INBOUND DIRECTION TYPE OF VESSEL ENCOUNTERS IN CHANNEL SEGMENT FIVE PULLWORD MATRIX 5 ROW/COLUMN 1 2 5 1 0 i O 2 0 0 0 J 1 1 1 COLUMNS INDICATE VESSEL TYPES IN OUTBOUND DIRECTION ROWS INDICATE VESSEL TYPES IN INBOUND DIRECTION TYPE OF VESSEL ENCOUNTERS IN CHANNEL SEGMENT SIX PULLWORD MATRIX 6 ROW/COLUMN 1 2 3 1 1 1 I 2 0 2 13 3 2 6 1 16 COLUMNS INDICATE VESSEL TYPES IN OUTBOUND DIRECTION ROWS INDICATE VESSEL TYPES IN INBOUND DIRECTION 100 * 98 * 96 * 90 * 9H • 90 » 68 * 66 * 84 • 62 * ******* 80 * * * 78 * * * 76 * * * 74 * * * 72 » * * 70 * * * • 68 * * * • 66 * * * 64 * * * 62 * *• * 60 * * * 58 * • 56 ft * * 54 • * ft 52 * - * * 50 * * * 48 * *. * 46 * * * 44 • * * 42 * * . ft ******* 40 * * * * * 38 » * * * * 36 * * * * * 34 * * * * * 32 * ******* * * * * 30 * * * * * * * 28 * • * * * * * 26 * * * • * ' * * 24 * * * * * * * 22 * * » * * * * 20 * * * * * * • * 18 * * * * ft ******* * * 16 * * * * • * * ******* * * 14 * * • * * * * * * * * 12 * * * • *' * * * * * * 10 * * • * ft * * * * * * 6 * * * * * * * * * * • * 6 * * * * * * * * * * * 4 * * * * » . * * * * ******* * * 2 * * •'• • * * * * * * * * * * 0 ********************************************************************** ******************************************* *********** S E C n t 3EG n 2 S E G * 3 S E G # 4 S E G * 5 S E G n 6 NO V E S S E L E N C O U N T E R S I N R E S P E C T I V E C H A N N E L S E G M E N T S * * * 6 5 0 » 6 4 0 * 6 3 0 * 6 2 0 * 6 1 0 * 6 0 0 * 5 9 0 • 5 8 0 * 5 7 0 * 5 6 0 * 5 5 0 * 5 4 0 * 5 3 0 • 5 2 0 * 5 1 0 * 5 0 0 * 4 9 0 * ******* ******* ******* 4 8 0 * • *• * * *• • * 4 7 0 * * *• • * * * 4 6 0 * * * * * * * 4 5 0 * . * * * * * * 4 4 0 * * * * * * * 4 3 0 * * * * 1 * * • 4 2 0 • * * * * * * 4 1 0 * * • * • *• * 4 0 0 * * * * * * * 3 9 0 * * * * *• * * 3 8 0 * • * * * • - * * ******* ******* ******* 3 7 0 * * * * * * * * * * * * * 3 6 0 * * * * * * * * * * * * • * 3 5 0 * • • * * * * * * * * * * 3 4 0 * * * * * * * * * * * * * 3 3 0 * * * * * * * * * * * * * 3 2 0 * • * . * * * * * * * * * * 3 1 0 • * *' * * * * * * * * ' * * 3 0 0 * * * * • * * * * * * * * 2 9 0 • * * * * * * * * * * * * 2 8 0 * • * * • - * * * * * * * * 2 7 0 • * * * * * * * * * * * * 2 6 0 • * * * * * * * * * * * * 2 5 0 • * * * * * * * * * * * * * 2 4 0 • • * * * * * * * * * * * 2 3 0 • • * * * * * * *' * * * * 2 2 0  * * * * * * * * * * * * 210 * * * * * * * * - • * • * * * 200 ******************************************************************************************************* ********************* S E G 0 1 S E G 0 2 S E G 0 3 SEG 0 4 S E G 0 5 S E G 0 6 Ox o V O L U M E OP V E S S E L T R A F F I C I N R E S P E C T I V E C H A N N E L S E G M E N T S I N B O U N D D I R E C T I O N * 650 * 640 * 630 * 620 * 610 * 600 * 590 • 560 » 570 * 560 • 550 * 540 * 530 * 520 * 510 * 500 * 490 * 4S0 * 470 * 460 * 450 * 440 * 430 * 420 * 410 * 400 * 390 * 380 * ******* 370 • * * 360 * * • 350 * * * 340 * * • 330 * * * 320 * • * 310 * * * 300 » * * 290 * • - * * 280 * * * 270 * • * 260 » * * 250 • * * 240 * • * 230 * * * 220 * * * 210 * • * 2 0 0 *******••*••*****•** ****** ******* ******* * * ******* 3E6 0 1 SEG 0 2 SEG 0 3 SEG 0 4 SEG 0 5 ********************* SEG 0 6 VOLUME OF VESSEL TRAFFIC IN RESPECTIVE CHANNEL SEGMENTS OUTBOUND DIRECTION ************************************************************** * T H E E X P E C T E D N U M B E R O F C O L L I S I O N S I N T H E C H A N N E L S E G M E N T S * *************************************************************** C H A N N E L # C O L L I S I O N S 1 . 1 1 1 8 9 E - 0 3 2 . 0 7 3 3 7 E - 0 2 3 . 0 9 5 9 7 E - 0 3 <t , 5 6 9 8 2 E - 0 « 5" . 1 3 2 8 9 E - 0 U 6 . 1 2 9 9 4 E - 0 3 T H E T O T A L N U M B E R O F C O L L I S I O N S I S l , U < l l 8 E - 0 2 ********************************** * B R E A K D O W N A M O N G V E S S E L T Y P E S * ********************************** C O L L I S I O N S I N V O L V I N G F R E I G H T E R S ! 1 2 X C O L L I S I O N S I N V O L V I N G T A N K E R S I 2 1 X C O L L I S I O N S I N V O L V I N G T O w S l 6 5 X END ***** TOTAL RUN TIME ( I N C L U D I N G A S S E M B L Y ) « 2 , 5 0 M I N U T E S ***** EXECUTION TERMINATED SSIGH 

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