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An analytical methodology for short run urban transportation policy questions Culham, Thomas Elwood 1978

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AN ANALYTICAL METHODOLOGY FOR SHORT RUN URBAN TRANSPORTATION POLICY QUESTIONS  by  Thomas Elwood Culham BA.Sc,  University of Waterloo, 1976  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER. OF 'APPLIED SCIENCE '  in  THE FACULTY OF GRADUATE STUDIES (Department o f C i v i l E n g i n e e r i n g )  WE ACCEPT THIS THESIS AS CONFORMING TO THE REQUIRED STANDARD  The University of B r i t i s h October,  ©  Columbia  1978  Thomas Elwood Culham, 1978  In p r e s e n t i n g an the  this thesis  in p a r t i a l  advanced degree at the U n i v e r s i t y Library  f o r s c h o l a r l y purposes may representatives.  be granted by  his  of  t h i s t h e s i s f o r f i n a n c i a l gain  CW«-  University of B r i t i s h  2075 Wesbrook Place Vancouver, Canada V6T 1W5  Date  Oct  /973  requirements f o r  Columbia, reference  the Head of my  It i s understood that shall  permission.  Department of  for  the  //je&gft/G Columbia  not  I agree and  f o r e x t e n s i v e copying o f  by  The  of B r i t i s h  s h a l l make i t f r e e l y a v a i l a b l e  I f u r t h e r agree t h a t p e r m i s s i o n  written  fulfilment of  study.  this  thesis  Department  copying or  that  or  publication  be allowed without  my  ii  ABSTRACT  The  purpose o f t h i s paper was t o develop an a n a l y t i c a l framework t o  answer s h o r t range p o l i c y q u e s t i o n s .  T h i s type o f framework i s needed  because u n t i l r e c e n t l y most models d e a l t w i t h l o n g range c a p i t a l investment d e c i s i o n s w h i l e many urban t r a n s p o r t a t i o n problems may be s o l v e d low  through  c a p i t a l cost p o l i c y decisions. The  l i t e r a t u r e i n d i c a t e d t h a t e q u i l i b r i u m t e c h n i q u e s were e s s e n t i a l  in providing  solutions to short run p o l i c y questions.  e q u i l i b r i u m theory i n general  The f e a t u r e s o f  were examined. The theory was then  discussed  i n terms of an a p p l i c a t i o n . I t was found t h a t the e q u i l i b r i u m s t a t e may be o b t a i n e d through a d i r e c t o r i n d i r e c t m o d e l l i n g approach. The d i r e c t approach u t i l i z e s a s i n g l e m o d e l l i n g step w h i l e the i n d i r e c t approach u t i l i z e s s e v e r a l sub-models. The s t a t e o f the a r t i s such t h a t i t appeared t h a t the s e q u e n t i a l  i n d i r e c t approach was the best method t o use.  A computer m o d e l l i n g framework was developed which i n c l u d e d i o n s and a d d i t i o n s  modificat-  t o a system produced a t the U n i v e r s i t y o f B r i t i s h  Columbia. The purpose o f the U.B.C. system was t o p r o v i d e d e t a i l e d a n a l y s i s of t r a f f i c movements over l o c a l i z e d t r a f f i c networks. The m o d e l l i n g contributions  o f t h i s paper were the d e t a i l e d d e s c r i p t i o n o f the t r a n s i t  u s e r through h i s t r i p from o r i g i n to d e s t i n a t i o n and the assembly o f an automobile assignment model, p a r k i n g  a l l o c a t i o n model, t r a n s i t  model and an a u t o - t r a n s i t demand model i n t o an e q u i l i b r i u m The  framework.  new system was t e s t e d on a s m a l l network. I t produced " r e a s o n a b l e  r e s u l t s " . Reasonable i n t h i s case (1)  assignment  implied:  t h a t any changes i n s e r v i c e l e v e l s o r p a r k i n g i n s h i f t s o f demand i n the a p p r o p r i a t e  costs w i l l r e s u l t  d i r e c t i o n and;  iii  (2)  t h a t changes i n demand w i l l be i n p r o p o r t i o n t o the change i n l e v e l o f s e r v i c e and v i c e v e r s a .  Two p a r k i n g p o l i c i e s were a n a l y s e d . The f i r s t  p o l i c y approximated the  case where a m u n i c i p a l i t y d e c i d e s t o i n c r e a s e the r a t e s i n i t s own p a r k i n g lots. The  P r i c e s were i n c r e a s e d on one o u t o f f o u r l o t s i n the t e s t network.  second p o l i c y approximated the case where the government i s a b l e t o  l e v y a t a x on a l l p a r k i n g l o t s . P r i c e s were i n c r e a s e d on a l l l o t s i n t h e t e s t network. The outcome produced by t h e model c o n f i r m e d  the e x p e r i e n c e  with parking p r i c e increases; that i s , f o r parking p o l i c i e s i n reducing congestion, i t i s necessary  t o be e f f e c t i v e  t o c o n t r o l a l l p a r k i n g spaces i n  the C.B.D.. A number of recommendations a r o s e from the a n a l y s i s o f t h e r e s u l t s from t h e t e s t network. I t was recommended t h a t f u r t h e r t e s t s be c a r r i e d out on a more network, and t h a t a s e t o f r e f i n e m e n t s  realistic  and s e n s i t i v i t y t e s t s be made on  some o f the sub-models i n t h e system. In g e n e r a l the model appeared t o be s e n s i t i v e t o changes i n a t t r i b u t e s of t r a n s p o r t a t i o n a l t e r n a t i v e s . The  development o f t h i s system was a step t o f i l l  t h e gap i n the  armoury o f a n a l y t i c a l t o o l s . F u r t h e r work and r e s e a r c h may show i t to' be useful i n practical  applications.  iv TABLE OF CONTENTS  Page  LIST OF TABLES  vi'  LIST OF FIGURES  viii  ACKNOWLEDGEMENTS  x  CHAPTER ONE:  Introduction  1  CHAPTER TWO:  Theoretical Considerations  6  2.1 CHAPTER THREE:  Transportation  Systems i n Equilibrium  C r i t e r i a f o r the Development of a Short Run Equilibrium Model  3.1  Approach to Equilibrium  3.2  The Modelling Framework  CHAPTER FOUR:  Solutions  The Computer System and Components  31  4.1  Features of the U.B.C. Framework  4.2  Components of the U.B.C. Model  4.2.1  Addressing the Parking Problem  4.2.2  The Parking A l l o c a t i o n Model  4.2.3  An Equilibrium Model for Vehicular  4.2.4  The Stochastic Vehicular Assignment Model  4.2.5  Vehicle Delay  CHAPTER FIVE:  16  Traffic  The U.B.C. Framework Modified  5.1  An Equilibrium Model f o r Transit  5.2  The All-or-Nothing Transit Assignment Model  5.3  Minimum Path Algorithm  5.4  Transit Travel Time Computation  5.5  Assignment of Passengers to the Network  5.6  The Mode Choice Model  5.7  A System Equilibrium Algorithm  43  V  TABLE OF CONTENTS (continued)  CHAPTER SIX:  An Application of the Modelling System  6.1  A Demonstration Using a Small Network  6.2  C a p a b i l i t i e s of the Transit Program  6.3  An I l l u s t r a t i o n of the Equilibrium Process  6.4  Problems and Anomalies  6.5  An Analysis of a Short Run Policy Question  CHAPTER SEVEN:  Conclusions  CHAPTER EIGHT:  Recommendations  99 106  BIBLIOGRAPHY  110  APPENDIX A: Development of a Modifier  113  APPENDIX B: The Computer Program BUS  128  vi LIST OF TABLES  Page  1.  Urban Scale Versus Planning Purpose  7  2.  Subsystem Models Versus Level of Service and Service Attributes  2(a)  Parking P o l i c i e s Used to I l l u s t r a t e the Program C a p a b i l i t i e s  28 &  and  the Equilibrium Process  66  3(a)  Minimum Transit Path Data for Parking Price Policy 2, Increment 3  68  (b)  Minimum Transit Path Data for Parking Price Policy 2, Increment 4  68  Travel Times From the Given Intersection  70  4.  to a l l Destinations  (a)  For Parking P r i c i n g Policy 2, Increment 3  70  (b)  For Parking P r i c i n g Policy 2, Increment 4  70  Car and Bus S p l i t s for the Given Intersection to A l l Destinations Parking Policy A Car and Bus S p l i t s for the Given Intersection to A l l Destinations  71  Parking Policy B  71  Bus  S t a t i s t i c s for Bus Line Number 3  74  (a)  For Parking P r i c i n g Policy 2, Increment 3  74  (b)  For Parking P r i c i n g Policy 2, Increment 4  74  5(a) (b)  6.  7(a) (b) 8.  Average Travel Times from Given Intersections to A l l Destinations for Each Iteration Between Policy 2, Increment 2 and 3 Average Auto Mode S p l i t From Given Intersections to A l l Destinations for Each Iteration Between Policy 2, Increment 2 and 3  75 75  Transition Parking Allocations for Each Iteration Between P o l i c y 2, Increment 2 and 3  76  (a)  1st Iteration  76  (b)  2nd  Iteration  76  (c)  3rd Iteration  77  (d)  4th Iteration  77  (e)  5th Iteration  78  Parking P r i c i n g P o l i c i e s  93  Aggregate S t a t i s t i c s of the System for the F i n a l State of Each Policy  96  9. 10.  101  vii  LIST OF TABLES  11.  (continued)  Page  The I t e r a t i v e P r o c e s s U s i n g Four Constant M o d i f i e r s , P a r k i n g P r i c e I n c r e a s e From $1.50 t o $2.50  124  (a) M o d i f i e r = .25  124  (b) M o d i f i e r = .50  124  (c) M o d i f i e r = .75  124  (d) M o d i f i e r  124  12.  =1.0  125  The I t e r a t i v e P r o c e s s U s i n g Two M o d i f i e r F u n c t i o n s  125  (a) P a r k i n g I n c r e a s e $1.50 t o $2.50 M o d i f i e r = f ( l o g i t f u n c t i o n ) (b) P a r k i n g I n c r e a s e $1.50 to $2.50 M o d i f i e r = 1-f dy/dx ( l o g i t  function)125  P a r k i n g I n c r e a s e $0.00 t o $1.00 M o d i f i e r = f Q o g i t f u n c t i o n ) •  125  (d) P a r k i n g I n c r e a s e $0.00 t o $1.00 M o d i f i e r = f d y / d x ( l o g i t f u n c t i o n )  125  (c)  13.  V a r i o u s P a r k i n g I n c r e a s e s and C o n g e s t i o n L e v e l s U s i n g t h e L o g i t Function Modifier  126  (a) P a r k i n g P r i c e I n c r e a s e $2.50 t o $2.75, M o d e r a t e l y Congested  126  (b) P a r k i n g P r i c e I n c r e a s e $2.50 t o $2.75, L i g h t l y Congested  126  (c)  126  P a r k i n g P r i c e I n c r e a s e $2.50 t o $3.50, M o d e r a t e l y Congested  (d) P a r k i n g P r i c e I n c r e a s e %2.50 t o $3.50, L i g h t l y Congested  126  viii LIST OF FIGURES  1.  A Flow Chart Showing the Major A c t i v i t i e s of the Paper  2.  A General Representation of a Transportation System i n Equilibrium  3.  The Effects of S h i f t s i n the Demand and Supply on Equilibrium i n  Page  3 11  a Transportation System  12  4.  Transportation Demand and F a c i l i t y Improvements  13  5.  A General Equilibrium,Model Under Short Run Assumptions  20  6.  An Equilibrium Model of the Auto Mode  22  7.  A Flow Chart of a Short Run A n a l y t i c a l Framework  25  8.  A Flow Chart of the U.B.C. Computer Framework  34  9.  A Flow Chart of the Modified Framework  10. (a)  34  Flow Chart of Main Program  44  (b)  Flow Chart of Minimum Path Subroutine: MINPTH  44  (c)  Flow Chart of Travel Time Subroutine: TIM  44  (d)  Flow Chart of Assignment Subroutine: ASSN  44  (e)  Flow Chart of Mode S p l i t Subroutine: SPLIT  44  (f)  Flow Chart of Bus Printout Subroutine: BNET  44  11.  A Demonstration Network  12. (a) (b) 13. (a) (b) 14.  62  Transition Travel Times Policy 2, Increment 2 to 3  83  Transition Mode S p l i t Policy 2, Increment 2 to 3  83  Transition Travel Times Policy 2, Increment 0 to 1  84  Transition Mode S p l i t Policy 2, Increment 0 to 1  84  Transition Travel Times and Volumes on Links into Parking Lot 1. Policy 2, Increment 2 to 3  87  (a)  Vehicles vs Iterations  87  (b) (c)  Time vs Iterations Intersection and Parking Lot #1  87 87  ix  LIST OF FIGURES(continued)  15.  Page  Transition Travel Times and Volumes on Links into Parking Lot #3 Policy 2, Increment 2 to 3 (a)  Vehicle Vs. Iterations  91  (b)  Travel time Vs. I t e r a t i o n  91  (c)  Intersection and Parking Lot #3  91  16.  Total Hours Travelled Vs. Total Travel Cost  17.  Auto Travel Time Vs Number of Iterations  94 115  (a)  Modifier = .25  115  (b)  Modifier = .50  115  (c)  Modifier = .75  115  (d)  Modifier = 1.0  115  18.  19.  91  Auto Travel Time Vs Number of Iterations  116  (a)  Modifier = f(Logit funtion)  116  (b)  Modifier = 1-f dy/dx' (Logit function)  116  (c)  Modifier = f (Logit function)  116  (d)  Modifier = 1-f  116  (Logit function)  Mode S p l i t Modified Test System  117  ACKNOWLEDGEMENTS  I wish t o express my g r a t i t u d e and thanks t o P r o f e s s o r s Brown and Navin f o r t h e i r guidance and encouragement throughout t h i s Without  thesis.  t h e i r h e l p and t h o u g h t f u l s u g g e s t i o n s and c r i t i c i s m t h e p r o j e c t  c o u l d not have been s u c c e s s f u l l y  accomplished.  CHAPTER  1.0  1  INTRODUCTION The urban planning process which developed during the 1950's and  1960's was  the  directed primarily towards the analysis of long range c a p i t a l  intensive transportation projects. In the past few years investments i n . large scale transportation projects have become expensive. Although t h i s increased expense has not excluded the necessity of providing costly  new  infrastructure, i t has shifted the focus of the transportation planner to the need for optimizing the operation of e x i s t i n g f a c i l i t i e s . The early planning  tools were designed to produce r e s u l t s for long  range investment projects. Few were developed which e x p l i c i t l y analysed short run transportation problems. None were r e a l l y designed to be sensitive to policy changes. Methods which have been introduced  recently i n an attempt to optimize  the system have included a variety of t r a f f i c management p o l i c i e s . They ranged from the provision of reserved bus lanes to r e s t r a i n t s on automobiles in selected areas of the c i t y . The demand side of the problem has also been addressed with f l e x i b l e work hours, car-pooling and various methods of p r i c i n g being attempted. Few  of these methods have been a n a l y t i c a l l y  evaluated before implementation, partly because there was  no  appropriate  a n a l y t i c a l framework available for such evaluations. Most of the work i n this area i s experimental, hence c i t i e s have become laboratories where untested hypotheses have been implemented and have met with varying degrees of success and  failure.  It has become apparent that an a n a l y t i c a l , systematic  approach to this  problem where the supply side, demand side, the transportation system and the interaction of these three elements are taken into f u l l account i s  needed. Work performed f o r a paper e n t i t l e d "An  Examination of the Costs  B e n e f i t s of V a r i o u s P a r k i n g P r i c i n g P o l i c i e s i n the C.B.D." was for  t h i s t h e s i s . A r e l a t i v e l y crude model was  done u s i n g a crude network. The p o l i c y q u e s t i o n s and  a more p r e c i s e a n a l y t i c a l framework f o r the  was  run  analysis  i n t h a t paper ^. -  purpose of t h i s paper i s to develop a more d e t a i l e d a n a l y t i c a l  framework. The parking  genesis  the a n a l y s i s  need f o r b o t h the a n a l y s i s of s h o r t  of the q u e s t i o n s wer.e r e c o g n i z e d The  developed and  the  and  methodology i s f o c u s e d p r i m a r i l y on  the a n a l y s i s of a l t e r i n g  charges i n the C.B.D.. With l i t t l e e f f o r t i t c o u l d be m o d i f i e d  handle a number of s h o r t  run  T h i s paper p r o v i d e s two  transportation  models which d e s c r i b e Some work (but not  to the  been addressed i n the past  the movement  a great  problems.  major c o n t r i b u t i o n s  these problems. Much work has  field  of m o d e l l i n g  to d e v e l o p i n g  of automobiles through a road network.  d e a l ) has  been expended i n d e s c r i b i n g the move-  ment o f a t r a n s i t passenger through the t r a n s i t network. L i t t l e been done to l i n k the s e r v i c e l e v e l s a r i s i n g on  the  two  dynamic sense to the demand l e v e l s on the networks. The paper i s the d e t a i l e d d e s c r i p t i o n of the o r i g i n to d e s t i n a t i o n and  to  work  has  networks i n a c o n t r i b u t i o n of t h i s  t r a n s i t user through h i s t r i p  the assembly of an auto assignment model,  a l l o c a t i o n model, t r a n s i t assignment model and  from  parking  an a u t o - t r a n s i t demand model  i n t o a dynamic framework. T h i s paper i s d i v i d e d i n t o f i v e s e c t i o n s . F i g u r e r a t e s the f l o w o f the work. The discusses  general  first  s e c t i o n examines the  e q u i l i b r i u m concepts. The  t h e o r e t i c a l a p p l i c a t i o n of the  1 graphically  illust-  literature  and  second s e c t i o n d e a l s w i t h a  concepts to s h o r t run p o l i c y q u e s t i o n s  and  d e l v e s i n t o the approaches a v a i l a b l e f o r p r o d u c i n g a t e c h n i q u e to p r o v i d e e q u i l i b r i u m s o l u t i o n s . In the  t h i r d s e c t i o n the assumptions and  functions  3.  FIGURE 1 .  FLOW CHART SHOWING THE MAJOR ACTIVITIES OF THE PAPER  DISCUSSION AND DEMONSTRATION OF GENERAL EQUILIBRIUM CONCEPTS  THEORETICAL APPLICATION OF GENERAL EQUILIBRIUM CONCEPTS TO SHORT RUN POLICY QUESTIONS  i  DISCUSSION OF AN EXISTING COMPUTER MODELLING SYSTEM; ITS S U I T A B I L I T Y AND SHORTCOMINGS  MODIFICATION OF THE EXISTING SYSTEM ACCORDING TO SHORT RUN EQUILIBRIUM,THEORY  APPLICATION OF THE MODIFIED SYSTEM TO A SMALL NETWORK AND ANALYSIS  •  4. of an e x i s t i n g computer m o d e l l i n g with respect The  to the theory  f o u r t h p a r t s e t s out  modelling  set out  system are d i s c u s s e d .  I t s shortcomings  i n the second s e c t i o n are a l s o  the m o d i f i c a t i o n s and  a d d i t i o n s to the  illustrated.  current  methodology. F i n a l l y , an a p p l i c a t i o n of the r e v i s e d m o d e l l i n g  system to a s m a l l s t r e e t and r e s u l t s i s given.  bus network i s made and  an a n a l y s i s of  the  • z  FOOTNOTES T. E. Culham, "An Examination o f the Costs and B e n e f i t s o f V a r i o u s P a r k i n g P r i c i n g P o l i c i e s i n the C.B.D.", Student Paper Number 21, Centre f o r 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 Columbia, 1977.  6.  CHAPTER 2 2.0  THEORETICAL CONSIDERATIONS T r a d i t i o n a l aggregate models of t r a v e l demand have proven to be i n -  adequate f o r s h o r t range p o l i c y planning''".  Three d i s t i n c t  t o p i c s must  addressed i n the development of a methodology which s o l v e s p o l i c y questions. which d e s c r i b e s must be  F i r s t , a general behavioural  transportation  assumption should  the p r o c e s s to be modelled. Secondly, a s e t of  be  stated  requirements  e s t a b l i s h e d which ensure t h a t the p r o c e s s does i n f a c t model  b e h a v i o u r . T h i r d l y , a t e c h n i q u e ought to be the s c a l e of the problem and  the  chosen which i s a p p r o p r i a t e  i s c a p a b l e of s a t i s f y i n g the s t a t e d  to  conditions.  Wardrop's f i r s t p r i n c i p l e s t a t e s t h a t t r a f f i c between o r i g i n s destinations w i l l  be  and  tend to s e t t l e i n t o an e q u i l i b r i u m s t a t e where no  driver  2 can reduce h i s j o u r n e y time by assumption was  generalized  choosing a new  route  to i n c l u d e a l l t r a v e l c h o i c e s  urban t r a v e l l e r . I t i s s t a t e d as f o l l o w s : T r a v e l by between o r i g i n s and  The  car or any  safety etc.  equilibrium costs  c o s t r e f e r s t o the monetary c o s t s of  . According  to F l o r i a n  the  other mode  incurred  changing the mode of  i n v e h i c l e t r a v e l time, out of v e h i c l e t r a v e l time and  general  a v a i l a b l e to  reduce the g e n e r a l i z e d  c h o o s i n g another route or by  concept of g e n e r a l i z e d  reliability,  behavioural  d e s t i n a t i o n s w i l l tend to s e t t l e i n t o an  s t a t e where no p e r s o n t r a v e l l i n g can i n h i s j o u r n e y by  . This  travel.  travel,  comfort, convenience,  the s i m p l e s t  and  d e f i n i t i o n of e q u i l i b r i u m i s t h a t e q u i l i b r i u m i s a steady  most state  that i s reached when the demand f o r t r a n s p o r t a t i o n g i v e s r i s e to a s e r v i c e 4 l e v e l t h a t m a i n t a i n s t h a t demand . The discussed  i n greater  d e t a i l i n p a r t one  A t h e r t o n et a l s e t by  s h o r t range p l a n n i n g  out  two  concept of e q u i l i b r i u m w i l l of Chapter  2.  b a s i c c o n d i t i o n s which must be  models"*. F i r s t ,  they should  be  be  satisfied  s e n s i t i v e to changes  7.  i n a t t r i b u t e s of t r a n s p o r t a t i o n  a l t e r n a t i v e s t h a t would r e s u l t from p o l i c i e s  b e i n g a n a l y s e d ( i . e . the models must be p o l i c y s e n s i t i v e ) . Secondly, t h e models must be s t r u c t u r e d choice  i n such a way t h a t they a c c u r a t e l y  r e f l e c t the  p r o c e s s o f an i n d i v i d u a l d e c i d i n g between a l t e r n a t i v e s .  P l a n n i n g may be done a t d i f f e r e n t urban s c a l e s r a n g i n g from  regional  to l o c a l m i c r o and have s e v e r a l purposes r a n g i n g from o p e r a t i o n a l t o s t r a t e g i c . T a b l e 1 i l l u s t r a t e s the r e l a t i o n s h i p between the urban s c a l e and purpose o f p l a n n i n g .  TABLE 1  X . \.  URBAN SCALE VERSUS PLANNING PURPOSE  PLANNING PURPOSE  URBANX. SCALE \ .  OPERATIONAL  FUNCTIONAL  STRATEGIC  X  REGIONAL SUBREGIONAL  -  X  X  URBAN  -  X  X  LOCAL URBAN  X  X  -  LOCAL MICRO  X  —  —  Wigan draws a f i n e but important d i s t i n c t i o n between the s c a l e s o f 'urban' and ' l o c a l urban' *\  The former r e f e r s t o the a n a l y s i s o f major  schemes o f c o n s t r u c t i o n w h i l e the l a t t e r r e f e r s t o the a n a l y s i s o f s h o r t run  low c a p i t a l c o s t  schemes. He d i s c u s s e s  the a p p l i c a b i l i t y o f e q u i l i b r i u m  8. techniques without  t o the v a r i o u s urban s c a l e s and comes t o the c o n c l u s i o n t h a t  e q u i l i b r i u m techniques  i t i s u n l i k e l y t h a t the r e s u l t s o f a l o c a l  urban a n a l y s i s would be o f any p r a c t i c a l v a l u e ^ . The methodology b e i n g developed  i n t h i s paper i s d i r e c t e d a t s o l v i n g problems a t the l o c a l urban  level. At the b e g i n n i n g  o f t h i s chapter a g e n e r a l i z e d b e h a v i o u r a l  was s t a t e d . In i t the concept  o f e q u i l i b r i u m was i n t r o d u c e d and was  d e f i n e d . In the d i s c u s s i o n above i t was r e c o g n i z e d techniques  assumption later  that e q u i l i b r i u m  p r o v i d e the t h e o r e t i c a l b a s i s w i t h which t o f a b r i c a t e a method- .  ology t o s o l v e s h o r t run p o l i c y q u e s t i o n s . The f o l l o w i n g d i s c u s s i o n enumerates a s e t of c o n d i t i o n s which a r e n e c e s s a r y  t o ensure c o n s i s t e n c y i n  e q u i l i b r i u m models. I t a l s o d i s c u s s e s the degree w i t h which these models meet the requirements  of Atherton. g  The  c o n d i t i o n s as s e t out by Manhiem a r e the f o l l o w i n g :  (1)  The l e v e l of s e r v i c e f a c t o r s such as i n v e h i c l e , out o f v e h i c l e t r a v e l times, d i s t a n c e , convenience e t c . e n t e r s a t each  stage  i n the sequence, i n c l u d i n g g e n e r a t i o n , u n l e s s i t i s e x p l i c i t l y found (2)  t o be s u p e r f l u o u s .  The same a t t r i b u t e s o f s e r v i c e should e n t e r a t each step the data i n d i c a t e s o t h e r w i s e . bus  (3) .  unless  S e r v i c e a t t r i b u t e s a r e bus f a r e s ,  frequencies, parking costs e t c .  The same v a l u e s o f the l e v e l o f s e r v i c e s h o u l d i n f l u e n c e each sub-model.  (4)  The l e v e l o f s e r v i c e p r o v i d e d by each mode should  i n f l u e n c e the  demand t o some degree. These a r e g e n e r a l c o n d i t i o n s which apply  t o a l l e q u i l i b r i u m models.  These c o n d i t i o n s a r e a p p l i c a b l e from the g e n e r a l d e f i n i t i o n and approach  9.  to the model through to the d e t a i l s of the V a r i o u s procedures may t r a n s p o r t a t i o n f l o w s . As s e t out The  be u t i l i z e d  sub-models.  i n o r d e r to a t t a i n e q u i l i b r i u m  l o n g as the procedure chosen meets the  above then the f i r s t  conditions  requirement of A t h e r t o n et a l w i l l be  second requirement w i l l be  satisfied  of  satisfied.  i f the model i s s t r u c t u r e d  so  that  the s i g n i f i c a n t s e r v i c e l e v e l s of the v a r i o u s modes are made a v a i l a b l e to a behavioural  c h o i c e model. The  the second requirement. The fulfill  conditions  of e q u i l i b r i u m p a r t i a l l y  s e l e c t i o n of a d i s a g g r e g a t e c h o i c e model w i l l  the remaining requirements. T h i s s e l e c t i o n w i l l be  i n the  paper.  2.1  Transportation  satisfy  Systems In  discussed  later  Equilibrium  B e f o r e d e l v i n g i n t o the development of the a n a l y t i c a l framework, a general w i l l be  explanation  of the n o t i o n  of a t r a n s p o r t a t i o n  system i n e q u i l i b r i u m  given.  A transportation  system i n e q u i l i b r i u m i s seen to have f o u r  which operate i n t e r a c t i v e l y . They are  the  components  following:  T,  The  transportation  i n f r a s t r u c t u r e which i s the b a s i c  supply.  A,  The  transportation  systems a s s o c i a t e d  activities.  socio-economic  These a c t i v i t i e s i n c l u d e l o c a t i o n s of work, r e c r e a t i o n and V,  The  demand which the a c t i v i t i e s put  takes the of the L.  The  on the  home.  system. T h i s demand  form of volume of t r i p s by v a r i o u s modes on  the l i n k s  system.  l e v e l of s e r v i c e on the system a r i s i n g out  t r a f f i c on the  system and  the  of the volume of  system c o n f i g u r a t i o n or  infra-  structure. The  l e v e l of s e r v i c e i n t h i s d i s c u s s i o n  components:  i s comprised of the  following  10. 1.  The s e r v i c e a t t r i b u t e s which are c o n t r o l l a b l e system such as bus f r e q u e n c i e s ,  2.  parameters  bus f a r e s , p a r k i n g charges e t c . .  The remaining p o r t i o n i s made up of what i s t y p i c a l l y as the l e v e l of s e r v i c e f a c t o r s distances  ; these a r e , t r a v e l times and  by the two modes, convenience e t c . .  The l e v e l of s e r v i c e as r e f e r r e d to here i s e q u i v a l e n t generalized  thought of  to the  c o s t concept. L a t e r i n the paper s p e c i f i c r e f e r e n c e s  idealized  will  be  made to s e r v i c e a t t r i b u t e s and the l i m i t e d l e v e l of s e r v i c e concept. For the g r a p h i c a l p r e s e n t a t i o n  and d i s c u s s i o n  i n p a r t s one and two of Chapter 2  the broader concept of l e v e l of s e r v i c e i s used. A f i n a l v a r i a b l e i s introduced the l i t e r a t u r e because  here which  i s not n o r m a l l y i n c l u d e d i n  i t i s a f u n c t i o n of the l e v e l of s e r v i c e . However,  f o r c l a r i t y i n the f o l l o w i n g d i s c u s s i o n , g e n e r a l i z e d  c o s t o r simply c o s t  of t r a v e l as f u n c t i o n o f the l e v e l o f s e r v i c e w i l l be C  =  the g e n e r a l i z e d  included.  c o s t o f t r a v e l as a f u n c t i o n of the l e v e l of  service Generally thinks  when one t h i n k s  of an improved  i s better. Figure in equilibrium.  of the l e v e l o f s e r v i c e improvement  s e r v i c e where t r a v e l times are s h o r t e r  2 i s a t y p i c a l representation  and  one  convenience  of a t r a n s p o r t a t i o n  In the l i t e r a t u r e the h o r i z o n t a l a x i s r e p r e s e n t s the  system total  demand and the v e r t i c a l a x i s the. l e v e l of s e r v i c e . Under these c o n v e n t i o n s one tends t o t h i n k t h a t the l e v e l of s e r v i c e i n c r e a s e s  up the v e r t i c a l  axis.  However, the diagram makes more sense i f one assumes t h a t the c o s t s of t r a v e l increase  up the v e r t i c a l a x i s and the l e v e l o f s e r v i c e  Each of the v a r i a b l e s above are v e c t o r s . structure i s a vector  of l i n k s w i t h a s s o c i a t e d  socio-economic a c t i v i t i e s are the p l a c e s  deteriorates.  The t r a n s p o r t a t i o n traffic  of r e s i d e n c e ,  infra-  characteristics.  The  r e c r e a t i o n and work  11  FIGURE  V  Q  2  T o t a l T r i p Volumes  A GENERAL REPRESENTATION OF A TRANSPORTATION EQUILIBRIUM  throughout  SYSTEM IN  the region.The demand i s the number o f persons moving between  these a c t i v i t i e s and may be s p e c i f i e d by p o p u l a t i o n day, by mode e t c . . F i n a l l y  subgroups, by time o f  the s e r v i c e l e v e l s a r e v e c t o r s  o f t r a v e l time,  d i s t a n c e , c o s t , comfort e t c . f o r each mode. Generally  t h e demand f o r t r a v e l i s a f u n c t i o n o f the l e v e l o f s e r v i c e  L on the system and the socio-economic a c t i v i t i e s A o f the r e g i o n . The volume o f t r a f f i c V on the system i s a r e s u l t o f t h a t demand and i s g i v e n by:  V = f(C,A) where  •  C = f(L)  1 2  Note t h a t the c o s t C i s a f u n c t i o n o f the l e v e l of s e r v i c e L and i t i s determined by the volume o f t r a f f i c V on the t r a n s p o r t a t i o n system T. C = f(L)  = f(V,T)  3  12  A g r a p h i c a l r e p r e s e n t a t i o n o f the e q u i l i b r i u m s t a t e i s a c h i e v e d by supposing t h a t equations 1 and 2 a r e continuous f o r the g i v e n A and T. A whole f a m i l y o f curves may be d e f i n e d f o r each o f the equations i n the p l a n e d e f i n e d by the aggregate  l e v e l o f s e r v i c e and t o t a l demand a x i s ;  r e f e r to F i g u r e 3. F o r each g i v e n A and every l e v e l o f s e r v i c e , t h e r e i s  A  V  FIGURE  3  V V  D  E  B  V  Total Trip Volumes  THE EFFECTS OF SHIFTS IN THE DEMAND AND SUPPLY:-. ON EQUILIBRIUM IN A TRANSPORTATION SYSTEM  a ' curve which d e s c r i b e s the demand on t h e system.  S i m i l a r l y , f o r each g i v e n  T and every demand t h e r e i s a s e p a r a t e curve which d e s c r i b e s the p o s s i b l e l e v e l of s e r v i c e a l o n g i t .  T h e i r i n t e r s e c t i o n d e f i n e s the e q u i l i b r i u m demand  and s e r v i c e l e v e l . F i g u r e 3 shows a p a i r df curves i n the f a m i l y o f curves of each  relationship.  13  An important notion of generalized equilibrium analysis i s that t o t a l demand f o r t r a n s i t i s not f i x e d . I t supposes that an improvement i n any :.. facet of the transportation system w i l l lead to an improvement in.the o v e r a l l system and hence increase the t o t a l number of t r i p s made. Figure 4 i l l u s t r a t e s this concept. The source of the additional demand l i e s i n the FIGURE TRANSPORTATION  4  DEMAND AND F A C I L I T Y  IMPROVEMENTS  T r i p s g e n e r a t e d due t o improvements  Total Person Trips  T o t a l t r i p s beforeimprovement  Auto trips Transit trips Time  latent demand - a topic which i s addressed i n greater d e t a i l i n Chapter 3. With this concept i n mind an i l l u s t r a t i o n of the i n t e r s e c t i o n of equation 1 and 2 w i l l be given with references  to Figure 3. I t must be  remembered that Figure 3 i s a general representation of the complete transportation system including a l l modes. The planner or engineer can d i r e c t l y influence the equilibrium of the system by influencing the service attributes of the modes, a l t e r i n g socioeconomic a c t i v i t i e s and changing the transportation system. An example of changes i n each of these areas w i l l be discussed. For example, point A on Figure 3 i s assumed to be the e x i s t i n g  14  equilibrium.  Service  level  and volumes o r demand A^ r e s u l t . In t h e f i r s t  case, t h e l e v e l of s e r v i c e i s i n c r e a s e d s e r v i c e . Suppose t h a t t h r o u g h . t h i s and  by i n c r e a s i n g the frequency of bus  change the bus becomes more r e l i a b l e  bus t r a v e l times a r e reduced. Two t h i n g s  occur. Some p e o p l e w i l l be  a t t r a c t e d t o t h e bus mode from t h e i r c a r s and new r i d e r s w i l l be a t t r a c t e d to both modes. The system reaches e q u i l i b r i u m a t p o i n t B w i t h new s e r v i c e l e v e l s B^ and B^ . The d i f f e r e n c e between A^ and B^ i s t h e generated demand. I t i s important t o note t h a t F i g u r e The  3 i s only a p i c t o r i a l  representation.  s l o p e of curve 1 c o u l d be e n t i r e l y d i f f e r e n t . I t may be v e r t i c a l i n t h e  range of t h e a n a l y s i s , i n which case no new demand would be generated.  Also,  a l t h o u g h one f a c t o r o f t h e l e v e l o f s e r v i c e has been made more a t t r a c t i v e i t may have produced an o v e r a l l n e t n e g a t i v e r e s u l t . In t h i s case t h e aggregate l e v e l o f s e r v i c e would be reduced. In t h e second c a s e , a new r a p i d t r a n s i t significant  of years of operation,  system i n f l u e n c e s c i t y increase The  It affects  improvements i n the l e v e l of s e r v i c e . When t h e f a c i l i t y  the new e q u i l i b r i u m c o n d i t i o n s period  system i s i n s t a l l e d .  are defined  opens,  by p o i n t B. However, over a  the improved l e v e l o f s e r v i c e o f f e r e d by t h e  location decisions.  The socio-economic a c t i v i t i e s o f t h e  and t h e new e q u i l i b r i u m c o n d i t i o n s  are described  d i f f e r e n c e i n demand between A^ and B^ r e p r e s e n t  by p o i n t D.  newly generated  from the e x i s t i n g p o o l o f demand. The d i f f e r n e c e between B^ and t r i p s generated by t h e growth o f the c i t y and by l o c a t i o n  trips  represent  decisions  i n f l u e n c e d by t h e i n s t a l l a t i o n o f t h e f a c i l i t y . In t h e t h i r d c a s e , t h e c i t y i n transportation  i s a l l o w e d t o grow w i t h o u t any improvement  services. Point E describes  l e v e l of s e r v i c e has i n c r e a s e d  t h e new e q u i l i b r i u m . The  i n c o s t from A^ t o E^ and A^ t o E ^ r e p r e s e n t s  newly generated t r i p s due t o t h e growth o f t h e c i t y .  15 FOOTNOTES 1.  T. J . A t h e r t o n , J , H, S u h r b i e r , and W. A. Jessiman, "Use o f D i s a g g r e g a t e T r a v e l Demand Models t o A n a l y s e Car P o o l i n g P o l i c y I n c e n t i v e s " , T r a n s p o r t a t i o n Research Board, 599., 1976, p. 35.  2.  J . G. Wardrop, "Some T h e o r e c t i c a l A s p e c t s o f Road T r a f f i c P r o c . I n s t . C i v i l E n g i n e e r s , P a r t I I 1952, p.345.  3.  J . H. S h o r t r e e d ( e d . ) , "Urban Bus T r a n s i t : A P l a n n i n g Guide", The T r a n s p o r t Group, Department of C i v i l E n g i n e e r i n g , U n i v e r s i t y of Waterloo, 1974, pp 93 - 102.  4.  M. A. F l o r i a n e t a l , "EMME: A P l a n n i n g Method f o r M u l t i - M o d a l Urban T r a n s p o r t a t i o n Systems", U n i v e r s i t e de M o n t r e a l P u b l i c a t i o n #62, Centre de r e c h e r c h e s u r l e s t r a n s p o r t s , March 1977, p.3.  5.  Atherton, l o c . c i t . .  6.  M. R. Wigan, M. A. F l o r i a n ( e d . ) , " E q u i l i b r i u m Models i n Use: P r a c t i c a l Problems and P r o p o s a l s f o r T r a n s p o r t P l a n n i n g " , T r a f f i c E q u i l i b r i u m Methods P r o c e e d i n g s o f the I n t e r n a t i o n a l Symposium, a t t h e U n i v e r s i t y o f M o n t r e a l , S p r i n g e r - V e r l a g , New York 1976, p. 18.  7.  Ibid.  8.  M. L. Manhiem, " P r a c t i c a l I m p l i c a t i o n s of Some Fundamental P r o p e r t i e s of T r a v e l Demand Models" Highway Research Record, 422, 1973, p.24.  Research",  16  CHAPTER 3  3.0  THEORETICAL DEVELOPMENT OF A SHORT RUN EQUILIBRIUM MODEL The  p r e v i o u s d i s c u s s i o n has d w e l l e d on t h e g e n e r a l  e q u i l i b r i u m from a long range p o i n t the concepts and g i v e a g e n e r a l  concepts o f  of view. I t s purpose was t o i n t r o d u c e  overview o f a t r a n s p o r t a t i o n  system i n  e q u i l i b r i u m . The f o l l o w i n g d i s c u s s i o n i s more s p e c i f i c . The c r i t e r i a  for  the development of a methodology f o r the a n a l y s i s of s h o r t r u n p o l i c i e s are s e t out.  The i d e a o f e q u i l i b r i u m i n terms o f t h e s o l u t i o n o f s h o r t r u n  p o l i c y questions are discussed.  Proceeding to the theory of the s t r u c t u r e  of t h e system, t h e m o d e l l i n g approach t o s h o r t  run e q u i l i b r i u m  solutions  i s addressed. F i n a l l y t h e framework o f t h a t approach i s e x p l a i n e d . The  s t a t e d purpose o f t h i s paper i s t o develop an a n a l y t i c a l framework  which p r o v i d e s s o l u t i o n s t o s h o r t  run p o l i c y questions..Implementation' of  a p o l i c y i m p l i e s t h a t t h e p l a n n e r wishes t o improve t h e e f f i c i e n c y of the e x i s t i n g system o r reduce i t s n e g a t i v e impacts such as p o l l u t i o n ,  noise  e t c . on s o c i e t y . In o r d e r to determine t h e e f f e c t s of a p o l i c y t h e p e r t i n e n t conditions  associated  w i t h t h e e x i s t i n g s t a t e o f e q u i l i b r i u m and those  a s s o c i a t e d w i t h t h e s t a t e o f e q u i l i b r i u m under t h e new. p o l i c y must be known. Of utmost importance i s t h e a b i l i t y t o a c c u r a t e l y p r e d i c t t h e c o n d i t i o n s due  t o the new s h o r t  r u n p o l i c y . The f o l l o w i n g i s a d i s c u s s i o n o f the  c r i t e r i a which were e s t a b l i s h e d  f o r the development o f a e q u i l i b r i u m model  to s a t i s f y t h e above g o a l . A s e t o f assumptions were made based on t h e c r i t e r i a and the v a l i d i t y o f these assumptions i s d i s c u s s e d to t h e g e n e r a l The  concepts o f e q u i l i b r i u m p r e v i o u s l y  with  respect  s e t out.  f o l l o w i n g c r i t e r i a were e s t a b l i s h e d f o r t h e development o f a new  e q u i l i b r i u m model:  17  1.  U t i l i z e the state of the art concepts as much as possible with regard to equilibrium models.  2.  The emphasis of the framework would be on the short run, giving results which would be applicable from the present to two or three years i n the future.  3.  The model could be applied i n an operational mode as well as a planning mode within two years.  4.  The model would tabulate and possibly evaluate cost-benefit factors of the proposed plan against the existing s i t u a t i o n .  5.  The framework would u t i l i z e e x i s t i n g models as much as possible, choosing them and assembling them into the framework so as to be consistent with equilibrium concepts.  6.  The model would focus on AM peak work t r i p s only.  7.  The model would consider both transit and automobile t r i p s i n equilibrium.  8.  Both the network i n t e r a c t i o n and the choice between the two modes would be considered.  9.  The choice process would consider the s i g n i f i c a n t l e v e l of service c h a r a c t e r i s t i c s of both modes.  In order to simplify the solution process the following assumptions were made. 1.  The t o t a l demand for t r a v e l would be fixed. Only t r i p making trade-offs between the two modes would be considered.  2.  The socio-economic a c t i v i t i e s w i l l not a l t e r s i g n i f i c a n t l y  during  the period of analysis. 3.  The transportation system w i l l not be changed during the analysis period.  18  The  first  assumption.is c r i t i c a l .  means t h a t t r i p g e n e r a t i o n  From a m o d e l l i n g  p o i n t of view i t  can be determined exogenously t o the model. I t  s i m p l i f i e s the p r o c e s s g r e a t l y . B r i e f l y ,  t h e model takes c u r r e n t  trip  d i s t r i b u t i o n t a b l e s f o r auto and t r a n s i t and computes t h e e q u i l i b r i u m s t a t e given  the c u r r e n t  l e v e l of s e r v i c e c o n d i t i o n s . This allows  the a n a l y s t t o  check whether the model a c c u r a t e l y p r e d i c t s observed data. A change i s then made i n a s e r v i c e a t t r i b u t e such as a change i n p a r k i n g  charges. The model  then computes the new e q u i l i b r i u m t r a n s i t - a u t o s p l i t and outputs the s e r v i c e l e v e l s a r i s i n g from the new s p l i t . t r a v e l . The f o l l o w i n g d i s c u s s e s  I t does not a l t e r the t o t a l demand f o r  the v a l i d i t y of t h i s  assumption.  T o t a l demand f o r t r a v e l may be a l t e r e d i n two ways. 1.  The socio-economic a c t i v i t i e s i n a r e g i o n may i n c r e a s e growth i n p o p u l a t i o n  due t o  and employment o p p o r t u n i t i e s . Hence, t h e  t o t a l demand f o r t r a v e l i n c r e a s e s . 2.  Latent  demand may be induced t o use the system through  increased  s e r v i c e l e v e l s ( i . e . lower t r a v e l l i n g c o s t s ) . The  assumption t h a t socio-economic a c t i v i t i e s do n o t change s i g n i f i c a n t -  l y over one o r two years i s v a l i d p r o v i d e d i s not e x c e s s i v e commence d u r i n g  the growth r a t e i n t h e r e g i o n  and no new major h o u s i n g or employment developments the p e r i o d o f a n a l y s i s . An e x t e n s i o n  of t h i s  assumption  beyond the two year p e r i o d would r e q u i r e judgement i n a c c e p t i n g Latent 1.  demand i s d e f i n e d as t r i p s that"*":  a r e d e s i r e d and can be met by e x i s t i n g t r a n s p o r t a t i o n systems but are n o t attempted f o r reasons other  2.  its validity.  than poor l e v e l of s e r v i c e .  a r e d e s i r e d a t a p a r t i c u l a r time but cannot be met by t h e e x i s t i n g system.  3.  a r e not now d e s i r e d but may be d e s i r e d i n the f u t u r e and can be  19 met by e x i s t i n g systems. 4.  are not now  desired and cannot be met by the e x i s t i n g system.  It would appear that latent demand u n s a t i s f i e d by e x i s t i n g transportation systems for work t r i p s might have some significance to this model. It would also appear that changes i n t o t a l demand for work t r i p s are i n s e n s i t i v e to changes i n l e v e l of service. In the case of automobile-restraint measures 2  for work t r i p s , Heggie makes this statement : "Work journeys cannot be easily terminated (except for temporary or part time work) and t r a v e l l e r s can usually be forced to use public t r a n s i t . " This suggests that lowering or r a i s i n g the service l e v e l s would not greatly influence latent demand over a short period. It must be noted however that this assumption loses v a l i d i t y over time as people can make adjustments in their place of residence or place of employment. One  of the remaining assumptions has already been discussed. That i s ,  t o t a l demand i s a function of socio-economic a c t i v i t i e s . To be consistent with the fixed demand function i t i s necessary that •-"the'v." socio-economic a c t i v i t i e s remain unaltered as well. The assumption that the transportation system remains unchanged during the analysis period i s v a l i d provided  that no infrastructure becomes  operational during that period. These assumptions a l t e r the form of Figure 3 from a family of i n t e r secting curves to a single v e r t i c a l l i n e . Equation 1 transforms from V = f (L,A)  1  to V = Z where Z i s a  4 constant.  20 S i n c e V,  and  of s e r v i c e can  T of e q u a t i o n 2 are  c o n s t a n t s but  the aggregate  level  f l u c t u a t e , e q u a t i o n 2 transforms from  C = f ( L ) = f(V,T)  2  to C = f(L) =  5  f(V ,V ) T  where T and A are  A  s u b s c r i p t s d e n o t i n g the  V i s the volume of t r a f f i c It  i s h y p o t h e s i z e d t h a t by  auto modes.  on each mode.  a l t e r i n g the s p l i t between the auto  t r a n s i t modes the aggregate l e v e l of s e r v i c e can be The  t r a n s i t and  and  altered.  e q u i l i b r i u m s t a t e of the system i s a p o i n t d e f i n e d by E q u a t i o n 4  on the l i n e V = Z ; r e f e r to F i g u r e  5.  FIGURE  5  A GENERAL EQUILIBRIUM MODEL UNDER SHORT RUNASSUMPTIONS  Cost of  L  Travel  V  f(v , T  v) A  f(L)  Total  Volume  M a x i m i z a t i o n of the aggregate l e v e l of s e r v i c e may  not  be  the g o a l  the c i t y p l a n n e r or e n g i n e e r . From the p o i n t of view of s o c i e t y , t h e r e be  factors outside  the l e v e l of s e r v i c e f u n c t i o n or f a c t o r s which  of may  are  improperly r e p r e s e n t e d i n i t . Such examples are energy consumption, p o l l u t i o n or n o i s e problems. The  b e n e f i t s to s o c i e t y at l a r g e however, must be  balanced  21  against  the aggregate cost t o the t r i p makers due to the reduced l e v e l - o f  service. R e t u r n i n g t o the main t o p i c , i n the system sense then, the e q u i l i b r i u m s o l u t i o n i s redundant. I t i s simply the sum o f a l l l e v e l o f s e r v i c e p l o t t e d on the s t r a i g h t l i n e i n F i g u r e  factors  5. The problem l i e s i n d e t e r m i n i n g  those l e v e l o f s e r v i c e f a c t o r s f o r both modes i n e q u i l i b r i u m .  The g e n e r a l  e q u a t i o n f o r the l e v e l o f s e r v i c e i s :  L = f(v ,v ) T  6  A  where L = L  M  + L,  T The  7  A  l e v e l o f s e r v i c e f o r each mode i n e q u a t i o n 7 a r e f u n c t i o n s  o f the  volumes o r demands on both the mode networks. L L  The  T  «  A "  8 f  2  (  V V  "  9  demands on both t h e networks i n t u r n a r e dependent on the l e v e l o f  s e r v i c e on b o t h the networks. V  V  A " 3 T» A> f  T - 4 f  ( L  ( L  L  T' A L  )  1  .  1  0  1  These e q u a t i o n s a r e s i m i l a r i n form t o those p r e s e n t e d f o r the g e n e r a l case. F i g u r e  6 i s a p i c t o r i a l representation  o f the e q u i l i b r i u m s t a t e f o r  the automobile mode o n l y . A s i m i l a r graph c o u l d be developed f o r the t r a n s i t mode i n e q u i l i b r i u m . There i s a f a m i l y of curves d e s c r i b i n g given  the auto demand V  l e v e l of s e r v i c e of t r a n s i t L^. S i m i l a r l y , there  i s a family of  v e r t i c a l l i n e s d e s c r i b i n g the l e v e l o f s e r v i c e o f the auto L given &  demand of t r a n s i t V . T  f o r every  f o r every  22  FIGURE 6  AN EQmLIBRItM MODEL OF THE AUTO MODE  The  t r a n s i t and  automobile modes a r e a t . e q u i l i b r i u m at p o i n t A.  l e v e l of s e r v i c e f o r autos i s reduced by adding a p a r k i n g immediate r e s u l t i s an  increase  i n the c o s t s of d r i v i n g from A^  However, a f t e r the system u s e r s have had  a chance to r e a c t  p r i c e s the system s e t t l e s i n t o e q u i l i b r i u m a t p o i n t B. auto t r a v e l i s r e p r e s e n t e d by b e i n g the s h i f t The  to  addressed i n t h i s paper. Given the c u r r e n t the new  B^,  the d i f f e r e n c e between  Stated  b r i e f l y , the problem i s as  e q u i l i b r i u m s t a t e of the  determined.  new  new  demand f o r  B^  and  A^  t r a n s i t and  follows. auto modes,  e q u i l i b r i u m c o n d i t i o n s when a change i s made i n Once the hew  found, i t s o p e r a t i o n a l d i f f e r e n c e s and be  to the  D^.  above i s p r e c i s e l y the problem which i s b e i n g  l e v e l of s e r v i c e of e i t h e r mode?  may  The  to  The  transit.  process described  what w i l l be  charge.  The  the  e q u i l i b r i u m s o l u t i o n has  c o s t b e n e f i t s over the p r e v i o u s  been state  23  3.1  Approach to Equilibrium Solutions An equilibrium model may be structured i n two ways. According to 3  Manhiem  the equilibrium state may be obtained through a direct or i n d i r e c t  approach. The direct approach u t i l i z e s a single modelling step while the i n d i r e c t approach u t i l i z e s several sub-models. An econometric model which estimates the t r i p generation, t r i p d i s t r i b u t i o n , mode s p l i t and assignment in one step i s a d i r e c t approach. The Urban Transportation Model System (UTMS) estimates each of the above segments of the problem i n four d i f f e r e n t sub-models and i t i s an i n d i r e c t approach. Although UTMS has been very widely used and accepted, i t has many short-comings.  Its problems and l i m i t a t i o n s 4  with respect to equilibrium c r i t e r i a are discussed by Manhiem . It i s generally recognized however, that the i n d i r e c t approach has many advantages.  It allows the analyst to c a l i b r a t e the parameters of each  of the sub-models and run the models separately. This means that the process can be stopped at any time and examined. If the results are unreasonable, alterations can be made or the erroneous sub-model may be recalibrated and the process may  continue without necessarily s t a r t i n g from the beginning  again. Although direct models are t h e o r e t i c a l l y the best at s a t i s f y i n g equilibrium conditions, there are problems associated with them. Button"* discusses a number of d i r e c t approaches and came to the following general conclusions: 1.  the creation of a workable model has eluded the analyst;  2.  to date, results have shown wide divergences i n the parameters obtained ; • a consequence partly resulting from the assumptions  3.  no employed. satisfactory method has been devised to ensure that the  24  p r e d i c t i o n s s u p p l i e d by e x p l i c i t models f a l l w i t h i n t h e bounds of  what i s thought  intuitively  Given t h e s t a t e o f t h e a r t , i t appears is  possible.  that the s e q u e n t i a l i n d i r e c t  approach  t h e b e t t e r method t o use i f a p r a c t i c a l m o d e l l i n g system i s b e i n g  developed. Other advantages a r e o f f e r e d by t h e i n d i r e c t approach.  Figure 7 '  i l l u s t r a t e s t h e sequence o f s t e p s embodied w i t h i n the framework  developed.  T h i s sequence of s t e p s a l l o w s changes t o be i n t r o d u c e d a t any p o i n t i n t h e system. F o r example: i f t h e p a r k i n g p r i c e s a r e changed, then those changes would be i n t r o d u c e d t o t h e p a r k i n g a l l o c a t i o n s t e p . The system then through  proceeds  t h e sequence o f s t e p s i t e r a t i n g u n t i l e q u i l i b r i u m i s a t t a i n e d . The  n a t u r e o f the i n d i r e c t approach i m p l i e s t h a t t h e p a r k i n g a l l o c a t i o n initially  will  be made w i t h o u t knowing t h e c o n g e s t i o n l e v e l s a r i s i n g out o f any  changes i n c o n g e s t i o n . S i m i l a r l y , t h e mode c h o i c e w i l l  initially  be made  w i t h o u t knowledge o f t h e c o n g e s t i o n l e v e l s a r i s i n g out of p r i c e changes and subsequent mode s h i f t s . I t was h y p o t h e s i z e d t h a t t h e commuter makes d e c i s i o n s based  on p r i c e s  and l e v e l s o f c o n g e s t i o n e x p e r i e n c e d , n o t those a n t i c i p a t e d . I t i s u n l i k e l y t h a t p r i c e i n c r e a s e s would be a d v e r t i s e d and a l s o  , t h e commuter would n o t  t h i n k o f o r be capable of e s t i m a t i n g the e q u i l i b r i u m c o n g e s t i o n l e v e l  after  a p r i c e change. The i n i t i a l  charge  and  d e c i s i o n w i l l be based  on t h e new p a r k i n g  the o l d c o n g e s t i o n l e v e l s . Because of the l a g i n change o f c o n g e s t i o n  l e v e l s behind p r i c e changes t h e system may n o t proceed step b u t must proceed T h i s same concept the u s e r ' s response  through  t o e q u i l i b r i u m i n one  several steps.  i n v o l v i n g a change i n t h e t r a n s p o r t a t i o n system and  over time i s d i s c u s s e d by Hutchinson^.  The c o n t e x t o f  the d i s c u s s i o n i n h i s paper i s d i f f e r e n t than t h e context p r e s e n t e d  here.  FIGURE  7  FLOW CHART OF A SHORT RUN ANALYTICAL FRAMEWORK  "NETWORK DATA  NETWORK 1 GENERATION FOR TRANSIT, AUTO AND PEDESTRIAN  WALK TRAVEL TIME BETWEEN SELECTED ORIGINS AND DESTINATIONS  ASSIGNMENT' PASSENGERS TO TRANSIT  AUTO ASSIGNMENT  PARKING ALLOCATION  6  MODE SPLIT  EXISTING TRANSIT DEMAND  FEEDBACK REVISED TRANSIT DEMAND  EXISTING AUTO TRAVEL DEMAND EQUILIBRIUM 7 ALGORITHM CONVERGENCE TEST  FINISH  FEEDBACK REVISED AUTO DEMAND  26  It deals with the problem of c o n t r o l l i n g the response of commuters during the t r a n s i t i o n period to the i n s t a l l a t i o n of new  :  f a c i l i t i e s . Its s i g n i f i c a n -  ce to this paper i s : 1.  i t recognizes that there i s a transitory period  and;  2.  that decisions which lead to t r a v e l patterns are based on congestion l e v e l s during the transitory period.  A model which proceeds through several steps to a t t a i n a state of equilibrium may  i n actual fact be approximating the r e a l s i t u a t i o n . It must be noted  here that this model does not attempt to pin down the mechanism which • operates during the transitory period nor develop a function which accurately describes the approach to equilibrium. The purpose of this discussion i s simply to show that the i n d i r e c t approach to equilibrium may  be close to  the process which the system goes through to a t t a i n equilibrium. 3.2  The Modelling Framework An i n d i r e c t approach was  u t i l i z e d f o r the equilibrium model developed  i n this paper. The framework includes the following seven steps: 1.  Generate pedestrian, automobile and t r a n s i t networks.  2.  Determine walking times between selected o r i g i n s and destinations.  3.  Allocate automobiles to parking spaces so that walking and  parking  charges are traded o f f and the a v a i l a b i l i t y of space i s constrained. A.  A multipath p r o b a b i l i t y assignment of auto t r a f f i c to a network which interacts with the bus t r a f f i c .  5.  *~ J.-.  An all-or-nothing assignment of t r a n s i t users to a bus network which interacts with the automobile t r a f f i c .  6.  Determine the demand f o r each mode through a l o g i t model.  27  7.  An application of an equilibrium algorithm f o r fixed demand and a convergence test.  The d e t a i l s and assumptions embodied i n these steps w i l l be discussed l a t e r . System equilibrium i s achieved through the i t e r a t i o n of steps 2 through 7 and i s controlled by step 7. System equilibrium conditions are met by the feedback of the appropriate service and demand l e v e l s . Steps 4 and 5 are computations of equilibrium for the single class user of auto and transit  respectively.  Each of the steps 2 through 5 provide data to the mode s p l i t i n step 6. Computation of walk t r a v e l times was excluded from the i t e r a t i v e process because i t was thought that walk times would not be affected by changes i n the l e v e l of t r a f f i c . Figure 7 i l l u s t r a t e s the flow through the seven steps. This flow chart was not designed to i l l u s t r a t e the computer programs and . their linkages but to show the t h e o r e t i c a l form of the system. Table 2 demonstrates more c l e a r l y the u t i l i z a t i o n of demand and supply data by the models i n the system. The supply side i s divided into service attributes and l e v e l of service factors. The service attributes are parking charges, bus fares and frequency of bus service. The l e v e l of service factors are auto walk times, auto invehicle times, bus walk and wait times, and bus invehicle times. The models i n the table are l i s t e d i n the order of execution. By r e f e r r i n g to Table 2 and Figure 7 i t i s easy to trace through the process and determine where the data i s computed and u t i l i z e d . The exogenous demand data provided to the system i s i n the form of origin-destination t r i p s by car and by t r a n s i t . The parking a l l o c a t i o n model uses parking charges and auto walk times to transform the person 0-D t r i p s by auto into vehicle 0-D t r i p s . The process moves along to the vehicle assignment model u t i l i z i n g the vehicle origin-destination (0-D) compute the auto invehicle t r a v e l times and perform the vehicle  t r i p s to assignment.  TABLE 2  SYSTEM SUB-MODELS VERSUS LEVEL OF SERVICE AND SERVICE  1  SERVICE  MODEL  DEMANDS  parking allocation  person t r i p s by auto  vehicle assignment  vehicle 0-D trips  transit assignment  person 0-D t r i p s by t r a n s i t  mode split  person t r i p s by auto and transit  PARKING CHARGES  LEVEL OF SERVICE  ATTRIBUTES  BUS FARES  ATTRIBUTES  FREQUENCY OF SERVICE  AUTO WALK TIMES  AUTO INVEHICLE TIMES  BUS WALK & WAIT TIMES  BUS INVEHICLE TIMES  X  X  X  X  X  X  X  X  X  X  X  X  X  29  The v e h i c l e t r a v e l times a r e t r a n s l a t e d i n t o average speeds on the l i n k s which s e t the maximum speed f o r the buses. The t r a n s i t u t i l i z e s these maximum speeds, the frequency  assignment model  o f bus s e r v i c e and the t r a n s i t  o r i g i n - d e s t i n a t i o n demand to compute bus walk, w a i t and i n v e h i c l e times i n o r d e r t o perform  the t r a n s i t assignment. The mode s p l i t model i s the p i v o t  p o i n t o f the system. I t i s through  the mode s p l i t  that the s e r v i c e l e v e l s  computed by the p r e v i o u s i t e r a t i o n a r e t r a n s l a t e d i n t o new demands f o r t h e next  iteration.  In t h i s manner a l s o , a l l s e r v i c e l e v e l s a r e i m p l i c i t l y  r e p r e s e n t e d throughout  the system by the r e v i s e d demands.  W i t h i n the i t e r a t i v e p o r t i o n o f the framework, the commuter i s a l l o w e d the f o l l o w i n g c h o i c e s : ( i ) t r a n s i t or auto mode; ( i i ) any number o f paths i n e i t h e r mode; ( i i i ) w i t h i n the auto mode a t r a d e o f f between p a r k i n g c o s t s and w a l k i n g  times  . The i n c l u s i o n  of a p a r k i n g a l l o c a t i o n model o f f e r s more  d e t a i l e d i n f o r m a t i o n on t h e t r a d e o f f between w a l k i n g and p a r k i n g  charges.  T h i s t r a d e o f f has i m p l i c a t i o n s on both t h e assignment o f auto t r i p s i n the congested charges  C.B.D. and the c h o i c e between t r a n s i t and auto.  g e n e r a l l y induce a s h i f t  Increased  parking  t o p a r k i n g l o t s f u r t h e r from the p l a c e o f  work^. T h i s s h i f t may have the e f f e c t o f r e d u c i n g t r a f f i c flows i n the v i c i n i t y of the zone where the i n c r e a s e s were made. The p a r k i n g  allocation  model a l s o has an i n p u t t o the c h o i c e process between auto and t r a n s i t . In t h i s case i t i s i n c l u d e d i n the g e n e r a l i z e d c o s t o f auto t r a v e l v e h i c l e time, m a r g i n a l  o p e r a t i n g c o s t s , p a r k i n g c o s t s and w a l k i n g  compared w i t h the g e n e r a l i z e d c o s t of t r a n s i t  ( intime) and  ( i n v e h i c l e time, bus f a r e ,  w a l k i n g , w a i t i n g and t r a n s f e r t i m e s ) . I f the g e n e r a l i z e d c o s t o f auto  travel  ( i n c l u d i n g t r a d e - o f f s ) which t h e d r i v e r may choose t o make i s t o o h i g h , he w i l l choose t r a n s i t .  then  In summary, t h i s framework a l l o w s f o r a s h i f t o f  d r i v e r s t o d i f f e r e n t p a r k i n g l o t s or a s h i f t t o t r a n s i t .  30  FOOTNOTES  1.  L. A, Hoel. et a l "Latent Damand For Urban Transportation", Trans^ portation Research, I n s t i t u t e , ..Carnegie-Mellon, University of Pittsgurgh, Pennsylvania, 19.68, p. 215.  2.  I. G. Heggie, "Consumer Respeonse to Public Transport Improvements and Car Restraint: Some P r a c t i c a l Finding. Working Paper No. 2 (revised)", Transport Studies Unit/ University of Oxford, 1976, p. 29.  3.  M. L. Manhiem, " P r a c t i c a l Implications of Some Fundamental Properties of Travel Demand Models", Highway Research Record, 422., 1973, pp. 21 - 38.  4.  Ibid., pp. 23 - 24.  5.  K. J. Button, "The Use of Economics i n Urban Travel Demand Modelling: A Survey", Socio-Economic Planning Science, Vol. 10, 1975, p. 65.  6.  B. G. Hutchinson, "A Framework For Short-Run Urban Transport Policy Responses", A paper written for presentation at the Annual Meeting of the Roads and Transportation Association of Canada, Vancouver B.C., 1977, pp. 165 - 171.  7.  D. W. G i l l e n , "Effects of Changes i n Parking Prices and Urban • Restrictions on Urban Transport Demands and Congestion Levels", u University of Toronto - York University Joint Program i n Transportation, 1975, p. 20.  ?  31  CHAPTER 4 4.0  THE COMPUTER SYSTEM AND COMPONENTS Up  to t h i s point  i n the paper t h e d i s c u s s i o n has d e a l t w i t h t h e  t h e o r e t i c a l aspects of e q u i l i b r i u m , questions, and  i t s a p p l i c a t i o n to short-run  the approach t o m o d e l l i n g a t r a n s p o r t a t i o n  the general  policy  system i n e q u i l i b r i u m  s t r u c t u r e o f that m o d e l l i n g system. The f o l l o w i n g  discussion  deals with the a c t u a l construction  o f t h e m o d e l l i n g system and r e l a t e s t h e  choice  imbedded i n the system back t o t h e  of the models and f u n c t i o n s  theory. Two o p t i o n s  were open i n t h e development o f the computer system. The  whole system c o u l d have been developed from s c r a t c h o r a system which f u l f i l l e d p a r t o f , o r a l l of t h e requirements o f the study c o u l d have been utilized.  I f a p a r t i a l system was a v a i l a b l e i t c o u l d be m o d i f i e d  and adapted  where n e c e s s a r y . A transportation planning  model f o r d e t a i l e d t r a f f i c a n a l y s i s had been  developed by t h e U n i v e r s i t y o f B r i t i s h Columbia and t h e C i t y o f Vancouver"'". The  model was designed t o study t h e o p e r a t i o n a l problems o f peak hour  v e h i c u l a r commuter t r a f f i c . high  I t i s most a p p r o p r i a t e l y  a p p l i e d t o areas o f  t r a f f i c a c t i v i t y such as t h e c e n t r a l b u s i n e s s d i s t r i c t  of a metro-'. ..  p o l i t a n a r e a o r a r t e r i a l s t r e e t s of a region-wide network d u r i n g demand. The framework c o n s i s t s o f a p a r k i n g  a l l o c a t i o n model and a  p r o b a b i l i s t i c assignment model which c o n s i d e r s auto and t r a n s i t t r a f f i c . ments of t h i s paper. nor  the t r a n s i t  the r e q u i r e -  side of trip-making  t h e c h o i c e p r o c e s s between t h e auto and t r a n s i t modes. To meet t h e  requirements o f t h i s paper, a t r a n s i t assignment model, mode s p l i t and  multipath  the p h y s i c a l i n t e r a c t i o n r o f  T h i s methodology p a r t i a l l y f u l f i l l s  I t does not c o n s i d e r  peak  equilibrium algorithm  model  would have t o be added t o the U.B.C. framework.  32  Short range p o l i c i e s and t r a f f i c management programs are directed at, and generally affect only the operational service l e v e l s of automobile and transit networks. The U.B.C. framework addresses the auto side of this problem.Mt has been used by the City of Vancouver for t r a f f i c analysis i n the C.B.D.. To develop a methodology from scratch would have been a d u p l i cation of the U.B.C. work. It was  decided then, to enlarge upon the existing  framework by adding the three missing components mentioned above. The following i s a description of the U.B.C. framework. Each of i t s :. components i s described i n d e t a i l and the s u i t a b i l i t y i n an equilibrium context i s discussed. The modifications to this framework and the additional components are discussed as well. 4.1  Features and Components of The U.B.C. Framework The transportation model was  developed for the purpose of providing  detailed analyses of t r a f f i c movements over l o c a l i z e d t r a f f i c networks. In order to accurately model vehicle delays, the t r a n s i t and pedestrian t r a f f i c and their interaction with auto t r a f f i c was modelled as w e l l . The framework was  designed  to be applied-, i n an area of high t r a f f i c a c t i v i t y such as the  central business d i s t r i c t or the a r t e r i a l streets of a region-wide network during peak hours. The framework was  set up so that i t would f u l f i l l the following  criteria: 1.  Reproduce observed t r a f f i c patterns.  2.  Forecast new  t r a f f i c movements after changes i n the road network,  parking system or o f f i c e concentration. 3.  Be inexpensive and quick to use.  4.  The output should be i n a form which i s easy to use and understand by a t r a f f i c  engineer.  33  The degree to which the models meet these c r i t e r i a i s discussed by 2 Navin . The model was put together as a group of programs, each program designed  to work independently  or i n t e r a c t i v e l y with the others. Figure 8  shows a flow chart of the programs. The processing commences with the pedestrian and v e h i c l e network builders which are contained i n the program DEBUG. It searches for l o g i c a l errors i n the network and produces a plot of the vehicle network. It also outputs pedestrian t r a v e l times. The program TRANSIT performs a similar function i n that i t sets and produces a plot of the t r a n s i t network. These two network programs provide data to both the parking a l l o c a i t o n model TRANS and the vehicle assignment model STOCH. 4.2  Components of The U.B.C. Model As already stated, the program DEBUG generates the vehicle and pedes-:/  t r i a n networks, checks for errors and produces a plot of the vehicle network. It also computes the pedestrian walking times from parking l o t s to places of work and walk times to and from bus stops. The TRANSIT takes as input bus route information and the headways. It generates a t r a n s i t network and computes the volume of buses on the l i n k s which are supplied to the vehicle assignment model STOCH. The purpose and t h e o r e t i c a l aspects of the parking a l l o c a t i o n model TRANS and the t r a f f i c assignment model STOCH w i l l be discussed i n greater detail. 4.2.1  Addressing The Parking Problem Generally transportation studies which included the choice of two or  more modes parking costs have been lumped with automobile costs to create a single t o t a l cost v a r i a b l e . Parking services however, are a d i s t i n c t  34 F/G  UR  £•  8  F^OW  CHART OF rHE UB.C. COMP(/rFG  7  ll &os  PATA:  /PLOT  I  op  ///FA0WAV5 j IgQfjTF*. FTC./  VEHICLE AVO NFrWOKK  PEPEST/VIA/V JBullDEP  I JV£MH-l£ ~i L  1 WAVS/71  It&Uii  /  VEH/CIC. FRafsi  T/ME-  7 p/i/cE^  \loB  IfifiRK/fJc  t o r j  IOCATIOAIS '•S/ZE em  1  />ss OP/&>/YS  ICAJME-A/T ra  /or  Aoros  I//VAV5I Aiioc/ir/OfiJ OF TO PAPK/fi/G  &  I  ULL  F/GURE  9  FLOW  CHART  OF THE MOO/F/ED /Peoe^TFjfKtj  FRAME WORK.  I  FINISH  tUDiCAree  L  PATH  OP  ITERATION/  PArfit  PAoce^-5/A/c  NOTE  •  / fl /  HETWOXKJD M . I  '/tar or AU7O ' VOLU/4E& ofJ t./tjKS t /wrtKsecr/otss /  Poorrsl  IJTOPS  WALK  —"7 TO  IPA#K//VG  , 1  I f i o r OF rR>*K,,r  FfiAMertQRK.  OAI r u e Fi£t>r irefiaT/otj THE ex/sr/*/c DErlArVDS ARE USED. O/V $UBGEQaEAIT /XA<IA/VOS A / ? f REVISED AUTOMATICALLY AMD £0<JiLi/3f!'UM fiLGORlTHrt.  AUTO fiAJO T*A*/6IT ITEPAriOM% THESE py r u e MOPE SPLIT-  nu7odi iors  35  product or factor input from transportation services and are complementary 3 to auto use . Work that G i l l e n has done suggests that drivers w i l l c a p i t a l i z e on guaranteed parking spots, spread costs by carrying passengers, and trade 4 off parking costs and walking costs. Other methods of avoidance of increased parking charges are: taking a t a x i , r e l y i n g on family members for a chauffeured l i f t to work, parking i l l e g a l l y , and employee reimbursements . It can be seen that determining where drivers park i s a complex problem with many variables. In the l i g h t of these avoidance methods enumerated above, the old assumption that automobile costs r i s e i n equal proportion to the increased parking costs i s f a l s e . These reduced r e a l parking costs would have a s i g n i f i c a n t effect on mode s p l i t calculations. Also as mentioned i n Chapter 3 section 3.2 these avoidance techniques have effects on the assignment of vehicles to the network. These effects are f e l t i n the most congested part of the c i t y , the C.B.D.. From the discussion i t would appear then that to be consistent with equilibrium concepts i t i s necessary to include a model which would attempt to describe the processes above. In e f f e c t , i t s purpose would be to c o n t r i bute a better description of the service levels f o r the auto mode and a better description of demand levels on the links i n the C.B.D.. 4.2.2.  The Parking A l l o c a t i o n Model TRANS  It would be d i f f i c u l t to model a l l of the avoidance techniques mentioned. Some can be accounted f o r i n existing parking models while others cannot. S h i f t i n g to taxi mode, being chauffeured and parking i l l e g a l l y cannot be modelled. There i s not s u f f i c i e n t empirical data available to formulate descriptions of the mechanisms involved i n these types of behaviour. Within a parking a l l o c a t i o n framework, guaranteed parking spots, employee reimburse-  36  ments and the t r a d e o f f of p a r k i n g charges and w a l k i n g times can be addressed. W i t h i n the l a r g e r framework of the paper the problem o f c a r r y i n g passengers can be addressed through the l o g i t model. The p a r k i n g a l l o c a t i o n model used was purpose i n mind. F i r s t l y ,  i t may  designed with a two-fold  be used t o determine the r e d i s t r i b u t i o n  of p a r k i n g a f t e r a l t e r a t i o n s i n the o r g a n i z a t i o n , p r i c i n g and  structure  of the downtown p a r k i n g system. Secondly, i t p r o v i d e s o r i g i n and  destination  d a t a f o r the t r a f f i c assignment program. Given t h a t the f i n a l d e s t i n a t i o n of the commuter i s known the model uses a l i n e a r programming approach and o p t i m a l l y a s s i g n s v e h i c l e s t o p a r k i n g l o t s on an uncongested  network.  Optimal l o c a t i o n as d e f i n e d by the model t h e o r y i s the s e t o f l o c a t i o n s which minimizes the t o t a l c o s t f o r the system o f commuters g i v e n the c o n t r a i n t of p a r k i n g l o t c a p a c i t i e s ^ . The c o s t s to be minimized a r e the c o s t of p a r k i n g and t h a t of w a l k i n g . The v a l u e p l a c e d on w a l k i n g i s determined by the socio-economic s t a t u s of the worker. A p r o v i s i o n i s i n c l u d e d i n the model which takes i n t o account workers w i t h h i g h incomes  or workers  who  have t h e i r p a r k i n g f e e s s u b s i d i z e d or guaranteed. They a r e lumped i n t o an i n e l a s t i c component of the demand. The f u n c t i o n t o be minimized i s : ( . 0 ( i , g , k , l ) x (W(g,k,l) + C ( l ) )  12  i>g>k,l where 0 ( i , g , k , l ) = the number o f t r i p s  i n group g from t r a f f i c  source  i , - w i t h ' f i n a l d e s t i n a t i o n i n zone k and p a r k i n g i n zone W(g,k,l) C(l)  =  1.  = c o s t o f w a l k i n g time f o r group g from zone 1 t o k. p a r k i n g charges i n zone  1.  37  The constraints imposed on the system are; \~~  0(i,g,k,l) = T(g,k)  13  —  1,1  i,g,k,l)  14  S(l)  where T(g,k) i s the number of t r i p s i n group g whose f i n a l , :*.  destination  i s zone k, and S(l)  i s the parking capacity i n zone 1.  The output from TRANS consists of vehicle o r i g i n / destination information which i s used i n the t r a f f i c assignment program, -and :  costs which are used i n the l o g i t  parking and walking  model.  There are several drawbacks with t h i s model. As noted previously i t does not take into account a l l of the behaviour  associated with drivers  and parking costs, and i t performs the a l l o c a t i o n based on an uncongested network. The a l l o c a t i o n of "parkers" to f a c i l i t i e s i s based on the o v e r a l l optimizing c r i t e r i a rather than that of actual driver behaviour. It would seem that a behavioural model which allocates parkers to f a c i l i t i e s based on optimizing t h e i r i n d i v i d u a l benefits would be more reasonable. The data requirements and a more complex c a l i b r a t i o n of the parameters i s required i n the behavioural models. The model used i n t h i s framework was  selected  because i t was readily available and i t i s an adequate and accepted t o o l for determining parking a l l o c a t i o n . 4.2.3  An Equilibrium Model f o r Vehicle T r a f f i c A t r a f f i c assignment model i s a method of determining the equilibrium  flows of vehicles on a road network. There i s a hierarchy to the application  38  of equilibrium models. At the beginning of t h i s paper such a model was described which considered the interaction of variable socio-economic a c t i v i t i e s over a multimodal transportation network with associated variable demand l e v e l s and r e s u l t i n g l e v e l s of service. For the o v e r a l l short run thesis of this paper this general model was constrained  to one of fixed  demands, fixed socio-economic a c t i v i t i e s and a fixed multimodal transportat^ ion network. The l e v e l of service i s variable and the equilibrium model consists of the i n t e r a c t i o n of the demand levels and service l e v e l s of the auto and t r a n s i t modes. In order to determine the demand l e v e l s and service levels of the two modes an equilibrium model i s needed which describes the interaction of the demand and service levels on the paths i n the network for each mode. There are numerous approaches available f o r solving single-mode equilibrium problems. T r a f f i c assignment mathematical programming, algorithmic approaches with fixed demands, and algorithmic approaches with varying demands are available . The t r a f f i c assignment classes of solution have by f a r predominated the other classes i n actual application and i n number of variants. The following deficiences have been noted i n these approaches i n solving network equilibrium problems^: 1.  Link t r a v e l times have often been kept constant, thereby ignoring the existence of l i n k supply functions.  2.  Origin-destination t r i p s have often been kept constant thereby ignoring the existence of t r a v e l demand functions.  3.  The number of paths t r a v e l l e d between each o r i g i n and destination have often been limited to one, making i t impossible, normally, to s a t i s f y Wardrop's f i r s t p r i n c i p l e .  4.  The accuracy of the approaches as approximations of equilibrium  39  has not been determined.  ( T h i s i n c l u d e s both t h e i r  convergence  p r o p e r t i e s ( i f they i n v o l v e i t e r a t i o n s ) , and t h e i r expected - : : e r r o r s upon completion.) The D i a l S t o c h a s t i c Assignment  used i n the framework p r e s e n t e d i n t h i s  paper a v o i d s a l l except the l a s t o f the d e f i c i e n c i e s mentioned  above. The  l i n k t r a v e l times are a f u n c t i o n o f the demand on the l i n k s . The  origin-  d e s t i n a t i o n t r i p s are v a r i a b l e through the l o g i t model, ( i . e . auto  drivers  can s w i t c h t o the t r a n s i t mode) and more than one path i s c o n s i d e r e d . C r i t i c i s m s have been l e v e l e d at the D i a l model from o t h e r s o u r c e s however, when assembling a m o d e l l i n g framework more than t h e o r e t i c a l  8 9 c o n s i d e r a t i o n s must be taken i n t o account m o d e l l i n g methodology was  ' . P r o b a b l y no matter what  s e l e c t e d i t would be s u b j e c t to t h e o r e t i c a l  c r i t i c i s m . Models w i l l always be somewhat l e s s than r e a l i t y . The model s e l e c t i o n must be made w i t h i n a s e t of time and r e s o u r c e c o n s t r a i n t s  and  must perform adequately the n e c e s s a r y f u n c t i o n s i n o r d e r to s o l v e the problem. The D i a l model i s s i g n i f i c a n t l y b e t t e r than a l l - o r - n o t h i n g assignment  t e c h n i q u e s ^ . C o n v e r s e l y , i t i s not the b e s t t e c h n i q u e a v a i l a b l e .  I t performs the f u n c t i o n s which a r e needed to s o l v e the problem b e i n g addressed. I t has been used by the T r a f f i c E n g i n e e r i n g Department o f the C i t y of Vancouver  f o r o p e r a t i o n a l t r a f f i c a n a l y s i s , whether i t produces  r e s u l t s s u f f i c i e n t l y a c c u r a t e f o r the requirements of t h i s paper i s somet h i n g which w i l l 'have to be 4.2.4  determined.  The S t o c h a s t i c V e h i c u l a r Assignment  Model  The v e h i c l e network i s l o a d e d w i t h t r a f f i c u s i n g the p r o b a b i l i s t i c m u l t i p a t h approach developed by Dial"'""'". T r i p s are a s s i g n e d to e f f i c i e n t paths between o r i g i n and d e s t i n a t i o n p a i r s . u t i l i z i n g an a l g o r i t h m which  40  precludes the necessity of enumerating the paths. The D i a l method has the following f i v e basic s p e c i f i c a t i o n s : 1.  A l l reasonable paths between a given o r i g i n and destination have a non-zero p r o b a b i l i t y of use.  2.  A l l reasonable paths of equal length should have equal p r o b a b i l i t y of  3.  use.  When there are two or more reasonable paths of unequal length the shorter should have higher probability of use.  4.  The model's user should have some control over the path "diversion probabilities.  5.  The assignment algorithm should not e x p l i c i t l y enumerate a l l paths.  An e f f i c i e n t path i s defined as one which proceeds i n the d i r e c t i o n of the destination and does not  "back-track".  The d i s t r i b u t i o n of t r i p s along routes with d i f f e r e n t travel times i s assumed to be determined  according to the decreasing exponential function:  (•  exp (  where  t  e  t . )  _  ^  15  P  t r a v  . ^ time along an e f f i c i e n t path e  i s a model parameter which determines  the dispersion of  t r i p s along paths of d i f f e r e n t lengths.  4.2.5  Vehicle Delay There are two components to v e h i c l e delay: the delay of acceleration;:  and deceleration due to the random encounteriof t r a f f i c signals, and volume delay caused by interaction with other streams of t r a f f i c . Delay due to the interaction of the flow of t r a f f i c between intersections i s considered to be minor compared to the delay at intersections. In general the intersection  41  c o n s t i t u t e s the r e g i o n of minimum c a p a c i t y of the l i n k t h a t o n l y volume d e l a y s are c o n s i d e r e d  . I t was  due to the i n t e r a c t i o n of t r a f f i c  i s considered  i s addressed by u t i l i z i n g  The program a l l o w s  assumed  at i n t e r s e c t i o n s  i n the model. The i n t e r a c t i o n o f t r a n s i t and  t r a f f i c with v e h i c l a r t r a f f i c restraint  12  pedestrian  as w e l l . The>problem o f c a p a c i t y  an i n c r e m e n t a l  approach to assignment.  the a n a l y s t t o break the assignment p e r i o d i n t o a number  o f s m a l l e r assignment p e r i o d s .  I t a l s o a l l o w s him t o a s s i g n any combination  of p r o p o r t i o n of the v e h i c u l a r l o a d t o the s e t of s m a l l e r  assignment  periods. For the f i r s t  assignment p e r i o d , i t assumes t r a v e l times due t o f r e e  flow c o n d i t i o n s and f o r each subsequent assingnment i t uses t r a v e l times computed by the p r e v i o u s  iteration.  42 FOOTNOTES  1.  C. Fisk, "A Transportation Planning Model f o r Detailed T r a f f i c Analysis", Transportation Research Series Report No, 11, The University of B r i t i s h Columbia, Department of C i v i l Engineering, 1977.  2.  F. P. D.Navin, C. F i s k , '. "A Downtown T r a f f i c Management System", Prepared f o r the Canadian Transportation Research Form Annual Meeting, St. Andrews, New Brunswick, 1977, p.13.  3.  D. W. G i l l e n , "The E f f e c t s of Parking Costs on Mode Choice", Resaerch Paper No. 23, The Department of Economics, The University of Alberta, 1975, pp. 2 - 3.  4.  D. W. G i l l e n , " E f f e c t s of Changes i n Parking Prices and Urban R e s t r i c t i o n on Urban Transport Demands and Congestion Levels", University of TorontoYork U n i v e r s i t y , Joint Program i n Transportation, 1975, pp. 20 - 25.  5.  C. F i s k , op. c i t . , pp. 11 - 13.  6.  E. R. Ruiter, "Implementation of Operational Network Equilibrium Procedures", Transportation Research Board, 491., 1974, p. 43.  7.  Ibid.  8.  J . D. Murchland, M. A. F l o r i a n (ed.), "The Structure of Model Research", T r a f f i c Equilibrium Methods, Proceedings of the International Symposium at the University of Montreal, Springer-Verlag, New York 1976, p. 8.  9.  J . E. B u r r e l l , M. A. F l o r i a n (ed.), "Multiple Route Assignment: A Comparison of Two Methods", T r a f f i c Equilibrium Methods, Proceedings of the International Symposium at the University of Montreal, SpringerVerlag, -New York, 1976.  10.  R. B. D i a l , "A P r o b a b i l i s t i c Multipath T r a f f i c Assingment Model Which Obviates Path Enumeration", Transportation Research Vol. 5, 1970, pp. 84 - 85.  11.  I b i d . , pp.89 -  110.  12.  C. Fisk, op. c i t . , pp.  18 - 19.  CHAPTER 5 5.0  THE U.B.C. FRAMEWORK MODIFIED In  Chapter 4 a c h o i c e was made t o u t i l i z e t h e computer m o d e l l i n g system  developed a t U.B.C. I t p a r t i a l l y s a t i s f i e d t h e t h e o r e t i c a l  requirements  o u t l i n e d i n Chapters 2 and 3. The a d d i t i o n o f a t r a n s i t assignment mode s p l i t model and an e q u i l i b r i u m a l g o r i t h m complete  those r e q u i r e m e n t s .  T h i s c h a p t e r d e a l s w i t h t h e f u n c t i o n s , d e t a i l s and assumptions the  model,  imbedded i n  a d d i t i o n a l work. The t h r e e new models a r e a l l c o n t a i n e d i n t h e program c a l l e d BUS.  I t i s executed a f t e r t h e v e h i c l e assignment  program; r e f e r t o F i g u r e 10.  There f o l l o w s a b r i e f d e s c r i p t i o n of the f u n c t i o n s o f t h e program. The t h e o r e t i c a l b a s i s o f these f u n c t i o n s a r e d e s c r i b e d i n g r e a t e r d e t a i l  later  i n t h i s c h a p t e r . The t r a n s i t assignment model a s s i g n s t r a n s i t t r i p makers t o bus r o u t e s . Walking, w a i t i n g and t r a n s f e r times a r e c o n s i d e r e d . The i n v e h i c l e bus times a r e a f u n c t i o n o f the number of s t o p s t h e bus makes, t h e number of persons l o a d i n g and o f f - l o a d i n g and t h e average speed o f the stream o f t r a f f i c .  The t r a f f i c  speeds a r e computed by the v e h i c l e  assign-  ment model and a r e s u p p l i e d to t h e t r a n s i t program. The mode s p l i t model takes t h e s e r v i c e l e v e l s computed by t h e p a r k i n g a l l o c a t i o n model, v e h i c l e assignment model and t r a n s i t assignment model and computes an e s t i m a t e d mode s p l i t . The e q u i l i b r i u m a l g o r i t h m computes a t r i a l mode s p l i t on the mode s p l i t  form t h e p r e v i o u s i t e r a t i o n and t h e one j u s t  based  calculated.  A new s e t o f o r i g i n s and d e s t i n a t i o n s f o r both modes a r e computed u s i n g the  mode s p l i t  p r o b a b i l i t i e s . The new auto 0/D i s i n p u t back i n t o t h e park-  ing  a l l o c a t i o n model and t h e t r a n s i t 0/D back i n t o the t r a n s i t  assignment  model. B e f o r e t h e i t e r a t i v e p r o c e s s i s begun a g a i n w i t h t h e p a r k i n g a l l o c a t i o n model, a t e s t i s made t o determine the change i n t r a v e l  times  Figure 10 fa) PlAiN  FLOV  fxocgsiAl  PEAO  IN  DATA  •DO I- 1, P OF  (6) SUBROUTINE  INITIALIZE TATi TABIC  CHART OF PROGRAM BUS  M/NPTH.  SuG/KrOr/N£  VECTOIS Tir?ies*9999?  ICALLPO  FPcMP,INPTU  oPl&l/VS  OO  <ZQNT/AIUP  r-^-DO  L-J,  oo/^Puie.  TIME S c f A D BUS $ TIME. 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FAvrt TO  SO\RCH  AIL INVEHICLE TP.AVEL PA rues MOST BE PE/AOVEO PPOM //sr eepope WFLK LINKS ARE CONSIDPPPQ .  A/NT) pJi//ipiO//\ Cv/AoLATIVE TRAVEL T/NJC IT/ LIST  FFONI  RETUAN.  ChTr.  LINKS/CUAIotflllVt TO NopE /Uro  yes ViPO  TAirtS^eAS ^TOP&  \A0&  [coA*fPA#£  6US  TO spur SA,seo aN/OAiA IOMAVTEO JBY T//E. COP Ae A/T /IfSGATlCll/  Cap,PJlE A TPIAL SPLIT BA^eoo/F DLL~> ANO A/ElAA SPLITS  LINES,  'w/|r/y THOSE. STo/eei? ATirpe PPiVIOUQ  imp  A?FAO OLD /AOOE SPLIT CO/JPUTFO BY PAE/IOL& ITEAATIQ/S F~fi?or* SFGUENTfAL PILE  '(.OMPOTE. AUTO ANO TP^NSTE OFpffiNOS CIS/N& TRIAL Aiooe. SPLIT.  TP/AL AIOA>E TO TA£  s E <Z PENT  our i3o&  STATISTICS LWE?,  [P//IEA. TIMB  slew TN TAPE  THA/EC TA&LE.  jyes \AQ/Q  I 5 T E P 3 I  TPAN3  SmRE A.NfKS  fiOS STOPS TO firJAL DESTIEIATION Mr///'/ PAECET WAir rime  OETCMINEL Fo* LiNKS  INAIK  rime.  •  ADO To Bot, sroP w * f S ANO ANTTA Cu/ficiT\ri'it TAAVf-L. T'rtFS t LINKS ifjTo rue L/sr.  AiOOL THE AAOPE-  CPNTIHUC  rVP/re \SPLITi WRITE, Aon  ECHO epplErlQ^  FE At 7H1E\  &OSLsNE5 PASS'NG  cunyieNr  BPS  AlETuAA/  OA/ THE.  =s TQP_  OcrefiMI/'E 7/A-/F 0Y ON me  i At  • PILE  L/NCS A'-K/li  7/>A:JPLTP>P:*/SrT i/AiK'i>.  CoA't6>N£ TAP Ac/70 \LlNXB &ETIA'FP/I E?CF> SroP$ INTO 6US A/A/KS  Ls-erppivii/vp, fivePAcjz SPFF-A) OP rt.-e SOS OVPP IT'S RocJTE. T 7?ET1}P~N~~  \CoikPaia /NVEHiciF. 1 r x k VBL TIKI e ON i3id\  \PAMOVE  SPLITS  A~WD TAP. AU7 O WfilCN 7AH BiTi* SAL6C7FA) r o s e PXiA/rp/} L/SPS .  PATHS  CONTINUE  AIPITE WOPE AC"? PAIS SFA/T \/TEAIP. TIO/-'  #DFS7iNfiriat&-  Srr?P PerefiMi»e WALK T>ME POA BUS \ WNTEH Tines i \iNrri rue LIST  CALL T/AJ DETERMINES /NVEMCLE. TRMEL TIME £ F/flA/SAF^ rime.  CAJTSPUT  '•—I  J  /Jo ^JXANSFEG  v/;;i7£ PSIESEA/T ~jQun//ey TIME ro s eo UF/ATIA, L FIL E.  W/R/rC  J-  CcwPor£ THE Afvf~<(!(g. OF PSrSzCtJCrtA?. rAAYE£l.liVc, /SAlWfLAl  P1/NP77/ A S S / /  CALL. CA//  Oo  p u p r  Zl  45  between i t e r a t i o n s .  I f the change i s below a predetermined l e v e l then t h e  p r o c e s s i s stopped.  5.1  An E q u i l i b r i u m Model F o r T r a n s i t B e f o r e p r o c e e d i n g t o t h e d i s c u s s i o n o f t h e theory  assignment i t may be u s e f u l t o d i s c u s s  b e h i n d the t r a n s i t  t h e term i t s e l f . When one speaks o f  v e h i c l e assignment one t h i n k s o f the assignment o f automobiles t o a v e h i c l e network. However, i n t h i s paper the term " t r a n s i t assignment" r e f e r s t o t h e assignment of t r a n s i t passengers n o t o n l y t o t h e t r a n s i t network b u t t o w a l k i n g l i n k s t o and from the network. T r a n s i t passengers a r e a s s i g n e d  t o paths on an a l l - o r - n o t h i n g b a s i s  w i t h o u t a c a p a c i t y r e s t r a i n t f u n c t i o n . T r a v e l times arecidetermined loaded not  on t h e  network for use i n t h e l o g i t model. These congested t r a v e l times a r e  used t o a f f e c t t h e assignment of people t o r o u t e s The  i n t h e t r a n s i t network.  use o f an a l l - o r - n o t h i n g assignment t e c h n i q u e may be q u e s t i o n e d  from an e q u i l i b r i u m p o i n t o f view. S i m i l a r l y , t h e l a c k o f a c a p a c i t y r e s t r a i n t f u n c t i o n may a l s o be q u e s t i o n e d . H e r e i n why  t h i s may be a c c e p t a b l e  can o n l y  appears a d i s c u s s i o n on  from a t h e o r e t i c a l p o i n t o f view. I t s v a l i d i t y  f u l l y be a c c e p t e d when these i d e a s a r e t e s t e d .  A t h e o r e t i c a l e q u i l i b r i u m assignment can be d e s c r i b e d  as a convex type  of f u n c t i o n . The s o l u t i o n i s l o c a t e d a t t h e minimum p o i n t of t h e f u n c t i o n . No u s e r can reduce h i s g e n e r a l i z e d  t r a v e l l i n g c o s t s by a l t e r i n g h i s  route.  T h i s s o l u t i o n has t h e c h a r a c t e r i s t i c t h a t each p a t h which i s used between any  p a i r o f p o i n t s has a c o s t which i s no g r e a t e r  than any other  path  between those p o i n t s . When d e a l i n g w i t h automobile assignment t h e n a t u r e o f t h e road network allows  f o r a c h o i c e between m u l t i p l e paths which have s i m i l a r c o s t s between  a g i v e n 0-D p a i r . A l l - o r - n o t h i n g assignment o f auto t r i p s a s s i g n s  a l l the  46  t r i p s t o paths which may be o n l y a few seconds s h o r t e r than p a r a l l e l paths. In c e r t a i n a p p l i c a t i o n s t h i s l e a d s t o u n r e a l i s t i c The  assignments.  t r a n s i t network d i f f e r s from the automobile network. The s e r v i c e  i s provided  on a c o a r s e r g r i d and hence t h e r e a r e fewer p a r a l l e l paths  w i t h s i m i l a r c o s t s . The p o s s i b i l i t y o f m u l t i p l e path use between any g i v e n 0-D p a i r i s reduced due t o the l i k e l i h o o d o f g r e a t e r d i f f e r e n c e s i n c o s t s between p a r a l l e l p a t h s . S i m i l a r l y , because t h e r e a r e g r e a t e r d i f f e r e n c e s i n c o s t s between p a r a l l e l paths t h e c o n s i d e r a t i o n o f c a p a c i t y r e s t r a i n t i s not  l i k e l y t o have a s i g n i f i c a n t e f f e c t on r o u t e c h o i c e i n t r a n s i t . Congest-  i o n i s l i k e l y t o i n c r e a s e t r a v e l times but i s n o t l i k e l y  to s i g n i f i c a n t l y  a l t e r t h e advantages of one route over another. Where the c o n g e s t i o n  effects  may have more impact i s i n the mode c h o i c e . I t i s f o r t h i s reason t h a t t r a v e l times on t h e f u l l y loaded  t r a n s i t network a r e computed.  More important i n t h i s paper i s the d e s c r i p t i o n of t r a n s i t The  travel  g e n e r a l i z e d c o s t s of t r a n s i t t r a v e l a r e more complex than auto  times.  travel.  Whereas t h e auto d r i v e r attempts t o minimize i n v e h i c l e t r a v e l time the t r a n s i t r i d e r deals with minimization and  i n v e h i c l e times.  I t i s widely  o f walk times, w a i t i n g , t r a n s f e r r i n g  accepted  t h a t the commuter v a l u e s  these components d i f f e r e n t l y . A l s o , the c a l c u l a t i o n o f t r a v e l times  a l l of relies  on d i f f e r e n t d e l a y functions. The problem i n t r a n s i t e q u i l i b r i u m s o l u t i o n s i s one o f a c c u r a t e l y d e s c r i b i n g the g e n e r a l i z e d c o s t s o f t r a n s i t An  travel.  attempt has been made i n t h i s paper t o address t h a t problem.  5.2  The A l l - O r - N o t h i n g  Assignment Model  This s e c t i o n deals with  a d e s c r i p t i o n of the computer model developed  f o r t h i s paper'.' F i g u r e 10 i s a d e s c r i p t i v e flow c h a r t o f the f u n c t i o n s performed by the program. There i s a main program and f i v e subprograms.  •  47  The  g e n e r a l f u n c t i o n s of the subprograms a r e : MINPTH:  Determines the minimum path  ASSN:  A s s i g n s passengers t o the minimum paths  SPLIT:  Performs the mode s p l i t  TIM:  Computes the t r a n s i t t r a v e l time on the l i n k s  BNET:  P r e p a r a t i o n of v e c t o r s f o r p r i n t - o u t of s e l e c t e d bus  and some of the e q u i l i b r i u m  functions  lines.  The purpose of t h i s i s t o i l l u s t r a t e the o r g a n i z a t i o n of the program. However, w i t h i n t h i s o r g a n i z a t i o n f i v e important f u n c t i o n s are performed. They a r e : (1) minimum path s e a r c h ; (2) t r a n s i t t r a v e l time computations; (3) assignment o f passengers t o the minimum p a t h ; (4) mode s p l i t and  computation  (5) e q u i l i b r i u m computations. Each of these f u n c t i o n s w i l l be addressed  w i t h r e f e r e n c e s t o the f l o w c h a r t . The main program reads d a t a , c o n t r o l s the s u b r o u t i n e s and w r i t e s out the  final results;  refer  are  a l s o w r i t t e n out:  to F i g u r e 1 0 ( a ) . The f o l l o w i n g e q u i l i b r i u m  statistics  - The average of the c u r r e n t and p r e v i o u s t r a v e l times from each  origin  to a l l d e s t i n a t i o n s by c a r and bus. - The number of people t r a v e l l i n g from each o r i g i n to a l l d e s t i n a t i o n s by each mode and the s p l i t . - The average change i n mode s p l i t between  iterations.  - The s t a t i s t i c s of bus usage such as numbers o f passengers on the bus, numbers a t the stop and the average speed of the bus.  5.3  Minimum Path A l g o r i t h m T h i s a l g o r i t h m f i n d s a minimum p a t h from the t r a v e l l e r ' s o r i g i n to h i s  d e s t i n a t i o n . T h i s i n c l u d e s w a l k i n g t o , and w a i t i n g f o r the bus, the  riding  bus, any t r a n s f e r r i n g n e c e s s a r y , and the f i n a l walk t o the d e s t i n a t i o n .  The a l g o r i t h m has two b a s i c f u n c t i o n s : a path g e n e r a t o r which generates  48  paths  and s t o r e s them i n a l i s t ,  the minimum paths from the l i s t '.(b)  and a minimum p a t h f i n d e r which removes and  s t o r e s them i n a t r e e t a b l e . F i g u r e 10  i l l u s t r a t e s the f l o w of the p r o c e s s i n g i n the s u b r o u t i n e MINPTH.  The path g e n e r a t i o n p r o c e s s i s broken i n t o t h r e e segments: 1.  the walk t o , and w a i t at the bus  2.  the t r i p on the bus,  3.  the walk to the  The  first  stop;  including transfers  and  destination.  segment u t i l i z e s the walk l i n k s and  by the program DEBUG and the o r i g i n s and  t r a v e l times  computed  destinations associated with  those l i n k s . A s e t of p e d e s t r i a n o r i g i n s and d e s t i n a t i o n s and a maximum walk time are d e s i g n a t e d by the a n a l y s t . The program DEBUG f i n d s nodes which are w i t h i n the maximum w a l k i n g  time from the o r i g i n s . The  generator s e l e c t s d e s t i n a t i o n nodes which are bus  stops and  r o u t i n e TIM  The  t o compute the w a i t time f o r the bus.  bus" s t o p s and  the nodes a t the bus  destination path  c a l l s the sub-  t o t a l time to the  stop are s t o r e d i n a  list.  The minimum path f i n d e r s e l e c t s the path to the bus stop w i t h  the  minimum t r a v e l time, s t o r e s i t i n a minimum path t r e e t a b l e and removes i t from the l i s t .  The paths to o t h e r bus stops remain i n the l i s t  to be  l a t e r on. A f u l l e r e x p l a n a t i o n of the minimum path f i n d e r w i l l be  used  given  later. The  second  segment of the path g e n e r a t o r uses the bus  stop node found  by the minimum path s e a r c h as an o r i g i n f o r l i n k s p r o c e e d i n g away from i t . The  l i n k c o n s i d e r e d must have bus  l i n e s on them. In t h i s path g e n e r a t i n g  p r o c e s s , the program takes t r a n s i t network d a t a from the program TRANSIT and superimposes i t upon the v e h i c l e network d a t a from program STOCH. In adding l i n k s t o the l i s t it  i s o n l y important  i t i s not important which bus  t h a t t h e r e i s a bus  line i s available,  l i n e a l o n g t h a t l i n k . Delays  due  49  to  t r a n s f e r r i n g and t r a v e l times a l o n g the l i n k s are computed i n s u b r o u t i n e  TIM.  The passenger  i s a l l o w e d t o make as many t r a n s f e r s as n e c e s s a r y to  reach h i s d e s t i n a t i o n . However, once on the bus he must remain on i t u n t i l he reaches h i s f i n a l bus stop d e s t i n a t i o n . He cannot get o f f , walk and reboard the bus. I f the d e s t i n a t i o n o f the new  l i n k i n segment 2 i s a bus  stop then the program c o n t r o l moves i n t o t h e t h i r d  segment.  The f u n c t i o n of the t h i r d segment of the path g e n e r a t o r i s much the same as the f i r s t .  In t h i s case d e s t i n a t i o n nodes and the c u m u l a t i v e  times i n c l u d i n g w a l k i n g are added to the l i s t .  A g a i n o n l y those d e s t i n a t i o n s  which are w i t h i n a maximum w a l k i n g time from the bus At  travel  stop are c o n s i d e r e d .  t h i s p o i n t , c o n t r o l of the program moves t o the minimum path  finder.  C o n t r o l can move t o the minimum p a t h f i n d e r a f t e r the second segment i f none of the d e s t i n a t i o n s of the new  l i n k s are bus s t o p s . C o n t r o l always  moves to the p a t h f i n d e r a f t e r the f i r s t of  the path g e n e r a t o r i s t o add new  and t h i r d segments. The  function  l i n k s to the paths and s t o r e the  d e s t i n a t i o n nodes of those l i n k s a l o n g w i t h the c u m u l a t i v e t r a v e l time to the nodes i n the l i s t .  In g e n e r a l , t h e r e are t h r e e s t e p s to the minimum  path f i n d e r f u n c t i o n . The  first  step i s t o f i n d the node w i t h the minimum  cumulative t r a v e l time i n the l i s t  and remove i t from the l i s t .  The  second  s t e p i s t o compare t h a t t r a v e l time w i t h what i s a l r e a d y s t o r e d f o r t h a t node i n the t r e e t a b l e . ( The t r e e t a b l e i n i t i a l l y number. ) I f the time from the l i s t  i s set to a very  i s l e s s than t h a t a l r e a d y s t o r e d  the o l d t r a v e l time i s r e p l a c e d by the new  large then  v a l u e . The f i n a l s t e p i s t o  r e t u r n c o n t r o l o f the program t o the second segment of the p a t h g e n e r a t o r . Here the d e s t i n a t i o n node o f the t r e e t a b l e becomes the o r i g i n node f o r the g e n e r a t i o n of new  l i n k s . I f the time from the l i s t  i s l a r g e r than what  i s a l r e a d y s t o r e d i n the t r e e t a b l e then c o n t r o l gees back to step one o f  50  the  minimum path f i n d e r . The p r o c e s s i s complete when no more l i n k s  be added to the paths and when the l i s t walk l i n k s the  i s emptied.  T r a n s i t T r a v e l Time All  In o r d e r to p r e v e n t  from becoming i n t e r m e d i a t e l i n k s , a l l nodes which a r e p a r t of  bus network must be removed from the l i s t  5.4  can  first.  Computation  components of t r a n s i t  travel  time are computed i n s u b r o u t i n e TIM  except the walk times t o and from the bus l i n e s . The t o t a l t r a n s i t  travel  time i s d e s c r i b e d m a t h e m a t i c a l l y i n t h i s manner: TT = f(WT) + f(W) + f ( I V ) + f (TF)  + f(WF)  where  time  TT = t o t a l t r a n s i t  travel  WT  = walk time t o the bus  W  = w a i t time and time to l o a d  IV = i n v e h i c l e TF = t r a n s f e r  16  time time  WF = walk time from the bus stop The f i r s t  l i n k i s a walk from the o r i g i n  t o any number of bus s t o p s  which are w i t h i n a maximum walk time s e t by the a n a l y s t . These walk times (as  a l r e a d y mentioned) a r e i n p u t s from the program DEBUG. Another p o r t i o n of the walk l i n k i s the w a i t time and t h i s i s comprised  of w a i t i n g f o r the bus to a r r i v e under  and w a i t i n g f o r the bus to l o a d and get  way. The amount of time spent w a i t i n g f o r the bus i s g i v e n by the f o l l o w i n g  equation. W = 0.13/( + 2 . 8 where  17  W = w a i t time /*  = mean headway ( i n t h i s program the o f f i c i a l headway i s used)  51  This equation was developed by J o l l i f f e and Hutchinson""" from data 2 collected by Lynam and E v e r a l l . It relates average observed waiting time to headway during peak t r a f f i c periods. It was noted that the equation broke 3 down at low headways . For this reason, wait times of bus l i n e s with headways less than 7 minutes were assumed to be half the headway. Where there", i s more than one bus l i n e available going i n the desired d i r e c t i o n the headway i s assumed to be the average of the l i n e s available. The loading time i s given by the number of persons times a  per person  boarding time set by the analyst. Off-loading i s assumed to take half as long as loading. If there are more than twice as' many persons off-loading as loading, then off-loading time determines the stopped time. When the walk paths to the available bus stops have been determined, invehicle t r a v e l times on the bus are computed. The bus routes are fixed on the road network and the headways are predetermined. The basic coding for the two networks i s the same. Bus t r a f f i c flows over road l i n k s designated for use by the transit network program TRANSIT. The bus l i n e s which t r a v e l on the l i n k s are used for headway calculations for transfers and so that u t i l i z a t i o n of p a r t i c u l a r l i n e s may be tabulated. Invehicle t r a v e l time on any l i n k i s given by the set of equations: IV = ST + ADT + RT  18  where IV = invehicle time ST = stopped time ADT = acceleration deceleration time RT = running time at average v e l o c i t y Stopped time i s given by the number of stops to pick up passengers and the  number of passengers boarding the bus. The acceleration/deceleration  52  time i s as f o l l o w s : ADT  = ( V / ACC  + V / DEC  ) x N  —  19  where V = average v e l o c i t y of the stream of ACC,  DEC  = a c c e l e r a t i o n / d e c e l e r a t i o n of the  N = number of bus The  traffic  stops a l o n g the  bus  link  average v e l o c i t y i s an i n p u t from the a u t o m o b i l e assignment program  STOCH. The  a c c e l e r a t i o n / d e c e l e r a t i o n parameters of the bus  a n a l y s t . The  running  are s e t by  the  time a t average v e l o c i t y i s t h e time t a k e n t o c o v e r  the d i s t a n c e of the l i n k not c o v e r e d by a c c e l e r a t i n g or d e c e l e r a t i n g . STOCH program c o n s i d e r s a t i o n and  The  i n t e r s e c t i o n delay, cornering v e l o c i t i e s , acceler-  d e c e l e r a t i o n of the v e h i c l e s from s t o p s . The  time t o t r a v e r s e a  l i n k i s g i v e n by the above mentioned components. R a t h e r than b r e a k i n g down i n t o t h e i r s e p a r a t e components f o r the t r a n s i t c o m p u t a t i o n s ,  them  the  average v e l o c i t y i s s i m p l y t a k e n t o be the d i s t a n c e of the l i n k d i v i d e d by the t r a v e l t i m e on t h a t l i n k . The the headways of the bus  t r a n s f e r time i s h a l f the average of  l i n e s g o i n g i n the d e s i r e d d i r e c t i o n up t o a  maximum of 5 m i n u t e s . T h i s assumption was  made on the b a s i s t h a t  during  r u s h - h o u r , buses w i t h headways g r e a t e r than 10 minutes w i l l meet a t t r a n s f e r p o i n t s so t h a t the maximum w a i t time i s 10 minutes and  the average w a i t  i s 5 m i n u t e s . There d i d not appear t o be much work done i n the f i e l d s t u d i e s of t r a n s f e r time. However, t h e s e assumptions seem t o be f o r rush-hour c o n d i t i o n s . As t h e r e are u s u a l l y a number of bus  time  of  reasonable lines  t r a v e l l i n g a l o n g the same r o u t e i t i s not p o s s i b l e t o d e t e r m i n e e x a c t l y w h i c h bus  l i n e the passenger i s on. The  t h a t a passenger has  o n l y way  t h a t the program knows :  t r a n s f e r r e d i s when none of the bus  l i n k are the same as on the p r e v i o u s  l i n e s on the p r e s e n t  l i n k . When t h i s o c c u r s the t r a n s f e r  53  t r a v e l time f u n c t i o n i s a c t i v a t e d . The minimum t r a n s i t paths a r e computed t w i c e . T h i s i s done so t h a t t h e l o a d i n g o f the system w i t h passengers can be taken i n t o account. The program computes t h e minimum paths from o r i g i n s t o a l l d e s t i n a t i o n s and a s s i g n s passengers t o t h e paths s e q u e n t i a l l y . I t i s not a simultaneous p r o c e s s whereby a l l minimum paths a r e computed and the passengers a r e loaded on t o the of  system a t once. Because passengers from more than one o r i g i n share p a r t s the same path,- the paths computed f i r s t  and a s s i g n e d f i r s t  a r e under-',  loaded and hence have low t r a v e l times. To overcome t h i s problem the minimum paths a r e computed once a g a i n w i t h the system f u l l y order to r e f l e c t  loaded. In  the d e l a y s t o passengers due t o o v e r l o a d e d buses  the w a i t  times a r e c o n s i d e r e d t o be double the headway i f the bus i s f u l l . To r e c a p i t u l a t e the t r a v e l times f o r t r a n s i t a r e comprised of walk times, w a i t t i m e s , t r a n s f e r times and i n v e h i c l e times. The i n v e h i c l e are  times  s e n s i t i v e t o the number o f automobiles s h a r i n g the same l i n k s and the  number o f p e o p l e u s i n g the bus system.  5.5  Assignment  o f Passengers t o the Network  ~  The s u b r o u t i n e ASSN a s s i g n s the passengers t o t h e minimum paths computed by MINPTH. Two assignments  a r e c a r r i e d o u t . T r a n s i t u s e r s a r e a s s i g n e d to  the  bus s t o p s as w e l l as t o the buses. T h e r e f o r e , i t i s p o s s i b l e t o determine  the  number o f p e o p l e w a i t i n g a t t h e stops and the number o f persons on the  bus. T h i s d a t a i s used i n the second e x e c u t i o n of MINPTH (see F i g u r e 10(a)) to  account f o r the d e l a y due t o p e o p l e b o a r d i n g and e x i t i n g the bus. The  i n s t a n t a n e o u s demand on a minimum p a t h i s g i v e n by t h e e q u a t i o n : ID = D x H / ( P x N B )  . 20  54  where ID = i n s t a n t a n e o u s demand a l o n g the e n t i r e r o u t e H = headway o f the bus D = t o t a l demand over the assignment  period  P = the l e n g t h o f the p e r i o d NB = number o f bus l i n e s on l i n k Instantaneous demand i s the average number o f p e o p l e a t a bus stop w a i t i n g f o r one bus l i n e or one bus a t any i n s t a n t throughout the assignment p e r i o d . T h i s i s computed f o r each o f t h e minimum p a t h s . Where these-paths share the same bus l i n e s , stops and t r a n s f e r p o i n t s , the i n s t a n t a n e o u s demands f o r the i n d i v i d u a l paths a r e added t o g e t h e r t o produce  the t o t a l  i n s t a n t a n e o u s demand on the system. One of the d i f f i c u l t i e s encountered i n the assignment  p r o c e s s i s t h a t where t h e r e i s more than one bus l i n e  serving  a bus stop o r a r o u t e i t i s not p o s s i b l e t o determine which one the passenger w i l l use. To overcome t h i s , where a number o f bus l i n e s a r e a v a i l a b l e the passengers a r e l o a d e d e q u a l l y among them. S i m i l a r l y , the average of the headways o f the buses a r e used t o compute w a i t times.  5.6  The Mode Choice Model The subprogram SPLIT c o n t a i n i n g the l o g i t model i s s e t up so t h a t w i t h  some a l t e r a t i o n s any c a l i b r a t e d l o g i t model may be used. The g e n e r a l i z e d c o s t components made a v a i l a b l e t o the mode s p l i t model a r e t h e : i n v e h i c l e t r a v e l times f o r b o t h modes, the w a l k i n g time f o r the auto mode, the p a r k i n g c o s t s , the d i s t a n c e t r a v e l l e d by c a r , and the out o f v e h i c l e t r a v e l  time  f o r bus u s e r s . The out-of-bus t r a v e l times i n c l u d e w a l k i n g , w a i t i n g and t r a n s f e r times. A l o g i t model a l r e a d y developed and c a l i b r a t e d by D. W. G i l l e n was  55  selected and put into the program f o r demonstration purposes'*. I f a study was being done i t would be necessary to c o l l e c t data and calibrate a l o g i t model to the p a r t i c u l a r c i t y being studied. In the model given below G(x) i s a : function of the choice variable and P  £  i s the probability of choosing  the auto mode. The form of the model i s : G(x) = -1.57 + 1.27TT/TC + .095FT/FC + .391 AGE - .81SEX + .233 SS + .129 Y - .615 EPC P  =  G e  (  x  )  /  (l  +  e  G ( x )  )  21 22  c where TT/TC =. r a t i o of door to door t r a v e l times f o r t r a n s i t and car respectively FT/FC = r a t i o of modal running costs AGE  = the age variable; AGE = 1 i f the user i s between 20 and 55, otherwise AGE = 0  SEX  = the sex variable, male = 0 •,- female = 1  SS  = s o c i a l status variable, SS = 1 i f the i n d i v i d u a l i s a middle manager or higher, otherwise SS = 0  Y  = gross income of the i n d i v i d u a l i n thousands of dollars  EPC  = the i n c l u s i v e parking price associated with choosing the auto mode f o r a given t r i p  P  c  = probability of taking the car  Since the demonstration network and a l l of the input data were fabricated, the variables of the l o g i t model were reduced to those l e v e l  s  of service factors and service attributes produced by the modelling system. If a f u l l scale study were being performed more s o c i a l factors could be included i n the analysis. The following simplifying assumptions were made about the input data to the l o g i t model. The modal cost of t r a n s i t was  56  assumed to be 35 cents and that of auto to be 10 cents per mile driven  '<  (1964'dollars). Although the program has the c a p a b i l i t y of handling three d i f f e r e n t socio-economic  groups, only one was used. A l l persons  travelling  to work were assumed to be between 20 and 55. F i f t y percent of the population was  assumed to be male, the other f i f t y percent female. S i m i l a r l y ,  fiftyi  percent of a l l C.B.D. employees were considered to be middle managers or higher and the remaining f i f t y percent were considered to be other types of workers. The average gross income of C.B.D. employees was assumed to be $5,000 (1964 d o l l a r s ) . Given these assumptions G i l l e n ' s equation then becomes: G(x) = -.83 + 1.27  TT/TC + .095(.35/MILES x .08) - .615EPC  23  It should be noted that this model was developed using data from the Metropolitan Toronto Regional Transportation Study (MARTS) done i n 1964. The parameters of the model are most appropriate to that year and place. It i s thought however, that f o r the purposes of demonstration  the above  equation w i l l y i e l d results which are responsive to changes i n t r a v e l times and parking costs.  5.7  A System Equilibrium Algorithm The transportation model presented i n this paper embodies three  equilibrium models ;.. one for each of the two modes and one for the two modes combined. The equilibrium of the two modes by themselves i s determined through assignment methods. The v a l i d i t y and assumptions of these methods have been discussed. The global equilibrium of the system (both modes combined) i s solved using an equilibrium algorithm. A general equilibrium algorithm f o r the single mode was suggested by Ruiter^. The equilibrium model, here follows the procedural framework outlined i n h i s paper and i s set  out as follows:  1.  Develop an i n i t i a l network s o l u t i o n S.  2.  Determine t h e b e s t d i r e c t i o n i n w h i c h t o p r o c e e d t o o b t a i n a new trial  solution.  3.  Develop a t r i a l  solution.  4.  O b t a i n a new s o l u t i o n .  5.  Determine whether S i s a s a t i s f a c t o r y f i n a l s o l u t i o n . I f i t i s n o t r e t u r n t o s t e p 2.  The i n i t i a l i z a t i o n  c o n s i s t s o f e x e c u t i n g a l l o f t h e s t e p s shown i n  F i g u r e 9. T h i s s e r v e s a f o u r f o l d purpose: (1) I t performs t h e i n i t i a l i z a t i o n and produces an i n i t i a l network s o l u t i o n .  (2) I t a l l o w s t h e a n a l y s t t o  determine whether t h e model i s a c c u r a t e i n p r e d i c t i n g t h e c u r r e n t  situation.  (3) R a t h e r than s t a r t i n g o f f t h e p r o c e s s w i t h f r e e f l o w s e r v i c e l e v e l s corresponding  t o z e r o f l o w c o n d i t i o n s , t h e network i s a l r e a d y l o a d e d .  This  reduces t h e number o f i t e r a t i o n s needed t o approach e q u i l i b r i u m a t t h e new p a r k i n g c o s t s . (4) I t t a b u l a t e s and s t o r e s t h e c o s t b e n e f i t f a c t o r s such as t r a v e l t i m e s , t o t a l d i s t a n c e t r a v e l l e d e t c . f o r comparison w i t h t h e c o n d i t i o n s o f t h e t r a n s p o r t a t i o n system under t h e new p o l i c y . A f t e r the i n i t i a l i z a t i o n process  i s complete t h e d i r e c t i o n f o r t h e  t r i a l s o l u t i o n and a new s o l u t i o n i s developed. The i n i t i a l i z a t i o n  computes  the mode s p l i t f o r t h e e x i s t i n g s i t u a t i o n and s t o r e s i t i n a f i l e f o r l a t e r use; r e f e r t o F i g u r e 10;Cei)v-. The new p a r k i n g charges a r e i n t r o d u c e d a t t h e p a r k i n g a l l o c a t i o n s t e p . The v e h i c l e and t r a n s i t assignment s t e p s a r e executed  and then t h e mode s p l i t s t e p i s executed.  The s i g n o f t h e d i f f e r e n c e  between t h e o l d mode s p l i t and t h e new mode s p l i t c a l c u l a t i o n s i n d i c a t e s the d i r e c t i o n o f t h e new s o l u t i o n . The t r i a l s o l u t i o n i s d e t e r m i n e d as a f u n c t i o n / o f t h e o l d s o l u t i o n , t h e d i r e c t i o n o f t h e new mode s p l i t , and t h e d i f f e r e n c e between t h e new and o l d mode s p l i t s .  I t i s n o t p o s s i b l e t o use t h e new mode s p l i t as t h e t r i a l  58  s o l u t i o n f o r t h e next i t e r a t i o n because overestimate the s o l u t i o n ( i . e . the  i n congested systems  on subsequent  s o l u t i o n r e v e r s e s d i r e c t i o n ) , The t r i a l  i t tends t o  i t e r a t i o n s , the d i r e c t i o n of  s o l u t i o n i s obtained i n t h i s  manner: M  When  *E M  When  M where the  Q  T  ^  Q  =  .5  M  0  +  <: =  M  0  -  ( M  N "  V  <;  24  .5 M  Q  + (1 - M ) Q  (MJJ - M )  25  Q  M = the auto mode s p l i t .computed by e q u a t i o n 2 2 and  subscripts  N = new 0 = old T = trial  The t r i a l mode s p l i t in  i s used t o determine t h e t r a n s i t and auto demands  t h e n e x t • i t e r a t i o n . The l e v e l o f s e r v i c e r e s u l t i n g from these demands i s  used t o determine a new mode s p l i t the  ( s t e p 4) and the t r i a l mode s p l i t on  p r e v i o u s i t e r a t i o n becomes t h e o l d mode s p l i t .  chosen as the moderator  because  The o l d mode, s p l i t was  i t was found t h a t i t worked w e l l .  A documents the work done t o determine t h i s  Appendix  finding.  The p r o c e s s c o n t i n u e s u n t i l t h e system converges. The convergence  test  (step 5) simply i n d i c a t e s t h e p e r c e n t change i n t r a v e l times from one i t e r a t i o n t o the next. S i n c e the i t e r a t i v e p r o c e s s i s i n the c o n t r o l o f the a n a l y s t i t can be h a l t e d a c c o r d i n g t o the judgement o f the a n a l y s t . In  summary, the e f f e c t s o f a p o l i c y change i n the t r a n s p o r t a t i o n  system a r e determined by e x e c u t i n g t h e computer models i n t h e f o l l o w i n g manner. The programs a r e r u n f i r s t w i t h c u r r e n t data and p o l i c i e s . The reason f o r t h i s i s o u t l i n e d above. The a n a l y s t then a l t e r s the p o l i c y v a r i a b l e i n the a p p r o p r i a t e program and commences the i t e r a t i v e p r o c e s s .  59  I f changes i n p a r k i n g charges were b e i n g examined, then the a n a l y s t would a l t e r the p a r k i n g c o s t s i n the p a r k i n g a l l o c a t i o n model and run t h a t program. Next, the v e h i c l e assignment program, and the ensueing programs i n the i t e r a t i v e p r o c e s s would be executed u n t i l the convergence c r i t e r i a were met.  FOOTNOTES  J. K, J o l l i f f e and T. P, Hutchinson, "A Behavioural Explanation of the Association Between Bus and Passenger A r r i v a l s at a Bus Stop", Transportation Science No. 3 Vol. 9, 1975, p. 280. D. A. Lynam and P. F. E v e r a i l , "Public Transport Journey Times i n London", Transport and Road Research Laboratory, LR. 413, 1971. J o l l i f f e and Hutchinson, op. c i t . pp. 279 - 280. D. W. G i l l e n , "Effects of Changes i n Parking Prices and Urban R e s t r i c t ion on Urban Transport Demands and Congestion Levels", University of Toronto - York University, Joint Program i n Transportation, 1975 pp. 28 - 35. E. R. Ruiter, "Implementation of Operational Network Equilibrium Procedures", Transportation Research Board 491, 1974, pp. 45 - 48.  61  CHAPTER 6 6.0  AN APPLICATION OF THE MODELLING SYSTEM The previous chapters discussed the t h e o r e t i c a l aspects of an e q u i l i -  brium model and the approach to constructing the model. The following sections delve into f i v e topics. The f i r s t discusses the network used f o r the demonstration. The second enumerates the capabi-"' l i t i e s of the t r a n s i t program. The t h i r d traces an example through the modelling process to obtain equilibrium. The fourth section i s concerned with the problems and anomalies encountered  i n the example problem. The  f i f t h and f i n a l topic deals with an example of how for  the system could be used  analyzing a short run policy question. Throughout this analysis the reasonableness of the results w i l l be  discussed. "Reasonable" i n this case implies: (1) any changes i n service levels or parking costs w i l l result i n s h i f t s of demand i n the appropriate direction and (2) that the changes i n demand w i l l be i n proportion to the change i n l e v e l of service and vice versa. 6.1  A Demonstration  Using A Small Network  In the development of a computer modelling framework, i t i s important to determine whether i t produces reasonable results before an application of the model i s made to a r e a l world problem. After the model has been shown .t'o meet these - c r i t e r i a there follows a stage where i t must be shown to be p r a c t i c a l , r e l i a b l e and economical"'". These c r i t e r i a are important i n s a t i s f y i n g the users' needs and must be defined by the p o t e n t i a l user. The purpose of this demonstration i s to determine whether the model produces reasonable r e s u l t s . The task of determining r e l i a b i l i t y and costs w i l l be l e f t c t o -.others..'  i ~ ~  o:  . -  i  goo.'  F/GURLZ  11  A  DEMONSTRATION  NETWORK  LEGENDi Bos  STOPS  ZOM£  005  LINES  TRAFFIC DIRECTION"-  PARKING  LOTS  Cy\//s/oA/—.  —-  63  A small network was  developed for the purposes of demonstration i n  which (see Figure 11) there are 4 parking l o t s , 4 bus l i n e s , and 8 d i f f e r e n t streets l a i d out on a grid. The east-west streets are 800 feet apart and the north-south streets 1000  feet apart. The network i s divided into 4 zones  with a parking l o t and entrance to the network i n each zone. The network i s intended to represent a C.B.D. with a r e s t r i c t e d number of access points. Due  to the fact that i t i s such -a small network some modifications  were made to the mode s p l i t model to make the input parameters more consistent with the choice s i t u a t i o n faced by the downtown commuter. It was assumed that car drivers had already driven an average of 5.6 miles to a r r i v e at the C.B.D. and had spent 20 minutes i n t h e i r cars. S i m i l a r l y i t was  assumed that the bus passenger had already spent 26 minutes on the bus.  The travel times and distances computed by the programs for each mode i n the C.B.D. would be added to these figures and input to the mode s p l i t model. In determining  the acceptability of the r e s u l t s , the assumptions  l i s t e d above and the size of the network should be kept i n mind. Some u n r e a l i s t i c a l l y large delays were obtained at the entry points and the parking l o t s . It was  thought that 'tehis was  due to the size of, and  configuration of the network. The effect of the large delays on the results w i l l be discussed l a t e r . The stochastic assignment model has been applied 2 to the C.B.D. of Vancouver and produced reasonable results . An origin-destination matrix for each of the modes - auto and t r a n s i t was  generated by t r i a l and error so that the network would be congested.  Several steps were involved i n the t r i a l and error process: (1)  Headways for the bus routes were selected.  (2)  The capacity of the parking l o t s and the prices charged were selected.  64  (3)  The demand l e v e l s for auto and t r a n s i t were selected.  (4)  The framework was run u n t i l the system had reached equilibrium.  (5)  The average speed f o r the automobiles on the network was used as an indicator of a congested network.  (6)  Steps one to f i v e were repeated u n t i l a reasonable l e v e l of congestion was attained (average automobile speeds less than 10 mph).  The demonstration was divided into three parts: (1) an i l l u s t r a t i o n of the c a p a b i l i t i e s of the transit program, (2) an i l l u s t r a t i o n of the equilibrium process and (3) an analysis of a short run p o l i c y question. In the f i r s t two, the differences induced i n the system by s p e c i f i c price changes were examined.  For example when demonstrating the c a p a b i l i t i e s of  the t r a n s i t program, the effects on detailed aspects of the transportation system were examined when a uniform increase of $1.00 was applied to a l l parking l o t s .  S i m i l a r l y the equilibrium process was examined by increasing  the prices on three l o t s by 2bi and the f i n a l l o t by 50^. This d i f f e r e n t i a l increase served to highlight important points i n the i t e r a t i v e process of obtaining equilibrium.  F i n a l l y the analysis of a short run p o l i c y question  entailed determining the aggregate effects on the transportation system due  to incremental price increases on one parking l o t only and incremental  price increases on a l l parking  lots.  A l l of these price changes mentioned above are referred to as p o l i c i e s . They are considered  to f a l l into two categories:  (1) s p e c i f i c changes of  prices on parking lots which occur once only, and (2) incremental changes of prices on parking lots which are applied several times.  The former are  referred to with alphabetic notation such as p o l i c y A, B, C, etc. and the l a t t e r with numeric notation such as policy 1, 2, etc.  65  6.2  C a p a b i l i t i e s o f The T r a n s i t Program  The f e a t u r e s and c a p a b i l i t i e s o f the p a r k i n g a l l o c a t i o n model and the. 3  v e h i c l e s t o c h a s t i c assignment model a r e w e l l documented by F i s k assignment model i s backed up w i t h an e x t e n s i v e g r a p h i c a l system and may  .  ,  The  V  ^ % ^  "  presentation  be used w i t h the m o d i f i e d framework f o r a n a l y s i s .  The expanded p o r t i o n of t h i s framework which now s i d e of t r a v e l can be o p e r a t e d i n two modes. examine the o p e r a t i o n o f the e x i s t i n g w i t h the automobile network.  i n c l u d e s the  transit  I t i s p o s s i b l e to a n a l y t i c a l l y  t r a n s i t system  i n a limited  interaction  On the o t h e r hand, i t i s p o s s i b l e to examine  s h o r t - r u n p l a n n i n g q u e s t i o n s where the a n a l y s i s i n v o l v e s a f u l l of  '  both the automobile network and  the t r a n s i t network.  Limited  interaction interaction  i m p l i e s u t i l i z i n g average v e h i c l e speeds on the roads t o determine maximum speed o f the buses.  An o p e r a t i o n a l examination might  the  entail deter-  m i n i n g the l o a d i n g of the buses, f i n d i n g out where people get on and o f f the  bus, d e t e r m i n i n g the paths passengers f o l l o w through the t r a n s i t  etc..  No  system  i t e r a t i o n of the m o d e l l i n g system would be n e c e s s a r y to perform  t h i s type of study. Full  i n t e r a c t i o n i m p l i e s the i n c l u s i o n of both the e f f e c t s of the  p h y s i c a l i n t e r a c t i o n o f the two modes and the i n t e r a c t i o n o f the demand f o r the  two modes.  A s h o r t - r u n p l a n n i n g examination might  the  e f f e c t of i n c r e a s e d bus f r e q u e n c i e s o r p a r k i n g charges on  r i d e r s h i p and g e n e r a l c o n g e s t i o n .  include determining transit  I t would be n e c e s s a r y to put the  frame-  work through s e v e r a l i t e r a t i o n s f o r t h i s type of a n a l y s i s . I t i s p o s s i b l e to o b t a i n the f o l l o w i n g i n f o r m a t i o n from the model:  transit  66  (1)  The minimum t r a n s i t path from any t r a n s i t o r i g i n to any destination.  This includes the invehicle travel time,  excess travel time, the number of passengers on the bus at any point i n the path, the bus l i n e s taken and transfer points. (2)  Equilibrium data which includes the auto invehicle travel time for the previous and current i t e r a t i o n , the invehicle t r a v e l time for the bus f o r the current i t e r a t i o n , and the mode s p l i t from each o r i g i n to a l l destinations.  (3)  The bus l i n e s t a t i s t i c s which include the number of persons on the bus and waiting at the stops, the time to travel from bus stop to bus stop which includes stopped time, the t o t a l time to run the route (one way) and the average speed over the route.  Two parking p o l i c i e s were tested i n order to show the c a p a b i l i t i e s of the transit program. 2(a).  They are p o l i c i e s A and B and are shown i n Table  The price difference between these p o l i c i e s i s $1.00 on a l l parking  lots.  TABLE 2(a)  PARKING POLICIES USED TO ILLUSTRATE THE PROGRAM CAPABILITIES AND  PARKING ZONE POLICY  THE EQUILIBRIUM PROCESS  1  2  A  2.00  2.00  2.50  1.50  B  3.00  3.00  3.50  2.50  C  1.50  1.50  1.25;  1.00  D  1.75  1.75  2.25  1.25  E  1.25  1.25  1.50  .75  F  1.50  1.50  1.75  1.00  ALL VALUES ARE IN DOLLARS  3  4  Tables 3, 4, and 5 show the data output f o r the test.  The minimum path  print-out allows the analyst to trace the path of a t r a n s i t user through any part of the system.  The effects of any changes i n the system on a  p a r t i c u l a r origin-destination pair can be e a s i l y detected.  Table 3(a)  shows a minimum path print-out from the 3rd Street entrance to 4th Avenue. This p a r t i c u l a r minimum path i s associated with parking p r i c i n g policy A. The t o t a l travel time i s 671 seconds or 11.1 minutes with % minute taken to transfer.  Since i n this case the destination point i s at a bus stop  and the bus l i n e i s a through l i n e (the people are already on the bus before i t enters the study area), the out-of-vehicle travel time i s low. As the bus enters the study area at 3rd Street there are 17 persons on the bus. At the stop at 1st Avenue and 3rd Street the passengers change from bus l i n e 3 to bus l i n e 1.  Also at that bus stop passengers transferred from  bus l i n e 1 to bus l i n e 3 to set the t o t a l departing : on bus l i n e 3 at 41 passengers.  The t o t a l on bus l i n e 1 departing • from the same bus stop i s 20.  Table 3(b) shows the same minimum path print-out under policy B which i s $1.00 greater on a l l l o t s than under policy A. on the t r a n s i t travel time on this p a r t i c u l a r path.  This has a profound effect I t i s now 388 seconds  or 6.4 minutes almost half of the time under policy A.  The price increase  also has the effect of increasing the number of riders on the bus to a maximum of 49. Table 4(a) and 4(b) show average t r a v e l times from the given i n t e r sections to a l l destinations for both the automobile and bus mode.  Note  this i s d i f f e r e n t from Tables 3(a) and 3(b) which give the travel time for an individual using the bus between a s p e c i f i c o r i g i n and destination. A comparison of Table 4(a) and 4(b) show that i n general the average travel times are reduced by half between policy A and B.  Both modes are effected  in the same manner indicating that the bus speeds are tied to the general l e v e l of congestion.  MINIMUM TRANSIT PATH DATA TABLE 3 (a)  PARKING PRICE POLICY A  t o t a l t r a v e l time (sees) 671. transfer, wait and walk time (sees)  PERSONS ON THE BUS  INTERSECTION  4th 4th 4th 3rd 2nd 1st  AVENUE AVENUE AVENUE AVENUE AVENUE AVENUE  TABLE 3 ( b )  4th 3rd 3rd 3rd 3rd 3rd  30.  STREET STREET STREET STREET STREET STREET  0. 11. 7. 7. 20. 41. 17.  INTERSECTION  NOTE:  1 1 1 1 1 3 3  PARKING PRICE POLICY B  t o t a l t r a v e l time (sees) 388. transfer, wait and walk time (sees)  4th 4th 4th 3rd 2nd 1st  BUS LINES AT THE NODE  AVENUE AVENUE AVENUE AVENUE AVENUE AVENUE  4th 3rd 3rd 3rd 3rd 3rd  30.  PERSONS ON THE BUS  STREET STREET STREET STREET STREET STREET  0. 13. 8. 8. 24. 49. 20.  BUS LINES AT THE NODE  1 1 1 1 1 3 3  Policy B i s a $1.00 increase i n parking prices on a l l parking l o  69  Page 69 omitted in numbering  70  TRAVEL TIMES FROM THE GIVEN INTERSECTION TO ALL DESTINATIONS  TABLE 4(a)  PARKING PRICING POLICY A  AUTO INTERSECTION  CURRENT TRAVEL TIME  BUS PREVIOUS TRAVEL TIME  IN VEHICLE TRAVEL TIME  EXCESS TRAVEL TIME  3rd STREET  4.5  4.5  9.2  0.7  4th AVENUE  4.4  4.4  4.4  3.9  1st AVENUE  3.6  3.7  6.1  0.7  3rd AVENUE  3.4  3.6  3.0  2.6  TABLE 4(b)  PARKING POLICY B  BUS  AUTO INTERSECTION  CURRENT TRAVEL TIME  PREVIOUS TRAVEL TIME  IN VEHICLE TRAVEL TIME  EXCESS TRAVEL TIME  3rd STREET  2.1  2.3  4.5  0.7  4th AVENUE  3.3  3.7  4.2  3.9  1st AVENUE  2.6  2.6  5.8  0.7  3rd AVENUE  2.3  2.1  3.1  2.6  NOTE:  P o l i c y B i s a $1.00 i n c r e a s e i n p a r k i n g p r i c e s on a l l p a r k i n g  lots  71 CAR AND BUS SPLITS FOR THE GIVEN INTERSECTION TO ALL DESTINATIONS TABLE 5(a)  PARKING POLICY A  INTERSECTION  PERSONS BY CAR  PERSONS BY BUS  AUTO SPLIT*  947.  1126.  .457  4th AVENUE  1038.  1084.  .489  1st AVENUE  986.  1285.  .434  3rd AVENUE  918.  1102.  .454  PERSONS BY BUS  AUTO SPLIT  3rd STREET  TABLE 5(b)  PARKING POLICY B  INTERSECTION  PERSONS BY CAR  3rd STREET  677.  1396.  .327  4th AVENUE  828.  1294.  .390  1st AVENUE  744.  1527.  .328  3rd AVENUE  -726.  1294.  .359  *  Auto s p l i t i s the proportion of tripmakers t r a v e l l i n g by car  NOTE:  Policy B i s a $1.00 increase i n parking prices on a l l parking lots  72  These results are not unreasonable given the nature of the network being used for demonstration.  The magnitude of the r e s u l t s , however, cannot  be construed as general indications of what might occur i n a c i t y where a l l parking prices were raised $1.00. Looking at Table 4(a), i t can be seen that normally travel by bus takes longer than by car.  Also, there was l i t t l e change i n the travel time  between the current i t e r a t i o n and the previous i t e r a t i o n .  This i s used as  quick check to determine whether the equilibrium process has converged or not.  Since the number of i t e r a t i o n s i s controlled manually, judgement i s  used to decide whether to terminate the process.  In this case the d i f f -  erences were considered i n s u f f i c i e n t to warrant any further i t e r a t i o n s . The bus l i n e s t a t i s t i c s shown i n Table 6(a) and 6(b) allow the analyst to determine the effects of any changes on any p a r t i c u l a r bus l i n e .  It i s  possible to determine where the maximum load point i s , the load p r o f i l e , the links of greatest delay and the average speed of the bus.  The $1.00  increase i n parking data also has an effect on bus operation.  For example,  the average speed of the bus almost doubles from 5.6 mph to 10.2 mph and the maximum number of people on the bus increases from 41 to 49. To r e i t e r a t e , the program provides information about the passenger's t r i p through the system, equilibrium s t a t i s t i c s which are indicators of the general state of the system and detailed information about the bus routes through the system.  6.3  An I l l u s t r a t i o n of the Equilibrium Process The following i s an example i l l u s t r a t i n g the process whereby equilibrium  of the system i s obtained after a change i n parking prices.  The purposes of  this test i s to show that a change i n parking a l l o c a t i o n has an effect on the outcome of the equilibrium state, and also, to trace the process through  73  to e q u i l i b r i u m .  The change i n p r i c i n g i s as shown i n T a b l e 2(a) under  p o l i c i e s C and D.  I n p o l i c y D, a l l p r i c e s  which i s r a i s e d 50c.  The d i f f e r e n t i a l  a r e r a i s e d 25<: except zone 3  increase  i n p a r k i n g p r i c e s was  chosen f o r d e m o n s t r a t i o n because when the p r i c e s a r e u n i f o r m l y there a r e no s i g n i f i c a n t changes i n the a l l o c a t i o n of cars The  o n l y changes that o c c u r a r e i n the mode s p l i t  ment.  D i f f e r e n t i a l p r i c e increases  increased  to p a r k i n g  and the v e h i c u l a r  result i n substantial  lots.  assign-  changes i n  p a r k i n g a l l o c a t i o n i n the case chosen. B e f o r e going s t r a i g h t i n t o the example, the theory behind the e q u i l ibrium  a l g o r i t h m g i v e n i n Chapter 5 s e c t i o n  5.7 w i l l be r e s t a t e d  example w i l l be e x p l a i n e d w i t h r e f e r e n c e s to the t h e o r y . framework f o r e q u i l i b r i u m  and the  The t h e o r e t i c a l  i s s e t out as f o l l o w s .  1.  Develop an i n i t i a l network s o l u t i o n S.  2.  Determine the b e s t d i r e c t i o n i n which t o proceed to o b t a i n a new t r i a l  solution.  3.  Develop a t r i a l  4.  O b t a i n a new s o l u t i o n .  5.  Determine whether S i s a s a t i s f a c t o r y f i n a l s o l u t i o n . i s not,  Recall  that  return  solution.  to step 2.  there are several  i t e r a t i o n s required  a f t e r a p a r k i n g p r i c e change i s made. make up one i t e r a t i o n .  If i t  After  Recall also  that  to o b t a i n several  equilibrium programs  the i n i t i a l network s o l u t i o n has been developed  subsequent i t e r a t i o n s c o n s i s t o f the e x e c u t i o n o f the p a r k i n g a l l o c a t i o n model (TRANS), v e h i c u l a r  assignment model (STOCH), and the t r a n s i t assignment-  mode s p l i t - e q u i l i b r i u m a l g o r i t h m model  (BUS).  BUS STATISTICS FOR BUSLINE! NUMBER 3 TABLE 6(a)  PARKING PRICING POLICY NUMBER A  headway = 1. minute b u s l i n e number = 3 b u s l i n e name = Georgia the average speed of the bus i s 5.6 mph. BUS STOP INTERSECTION PEOPLE ON THE BUS  1st 2nd 3rd 3rd  AVENUE AVENUE AVENUE AVENUE  NOTE:  3rd STREET 3rd STREET 2nd STREET 1st STREET  17. 41. 11. 13. 0.  17. 18. 0. 0. 0.  6.2 2.3 1.6 0.7 10.7  PEOPLE AT THE STOP  LINK, TIME & TOTAL TIME  BUS LINES AT THE STOP 0 3 3 3 2  3  3  PARKING PRICING POLICY NUMBER  headway = 1. minute b u s l i n e number = 3 b u s l i n e name = Georgia the average speed of the bus i s 10.2 mph. BUS STOP INTERSECTION PEOPLE ON THE BUS  AVENUE AVENUE AVENUE AVENUE  NOTE:  LINK, TIME & TOTAL TIME  TIMES ARE IN MINUTES  TABLE 6(b)  1st 2nd 3rd 3rd  PEOPLE AT THE STOP  3rd STREET 3rd STREET 2nd STREET 1st STREET  20. 49. 12. 15. 0.  20. 22. 0. 0. 0.  P o l i c y B i s a $1.00 increase on a l l parking l o t s  1.3 2.4  1.5 0.7 5.9  BUS LINES AT THE STOP 0 3 3 3 2  3  3  75  TABLE 7 (a)  AVERAGE TRAVEL TIMES FROM GIVEN INTERSECTIONS TO ALL DESTINATIONS FOR EACH ITERATION BETWEEN POLICY C AND D NOTE: The p r i c e increase i s 50c on parking l o t 3, 25c on a l l others  \  ITERATION NO.  1st MIN.  2nd MIN.  3rd MIN.  4 th MIN.  5th MIN.  3rd STREET  8.3  7.1  5.0  6.5  6.0  4th AVENUE  6.1  5  -9  5.6  5.9  4.7  1st AVENUE  6.1  5.0  4.4  4.5  4.5  3rd AVENUE  4.7  4.8  4.0  4.0  3.8  INTERSECTION  TABLE  \  7(b)  \.  AVERAGE AUTO MODE SPLIT FROM GIVEN INTERSECTIONS TO ALL DESTINATIONS FOR EACH ITERATION BETWEEN POLICY C AND D  ITERATION \. NO.  1st  2nd  3rd  4 th  5th  3rd STREET  .492  .478  .487  .481  .480  4th AVENUE  .566  .539  .515  .503  .513  1st AVENUE  .496  .483  .475  .475  .476  3rd AVENUE  .506  .478  .477  .477  .480  INTER-X. SECTION  * TIMES ARE IN MINUTES  76  TABLE 8  TRANSITION PARKING ALLOCATIONS FOR EACH ITERATION BETWEEN POLICY C AND D NOTE:  The p r i c e i n c r e a s e i s 50c on p a r k i n g l o t s , 25c on a l l others.  (a)  first  iteration  \ . parking \zone work zone  2  1  3  4  >v ^ \ 1  1315  «  1250  2  207  3  1243  4  191  (b)  second  1250  iteration  parking work zone  \  1  zone  2  1  v  4  1312  1250  2  4  Persons a r r i v i n g  206  1252  3  *  3  188  a t the p a r k i n g l o t  1250  77  TABLE 8 (cont'd)  (c)  TRANSITION PARKING ALLOCATIONS FOR EACH ITERATION BETWEEN POLICY C AND D  third  parking \zone work zone 1  iteration  1  2  3  4  1213 1250  2  166 1192  3 .  1250  175  4  (d)  fourth i t e r a t i o n  parking N . zone work zone I  1  2  3  1250  137  4  1211  2  3  1172  i /  4  158  1250  78 TABLE  8(cont'd)  TRANSITION PARKING ALLOCATIONS FOR EACH ITERATION BETWEEN POLICY C AND D  (e)  f i f t h iteration  parking ^v. zone work zone >v  1  1  3  4  1192  2  1250  3 4  2  127  1171 145  1250  79 The program BUS i s the l a s t program of the i t e r a t i o n to be executed. The output of BUS i s examined to determine whether another i t e r a t i o n should be undertaken or not.  I f the changes i n the auto travel times, or changes  i n the auto mode s p l i t between i t e r a t i o n s are small, then an equilibrium solution has been obtained and the i t e r a t i v e process i s stopped.  Table  7(a) and 7(b) show the travel times and auto mode s p l i t s f o r the i t e r a t i o n s between p o l i c i e s C and D. The f i r s t i t e r a t i o n travel times and mode s p l i t s shown i n Tables 7(a) and 7(b) are the conditions associated with the equilibrium C.  (see Table 2(a)).  with the same p o l i c y . S.  state of policy  Table 8(a) shows the parking a l l o c a t i o n associated The f i r s t i t e r a t i o n i s the i n i t i a l network solution  The second i t e r a t i o n commences when the parking price changes are made  and the parking a l l o c a t i o n model produces the parking configuration Table 8(b).  shown i n  The vehicle assignment model i s run and then the t r a n s i t  assignment mode s p l i t model i s run. The second i t e r a t i o n results of these two models are shown i n Tables 7(a) and 7(b).  The running of the three  models i n this order correspond with the process of determining the best direction i n which to proceed to obtain a new t r i a l solution, the second step i n the framework set out above. t r a n s i t mode s p l i t program, BUS.  The third step i s imbedded i n the  I t takes the i n i t i a l network solution S  (the mode s p l i t s associated with that solution), compares them to the one just found and develops a t r i a l solution using equations 24 or 25 from Chapter 5 section 5.7. The t r i a l mode s p l i t i s used to compute auto and t r a n s i t demands f o r the next i t e r a t i o n .  The average travel time and mode  s p l i t displayed i n Tables 7(a) and 7(b) i s used to determine whether the solution i s satisfactory or not.  I f i t i s not (and generally i t i s not  80  s a t i s f a c t o r y a f t e r the second i t e r a t i o n ) , the p r o c e s s r e t u r n s to s t e p 2. The newly computed auto and t r a n s i t demands a r e used i n the next of  the models.  parking p r i c e s .  iteration  The same s t e p s a r e f o l l o w e d through w i t h o u t changing the T h i s a l l o w s the mode s p l i t ,  f i g u r a t i o n s to converge.  t r a v e l times and p a r k i n g con-  The f i n a l and i n t e r m e d i a t e i t e r a t i o n s to e q u i l -  i b r i u m a r e shown i n T a b l e s 7(a) and 7(b) and 8(b) to 8 ( e ) . The p r e v i o u s d i s c u s s i o n t r a c e d the m o d e l l i n g p r o c e s s w i t h r e f e r e n c e s to  the theory.  The f o l l o w i n g d i s c u s s i o n touches on some of the changes i n  demands and t r a v e l times which  took p l a c e d u r i n g the p r o c e s s .  The p r i c e s f o r a l l zones were i n c r e a s e d by 25c except f o r zone 3 which was  i n c r e a s e d by 50c.  The 50c i n c r e a s e i n zone 3 r e s u l t s i n a s h i f t  of 188  auto u s e r s (150 c a r s ) from t h e p a r k i n g l o t i n zone 3 to the l o t i n zone 1. T a b l e s 8(a) and 8(b) show t h i s .  T h i s change r e s u l t s i n a r e d u c t i o n o f auto  t r a v e l time as shown i n T a b l e 7(a) between the f i r s t The auto mode s p l i t ion.  and second  iterations.  f o r i t e r a t i o n #2 i s shown i n T a b l e 7(b) second  iterat-  A l t h o u g h the t r a v e l times f o r the automobile were reduced due to the  parking s h i f t ,  the added i n c r e a s e i n p a r k i n g c o s t s and w a l k i n g c o s t s  t h i s g a i n and the auto s p l i t  i s smaller.  offset  The mode s p l i t o f the second  i t e r a t i o n i s used to compute the o r i g i n - d e s t i n a t i o n m a t r i c e s of the t h i r d iteration.  The change i n the mode s p l i t between the f i r s t  and second  i t e r a t i o n i s r e f l e c t e d i n the reduced numbers o f auto u s e r s i n the t h i r d iteration  (Table 7(b)).  The r e d u c t i o n i n auto d r i v e r s r e s u l t s i n f u r t h e r  r e d u c t i o n s i n auto t r a v e l times ( T a b l e 7(a) t h i r d i t e r a t i o n ) . for  The mode s p l i t  the t h i r d i t e r a t i o n i s computed based on these t r a v e l times.  A l l changes  i n the mode s p l i t a r e i n the same d i r e c t i o n except t h e one f o r 3 r d S t r e e t . The reason f o r i t s r e v e r s a l i n d i r e c t i o n w i l l be d i s c u s s e d l a t e r .  The o t h e r s  behave i n a manner as p r e d i c t e d by the e q u i l i b r i u m t h e o r y , see Chapter 5 s e c t i o n 5.7 and Appendix A.  There a r e anomalies i n the t r a v e l times and the  81  mode s p l i t of the fourth and f i f t h i t e r a t i o n s of the 3rd Street and 4th Avenue origins.  These w i l l a l s o be addressed l a t e r .  The t r a v e l times and mode  s p l i t s f o r 1st Avenue and 3rd Avenue show an asymptotic approach to the equilibrium state. 6.3.1  Problems and Anomalies Several problems were noted upon examination of the convergence  process.  The f i r s t problem was located i n the parking a l l o c a t i o n model.  The  25C increase i n zone 3 over the other zones resulted i n d r a s t i c changes i n the a l l o c a t i o n of automobiles to parking l o t s .  I t can be seen that of those  persons parking i n zone 3 and walking to zone 4 almost a l l (188) s h i f t to parking i n zone 1 and walking to zone 4.  This does not seem r e a l i s t i c .  In the case where one parking zone was made 25c more expensive than a l l others, one would expect some s h i f t but not a complete s h i f t .  The reason f o r t h i s  d r a s t i c change i s that the parking a l l o c a t i o n algorithm optimizes the tradeoff between parking costs and walking time f o r the whole system ( i . e . a l l u s e r s ) , not the i n d i v i d u a l . model.  Another possible problem was noted w i t h t h i s  Invehicle t r a v e l time was not considered to be important i n the  choice of parking l o t .  The choice was thought to be d i c t a t e d by the parking  cost and walking time.  In t h i s small demonstration network some l i n k s are  h e a v i l y congested; so much so that walking i s f a s t e r than d r i v i n g .  This  condition may occur o c c a s i o n a l l y i n the r e a l world and the d r i v e r may choose to park further away from h i s d e s t i n a t i o n and walk because walking i s f a s t e r . In a h e a v i l y congested network a few extra v e h i c l e s added to the l i n k s s i g n i f i c a n t l y a l t e r t r a v e l times and become important i n determining the equilibrium state.  82  It  appears t h a t a p a r k i n g a l l o c a t i o n model which o p t i m i z e s  i n d i v i d u a l ' s t r a d e - o f f between p a r k i n g  c o s t s and w a l k i n g  the  would be b e t t e r .  Some work should be done to determine whether i n v e h i c l e t r a v e l time be c o n s i d e r e d  should  i n the t r a d e - o f f .  When a p a r k i n g p r i c e i n c r e a s e r e s u l t e d i n a s h i f t of the a l l o c a t i o n of parked cars as w e l l as s h i f t s i n the mode s p l i t to  the system d i d not  e q u i l i b r i u m i n the f a s h i o n expected.,. I t converged by o s c i l l a t i n g  a value.  F i g u r e s 12(a) .and  ahow the convergence p a t t e r n s f o r t r a v e l time and mode s p l i t case and  F i g u r e 13(a)  and  13(b)  mode s p l i t s produced by  D; 25c  25c  of t r a v e l times and  The  F i g u r e 13  initial  p o l i c y i s C and  to the theory  on  parking  the f i n a l i s  the f i n a l i s F.  the system should have approached the  i b r i u m s t a t e a s y m p t o t i c a l l y ; r e f e r to Chapter 5, illustrates  the  i s the r e s u l t of a p r i c e i n c r e a s e of  on a l l p a r k i n g l o t s where the i n i t i a l p o l i c y i s E and According  that t h i s was  not  the  s e c t i o n 5.7  and  equil-  appendix A.  case.  S e v e r a l reasons were p o s t u l a t e d f o r the problem.  The  size, config-  u r a t i o n and  t r a v e l demands on the network produced some l i n k s w i t h  low  volumes and  low  and  t r a v e l times and  u n r e a l i s t i c a l l y high delays The number of models and  produced o t h e r s w i t h h i g h volumes  (over 20 minutes per automobile i n one  the manner i n which they  case).  i n t e r a c t caused problems.  The method of feedback of automobile t r a v e l time to the mode s p l i t model coupled w i t h  These  the i t e r a t i o n s between the e q u i l i b r i u m s t a t e s of  on a l l o t h e r l o t s .  r e f e r to f i g u r e 2 ( a ) .  F i g u r e 12  f o r the former  F i g u r e 12 i s the r e s u l t of a p r i c e i n c r e a s e of 50c  each p o l i c y .  only,  12(b)  show the p a t t e r n s f o r the l a t t e r case.  f i g u r e s i l l u s t r a t e i n g r a p h i c a l form the v a l u e s  3 and  about  When the p r i c e i n c r e a s e r e s u l t e d i n a s h i f t of the mode s p l i t  the system converged a s y m p t o t i c a l l y as expected.  lot  converge  the s m a l l s i z e of the network a l s o caused  difficulties.  .83  FIGURE 1 2 ( a ) TRANSITION TRAVEL TIMES  POLICY C TO D  NOTE: The price Increase i s 50<j; on parking l o t 3 25cfc on a l l others 3  Time in  8 h  minutes 7  3rd S t r e e t  6 4 t h Ave. 1st Ave. 3rd Ave.  4 \I  1  2  3  4  Iterations FIGURE TRANSITION MODE SPLIT  Auto mode split  12(b) POLICY C TO D  .550 530 4 t h Ave. .490 3rd S t r e e t 3rd Ave. 1st Ave.  2  3 Iterations  84  FIGURE TRANSITION TRAVEL TIMES Time in minutes  13(a) POLICY E TO F  12.0  3rd  Street  4th Ave. & 1st Ave.  3rd Ave. 1  2  iterations  3 FIGURE  TRANSITION MODE SPLIT  13 (b) POLICY E TO F  Mode split . 570  4th Ave.  3rd Ave. 1st Ave. 3rd S t r e e t  iterations  NOTE:  The p r i c e Increase I s 25<fc f o r a l l p a r k i n g l o t s  85  F i g u r e 12 shows the c o n f i g u r a t i o n of the network. entrances and f o u r p a r k i n g l o t s . the l i n k s around  these p o i n t s .  There a r e f o u r  Delay and c o n g e s t i o n i s c o n c e n t r a t e d on The volumes on the l i n k s not  directly  connected to them are such t h a t t r a v e l times a r e g e n e r a l l y a t s l i g h t l y g r e a t e r than f r e e f l o w c o n d i t i o n s .  One would expect d e l a y s a t e n t r a n c e s  to the C.B.D., such as the b r i d g e s to Vancouver v e h i c l e s converge.  and a t p a r k i n g l o t s where  However, one would a l s o expect the d e l a y s throughout  the network to be of the same magnitude as those a t the more h e a v i l y congested p o i n t s .  In the example, network t r a v e l times on most of the  l i n k s range between 25 and 100 seconds w h i l e those a t the congested areas range between 300 and 1000 work was  seconds.  T h i s c l e a r l y i s not r e a l i s t i c .  Some  done i n o r d e r to a l l e v i a t e t h i s problem by a d j u s t i n g the network  and the l o c a t i o n of the p a r k i n g l o t s .  However, adjustments had to be made  through a t r i a l - a n d - e r r o r approach and proved to be time-consuming, and c o s t l y i n computing i t was  costs.  A f t e r s e v e r a l adjustments  d e c i d e d to go ahead w i t h the example r u n s .  on the example run's then, was  and some improvement  The d i f f i c u l t y  encountered  l a r g e changes i n t r a v e l times w i t h s m a l l  changes i n volumes on h e a v i l y congested l i n k s .  T h i s phenomenon of h a v i n g  a few u n r e a l i s t i c a l l y congested l i n k s and the remainder b e i n g  lightly  congested had r e p e r c u s s i o n s on the r e s u l t s throughout the a n a l y s i s . Perhaps  one o f the advantages  of the problem mentioned  above i s t h a t  i t h i g h l i g h t e d the weaknesses i n the l o g i c of the system and made i t much e a s i e r to l o c a t e f a u l t s and make recommendations. The second d i f f i c u l t y was the m o d e l l i n g system. systems which are:  found t o have i t s source i n the n a t u r e o f  W i t h i n the o v e r a l l system t h e r e are t h r e e sub-  can a l t e r demands on the v e h i c u l a r and t r a n s i t network.  the p a r k i n g a l l o c a t i o n ,  the v e h i c l e assignment  They  and mode s p l i t models.  In the example chosen f o r demonstration a l l t h r e e make changes to the demand.  86 When parking prices are uniformly increased only the mode s p l i t and the vehicle assignment model make changes to the demand.  The reason f o r this  i s that none of the parking l o t s gain an advantage over the others i n terms of walking and parking costs. in this case.  The approach to equilibrium i s faster  When prices are increased d i f f e r e n t i a l l y a l l three sub-  systems interact: and the approach takes longer. The problem was seen to be two-fold.  I t appears that f i r s t l y , the  number of systems interacting has a s i g n i f i c a n t effect on the approach to equilibrium and secondly, the degree of interaction or independence of the systems from one another.  Each of the models operates independently i n  time and the models interact by passing aggregated another.  demand data between one  This i s a sequential process and the d i f f i c u l t y with i t l i e s i n  the fact that each sub-system —  except the mode s p l i t model —  perform  their functions without any consideration of what has happened i n the other sub-systems or i n the previous i t e r a t i o n . To i l l u s t r a t e t h i s , the intersection of 3rd Street and 1st Avenue w i l l be examined more closely.  Figure 14(c) shows the intersection i n  d e t a i l with the location of parking l o t #1. important to this analysis are shown.  Figures 13(a) and 13(b) show the  travel times and the volumes on congested each of the i t e r a t i o n s .  Only the links which are  links at this intersection f o r  This intersection i s a good i l l u s t r a t i o n of the  interaction of the three models through the i t e r a t i v e process.  The impact  of the parking a l l o c a t i o n model i s noticed i n the second i t e r a t i o n .  The  parking price increase reallocates cars from parking l o t #3 to parking l o t #1 and an increase i n volumes on l i n k s 99, 31 and 77 are seen.  These  links enter the parking l o t . Correspondingly there i s a decrease of t r a f f i c on l i n k 98 which feeds a l l the other parking l o t s .  87  FIGURE 14:  TRANSITION TRAVEL TIMES AND VOLUMES ON LINKS INTO PARKING LOT I  POLICY 2 INCREMENT 2 TO 3.  (a) Vehicles Vs Iterations  (b) Time Vs Iterations  Vehicles  1  Sees«  2  3  (c)  4  5  1  2  3  Intersection showing Parking Lot #1 31  STREET  4  5  88  The effect of the assignment model i s seen i n the computation of the travel time.  The t r a v e l times on l i n k s 31 and 77 increase while on l i n k s  99 and 98 they decrease.  One would expect there to be less travel time on  l i n k 98 because there are fewer vehicles turning l e f t .  However, on l i n k  99 the" travel time i s also less although there are more vehicles on that link.  This i s due to the reduced interference with cars turning l e f t on  l i n k 98. On the t h i r d i t e r a t i o n the impact of the mode s p l i t model i s seen i n the change of volume of vehicles on the l i n k s .  I t must be remembered  that the mode s p l i t i s based on the whole journey time and i s influenced by travel time and parking costs.  The mode s p l i t takes the parking prices  and the travel times computed as a r e s u l t of the parking a l l o c a t i o n , and the assignment of vehicles, and computes the aggregate demands for the next iteration.  In this case i t i s the third i t e r a t i o n .  This i s the f i r s t time  that the effects of the price changes and travel time changes are passed on to the mode s p l i t .  On links 31, 98 and 77 there are reductions i n volumes  and there i s an increase i n volumes i n l i n k 99.  The combination of increased  travel time, increased parking charges and increased average walking times due to the reallocation of parked cars caused the mode s p l i t to reduce the number of cars t r a v e l l i n g to parking l o t 1 v i a l i n k 77 and 31. Link 98 carries t r a f f i c to a l l other parking l o t s from the entrance at 3rd Street and probably l o s t vehicles because of increased parking charges i n other lots.  Link 100 i s not important because i t carries only 14 to 20 cars.  99, on the other hand, gained auto t r a f f i c .  Link  Most of the t r a f f i c on this  l i n k goes d i r e c t l y to parking l o t 1, so the reduction i n t r a v e l time on this l i n k between interation 1 and 2 was s u f f i c i e n t to offset the parking charge increase and induce more t r a n s i t riders to take the car for this trip.  89  The fifth  p r o c e s s continues  iterations.  I t can be  i s q u i t e complex.  i n t h i s manner through the  When a l l three models are making changes i n t r a v e l time and  In the t h i r d , f o u r t h and  fifth  models i n t e r a c t , the system s e t t l e s down. of the drawbacks of u s i n g  i t e r a t i o n s where o n l y  I t appears that t h i s may  i n d i r e c t approaches.  or systems i n t e r a c t i n g , the g r e a t e r reach e q u i l i b r i u m .  Since  and  The  smaller  set out p r e v i o u s l y , perhaps work  incremental  a l s o be other methods which c o u l d be  noted here may  simply  the  to  T h i s c o u l d be  ( r e f e r to Chapter 5,  should  achieved  s e c t i o n 5.7).so  changes i n the mode s p l i t  when  There  may  examined.  emphasized t h a t b e f o r e be  for a  the number of models  l a r g e changes i n t r a v e l time between i t e r a t i o n s were d e t e c t e d .  the system should  defined  the number of i t e r a t i o n s r e q u i r e d  by m o d i f y i n g the e q u i l i b r i u m a l g o r i t h m  ed;  one  However,  more independent  the g r e a t e r  be done to reduce the independent of the models.  I t must be  be  i t i s not p o s s i b l e to reduce the number of models  be c o n s i s t e n t w i t h the theory  t h a t i t would a l l o w  two  does produce r e a s o n a b l e r e s u l t s (as  models are i n the s e q u e n t i a l p r o c e s s ,  and  v e h i c u l a r volumes i s  the b e g i n n i n g of Chapter 5 ) ; r e f e r to Chapter 3, s e c t i o n 3.1  d i s c u s s i o n on d i r e c t and  process  simultaneously,  an i n d i r e c t approach to e q u i l i b r i u m .  the approach does converge and at  and  seen from the d i s c u s s i o n above t h a t the  the amplitude of the o s c i l l a t i o n s quite large.  t h i r d , fourth  any  of these changes can be  t e s t e d on a more r e a l i s t i c network.  be a r e s u l t of the network used.  The  consider-  problems  90  The f i n a l problem noted was  the computation of the a u t o m o b i l e t r a v e l  time which i s used t o compute the mode s p l i t .  The s t o c h a s t i c  assignment  model d i d n o t compute the c u m u l a t i v e t r a v e l time from o r i g i n t o d e s t i n a t i o n . I t was n e c e s s a r y t o add a f u n c t i o n t o the assignment model w h i c h would extract this information.  I t was thought t h a t a minimum p a t h s e a r c h a p p l i e d  a f t e r the v e h i c u l a r assignments had been completed, and the t r a v e l times a s s o c i a t e d w i t h t h a t assignment had been computed would be adequate.  I t was  expected t h a t t h e r e would n o t be a s i g n i f i c a n t d i f f e r e n c e i n t r a v e l time between a s e t of p o s s i b l e r o u t e s c o n n e c t i n g an o r i g i n and a d e s t i n a t i o n . F u r t h e r , i t was  thought t h a t the m a j o r i t y of v e h i c l e s would t r a v e l the  r o u t e of s h o r t e r time and hence, t h i s method of computing a u t o m o b i l e t r a v e l would be a good a p p r o x i m a t i o n of the j o u r n e y time.  I t must be p o i n t e d out  a g a i n t h a t the assignment on t h i s network produced t r a v e l times on most of the l i n k s under 100 seconds and on the remainder over 300 seconds.  To  r e i t e r a t e : the l i n k s w i t h h i g h t r a v e l times a r e h e a v i l y l o a d e d , they a r e d i r e c t l y connected t o the e n t r a n c e s of the network or t h e p a r k i n g  lots,  and they d i f f e r g r e a t l y w i t h i n the range of 300 to 1300 seconds.  For  example:  l i n k s 43 and 21 e n t e r i n g the p a r k i n g l o t i n zone 3 have t r a v e l  times of 1300 and 500 seconds r e s p e c t i v e l y on the f i r s t i t e r a t i o n ; r e f e r to F i g u r e 15(b) and 1 5 ( c ) .  The l i n k s c o n n e c t i n g t h e s e l i n k s have t r a v e l  times under 100 seconds, w i t h the e x c e p t i o n of one case w h i c h i s 830 seconds and t h a t i s due t o the t r a f f i c e n t e r i n g the network a t 3rd Avenue. The minimum p a t h s e a r c h can a v o i d the l i n k w i t h the t r a v e l time of  1300  seconds by t a k i n g a c i r c u i t o u s r o u t e through the network and compute j o u r n e y times w h i c h a r e c o n s i d e r a b l y l e s s than t h e average.  91 FIGURE 15:  TRANSITION TRAVEL TIMES AND VOLUMES ON LINKS INTO PARKING LOT 3  POLICY 2 INCREMENT 3.  (c)  Intersection Showing Parking Lot 3  92  If the network was  representative of r e a l world conditions, and delays  on a l l links were of the same magnitude, this problem would not be s i g n i ficant.  I t i s recommended, however, that the s e n s i t i v i t y of the results  to the use of the minimum path search to obtain auto journey times be examined using a r e a l i s t i c network. 6.4  An Analysis of A Short Run Policy Question The small network was used to perform the analysis.  The results from  this analysis w i l l be very general indications of the effects of parking price increases on congestion. i c a l l y congested posed.  As already noted, there are some u n r e a l i s t -  l i n k s i n the network.  The f i r s t was:  short run policy questions were  what would be the effect of r a i s i n g the cost of  parking i n parking l o t #3 by increments increase of $1.00.  Two  of 25c  three times with a f i n a l  The second entailed determining  the effect of increasing  parking prices on a l l parking l o t s i n the same manner as above.  There was  one exception i n this case where the prices of parking l o t #3 were increased 50c on the second increment. d e t a i l previously.  This i s the scenario which was analysed i n  Table 9 shows the price increase for the two p o l i c i e s  in each parking l o t . The reason that the two d i f f e r e n t p o l i c i e s were selected for analysis was because m u n i c i p a l i t i e s generally control only a f r a c t i o n of the parking spaces i n the C.B.D.  The f i r s t policy approximates  the case where the municipality decides to increase the rates i n i t s own parking l o t s .  The second policy approximates the case where the government  is able to levy a tax on a l l parking l o t s . With the data output from the programs, i t i s possible to examine the p o l i c i e s at several l e v e l s . costs can be examined.  Total hours of t r a v e l time versus t o t a l travel  The s h i f t i n the mode s p l i t for each of the d i f f e r e n t  p o l i c i e s can be looked at.. Usage and s t a t i s t i c s on p a r t i c u l a r bus l i n e s can  93  TABLE 9  PARKING PRICE POLICIES  PARKING ZONES ORIGINAL POLICY  1  2  3  4  1.25  1.25  1.50  .75  increment #1  1.25  1.25  1.75  .75  #2  1.25  1.25  2.00  .75  #3  1.25  1.25  2.25  .75  #4  1.25  1.25  3.25  .75  increment #1  1.50  1.50  1.75  1.00  #2  1.75  1.75  2.25  1.25  #3  2.00  2.00  2.50  1.50  #4  3.00  3.00  3.50  2.50  POLICY #1  POLICY #2  A l l Prices are i n Dollars  NOTE:  Policy #1 i s an Incremental Increase of the Parking Price in Parking Lot 3 only. Policy #2 i s an Incremental Increase of the Parking Price on a l l Parking Lots  94  be examined. The e f f e c t o f the changes on the i n d i v i d u a l ' s t r a n s i t  trip  can be t r a c e d . G e n e r a l l y , the purpose to i n d u c e more e f f i c i e n t transit  f o r the purpose  of i n c r e a s i n g p a r k i n g p r i c e s i n the C.B.D. i s  use o f the auto and b e t t e r u t i l i z a t i o n o f p u b l i c o f r e d u c i n g road c o n g e s t i o n . T h e e f f e c t i v e n e s s o f  these p o l i c i e s i s g e n e r a l l y measured i n the number o f hours o f t r a v e l saved. F i g u r e 16 i s a p l o t  o f the t o t a l hours  c o s t s f o r each p o l i c y . The t o t a l hours  FIGURE  time  t r a v e l l e d v e r s u s the t r a v e l  t r a v e l l e d i n c l u d e w a l k i n g time and  16  TOTAL HOURS VERSUS TOTAL TRAVEL COSTS 2200  r  Total Hours  9000  10000  11000  12000  13000 $  T o t a l Costs invehicle  time f o r both modes. The t r a v e l c o s t s i n c l u d e ; p a r k i n g charges,  bus f a r e s , and the m a r g i n a l c o s t o f d r i v i n g t h e c a r . The m a r g i n a l c o s t o f d r i v i n g was approximated  by assuming t h a t the average  t r i p was 6 m i l e s and  the g a s o l i n e c o s t s were 10c p e r m i l e (1964 d o l l a r s ) . The  first  price increase i n policy 1 results i n a s i g n i f i c a n t reduction  i n t o t a l numbers of hours  travelled  and a s l i g h t  r e d u c t i o n i n the t o t a l  cost  95  of t r a v e l . congested  This r e s u l t can partly be attributed to the u n r e a l i s t i c a l l y links and may  not be v a l i d .  One would expect an increase i n  t o t a l travel time with a r e a l l o c a t i o n of parked cars due to a p r i c e increase. A price increase on one l o t should r e s u l t i n either a s h i f t to another l o t which i s further from the f i n a l destination and therefore a longer walk, or a s h i f t to t r a n s i t which i s usually slower than the automobile.  This i s a  case of the parking a l l o c a t i o n model not taking into account the fact that there may be a trade-off between walking and driving when driving i s the more time consuming.  The remaining results appear more r e a l i s t i c .  i s much more e f f e c t i v e i n reducing congestion. society are much greater.  Policy 2  However, the costs to  If one were to r a i s e the parking prices to the  highest l e v e l shown f o r policy 2, the cost to society would be $2,669 and the t o t a l time savings are 906 hours.  The value of time would have to be  no less than $2.90 per hour to j u s t i f y this course of action.  On the other  hand, i f one were to raise the prices to the highest l e v e l shown i n policy 2, the cost to society would be $473 and the time savings 437 hours.  The  value of time i n order to j u s t i f y this course of action would have to be at least $1.08.  In terms of unit cost to society, policy 1 i s better.  However, i t i s not as successful at reducing congestion as policy 2.  It  should be noted that there are other costs or savings which were not taken into account here.  For example:  noise, p o l l u t i o n , and the costs of savings  to the bus operator were not included.  By developing and applying the proper  functions, a l l of these factors could be obtained from the models.  96 TABLE 10  AGGREGATE STATISTICS OF THE SYSTEM FOR THE FINAL STATE OF EACH POLICY  POLICY ORIGINAL POLICY  STATISTIC  POLICY #2 INCREMENT #4  POLICY #1 INCREMENT #4  Average t r a n s i t Share of the Demand  46.9%  48.4%  65%  Average Speed of the Bus  7.27 MPH  7.88 MPH  10.43 MPH  Average Speed of the Car  4.15 MPH  6.18 MPH  16.22 MPH  7.5  9.15 MPH  *Average Speed of the Car with High Link Delays Adjusted  *N0TE:  MPH  The average speed of the car i s lower than the bus i n the f i r s t two p o l i c i e s because the bus does not travel over some of the heavily travelled l i n k s . There were 6 links with travel times greater than 300 seconds (5 min or less than 2.3 mph.). In order to demonstrate the d i s t o r t i o n created by these large delays, the average speeds were recalculated by reducing the t r a v e l times on these p a r t i cular l i n k s to 200 seconds.  Table 10 shows the aggregate transit s t a t i s t i c s for the d i f f e r e n t parking p o l i c i e s .  Policy 1 results i n very l i t t l e change i n the average  speed of the buses and l i t t l e change i n the numbers of people using the bus. Policy 2, on the other hand, shows considerable improvement i n both the t r a n s i t ridership and the average speed of the buses.  The benefits of  policy 1 are due to a s l i g h t reduction i n congestion only.  The benefits  of policy 2 are a result of a considerable reduction i n congestion, increased ridership of t r a n s i t , increased speed fo the buses and reduced p o l l u t i o n and noise due to the fewer number of cars on the road.  Although  generalized conclusions should not be drawn from t h i s analysis because of the problems with the network, i t appears that the analysis confirms the  97  experience with parking p r i c e i n c r e a s e s .  That  i s , t h a t where the  m u n i c i p a l i t y attempts to i n c r e a s e the p r i c e s of p a r k i n g l o t s under i t s control, l i t t l e  i s gained i n t h e way o f reduced  transit ridership.  I t suggests  c o n g e s t i o n or i n c r e a s e d  that f o r parking p o l i c i e s  to be e f f e c t i v e  i n r e d u c i n g c o n g e s t i o n and i n c r e a s i n g t r a n s i t r i d e r s h i p , i t i s n e c e s s a r y to  c o n t r o l a l l p a r k i n g - which i n c l u d e s i l l e g a l p a r k i n g ,  off-street  p a r k i n g , s t r e e t p a r k i n g and p a r k i n g p r o v i d e d f r e e by employers. The m o d e l l i n g system developed  f o r t h i s paper i s capable o f a n a l y s i n g  changes i n the bus system and auto network as w e l l as the p a r k i n g  system.  Bus l i n e s may be dropped or added; the f r e q u e n c i e s may be changed o r bus stops may be r e l o c a t e d and the e f f e c t of e x c l u s i v e bus l a n e s may be t e s t e d . The  s t r e e t network may be changed, new l i n k s may be added or dropped, the  d i r e c t i o n o f flow on the s t r e e t s may be changed and t r a f f i c i n t e r s e c t i o n d e s i g n may be changed.  l i g h t s and  B e f o r e any new a n a l y s i s should be  done, the m o d e l l i n g system should be t e s t e d on a more r e a l i s t i c  network.  FOOTNOTES  F.P.D. Navin, C. Fisk, "A Downtown T r a f f i c Management System", Prepared f o r the Canadian Transportation Research Form Annual Meeting, St. Andrews, New Brunswick, 1977, p.9. Ibid., pp. 13-14. C. Fisk, "A Transportation Planning Model for Detailed T r a f f i c Analysis", Transportation Research Series Report No. 11, The University of B r i t i s h Columbia, Department of C i v i l Engineering, 1977.  .99  CHAPTER 7 7.0  CONCLUSIONS The  purpose of t h i s paper was  to develop an a n a l y t i c a l framework to  answer s h o r t range p o l i c y q u e s t i o n s .  This  type of framework i s needed  because u n t i l r e c e n t l y most models d e a l t w i t h long range c a p i t a l investment d e c i s i o n s w h i l e many urban t r a n s p o r t a t i o n problems may  be  solved  through  s h o r t range p o l i c i e s . First,  the  t h e o r e t i c a l considerations  framework were examined. The framework to be  literature  of the s h o r t range  planning  i n d i c a t e d that i n order f o r  r e s p o n s i v e to p o l i c y changes i t must be  the  s e n s i t i v e to changes  i n a t t r i b u t e s of t r a n s p o r t a t i o n a l t e r n a t i v e s t h a t would r e s u l t from p o l i c i e s b e i n g analysed"'". A l s o the c h o i c e  i t must be  structured  i n such a way  p r o c e s s of an i n d i v i d u a l d e c i d i n g between the a l t e r n a t e  p o r t a t i o n modes. Changes i n p a r k i n g  developed has  been shown to be  the d i f f e r e n t modes and  Several  conditions  to ensure c o n s i s t e n c y  The  m o d e l l i n g system  r e s p o n s i v e to changes i n s e r v i c e l e v e l s of  reflect  model's p r e d i c t i o n s cannot be  trans-  p r i c e s i n the demonstration network  r e s u l t e d i n changes i n t r a v e l times and mode s p l i t s .  are as  that i t r e f l e c t s  the c h o i c e p r o c e s s . The  obtained u n t i l a f u l l  a c c u r a c y of  the  s c a l e network i s t e s t e d .  enumerated by Manhiem were deemed as b e i n g n e c e s s a r y  i n t h i s type of a model. The  equilibrium  conditions  follows:  (1)  The  l e v e l of s e r v i c e must e n t e r  unless (2)  The  at each stage i n the  i t i s e x p l i c i t l y found to be  sequence  superfluous.  same a t t r i b u t e s of s e r v i c e should e n t e r  at each step  unless  the data i n d i c a t e s o t h e r w i s e . (3)  The  same v a l u e s of the l e v e l of s e r v i c e s h o u l d i n f l u e n c e  sub-model.  each  100  (4)  The l e v e l of service provided by each mode should influence the demand to some degree.  The degree to which the modelling system meets these requirements w i l l be addressed i n the same order as they are l i s t e d above. (1)  The system developed i n t h i s paper computes four l e v e l of service  factors. They are the auto and t r a n s i t in-vehicle and out of vehicle t r a v e l times. Table 2 shows each of the models i n the system and indicates whether the l i s t e d levels of service are considered i n the models. The models i n the table are l i s t e d i n the order i n which they are executed. It i s easy to trace through the process and determine where each of the l e v e l s of service are u t i l i z e d . It begins with the parking a l l o c a t i o n model which, using the parking charges and auto walk times, transforms the person 0-D  t r i p s by auto into vehicle 0-D  t r i p s . The person 0-D  t r i p s are  i n the form of ultimate o r i g i n and destination while the vehicle 0-D  trips  are i n the form of ultimate o r i g i n and parking l o t destination. I t was suggested i n Chapter 6 section 6.4 that the i n c l u s i o n of the auto in-vehicle t r a v e l times might improve the a l l o c a t i o n . The remaining two t r a n s i t l e v e l s of service are unnecessary i n the parking a l l o c a t i o n modellhecause they are irrelevant to a decision which considers a trade-off between parking costs and walking time. The process moves along to the vehicle assignment model u t i l i z i n g the vehicle origin-destination t r i p s and the auto in-vehicle t r a v e l times to compute the vehicle assignment. Chapter 4 section 4.2.5  discusses how  t r a v e l times are incorporated i n the assignment model. The vehicle t r a v e l times are translated into average speeds on the l i n k s which set the maximum speed for the buses i n the t r a n s i t assignment. The computation of bus i n vehicle t r a v e l times and walk-wait times i s described i n Chapter 5 section  TABLE 2  SYSTEM SUB-MODELS VERSUS LEVEL OF SERVICE AND SERVICE SERVICE  MODEL  DEMANDS  parking allocation  person t r i p s by auto  vehicle assignment  vehicle 0-D trips  transit assignment  person 0-D t r i p s by t r a n s i t  mode split  person t r i p s by auto and transit  PARKING CHARGES  LEVEL OF SERVICE  ATTRIBUTES  BUS FARES  ATTRIBUTES  FREQUENCY OF SERVICE  AUTO WALK TIMES  AUTO INVEHICLE TIMES  •BUS WALK & WAIT TIMES  BUS INVEHICLE TIMES  X  X  X  X  X  X  X  X  X  X  X  X  X  102  5.4. The mode s p l i t model i s the p i v o t p o i n t of the system. l e v e l s are r e p r e s e n t e d . I t i s through  the mode s p l i t  that the s e r v i c e  computed by the p r e v i o u s i t e r a t i o n are t r a n s l a t e d i n t o new next i t e r a t i o n .  A l l service  In t h i s manner a l s o , a l l s e r v i c e l e v e l s a r e  levels  demands f o r the implicitly  r e p r e s e n t e d through out the system by the r e v i s e d demands. (2)  The a t t r i b u t e s of s e r v i c e are the p a r k i n g charges, bus  frequency of bus direct  fares  and  s e r v i c e . These e n t e r the sub-models where they have a  impact. As i s the case w i t h the l e v e l of s e r v i c e f a c t o r s , they a r e  i n d i r e c t l y r e p r e s e n t e d i n a l l systems through the mode s p l i t . (3)  Where the l e v e l of s e r v i c e f a c t o r s a r e r e p e a t e d i n the d i f f e r e n t  sub-systems they are the same v a l u e throughout a f t e r the mode s p l i t  and when a new  any g i v e n i t e r a t i o n .  It i s  i t e r a t i o n begins t h a t the l e V e l of  s e r v i c e f a c t o r s a r e changes. (4) for  The  l e v e l of s e r v i c e p r o v i d e d by each mode i n f l u e n c e s the demand  t r a v e l by the two modes through the mode s p l i t  model.  From a t h e o r e t i c a l p o i n t of view a l l of the e q u i l i b r i u m c o n d i t i o n s s e t out by Manhiem have been met,  however, an examination  of the impact  of  i n c l u d i n g the auto t r a v e l times i n the p a r k i n g a l l o c a t i o n model has  been  recommended. The m o d e l l i n g system was  t e s t e d u s i n g a s m a l l network. S e v e r a l  recommendations and c o n c l u s i o n s a r o s e out o f t h i s t e s t procedure. of  t e s t i n g was  to show t h a t the system produced  The  reasonable r e s u l t s . I t  d e f i n e d t h a t t o be " r e a s o n a b l e " the r e s u l t s should meet the  purpose was  following  criteria: (1)  any changes.in s e r v i c e l e v e l s or p a r k i n g charges would r e s u l t i n s h i f t s of demand i n the a p p r o p r i a t e d i r e c t i o n ;  103  (2)  that the changes i n demand w i l l be p r o p o r t i o n a t e to the change . i n l e v e l of s e r v i c e and v i c e v e r s a .  The  s i z e and  c o n f i g u r a t i o n of the demonstration  network produced  d e l a y s on some l i n k s which were not r e p r e s e n t a t i v e of d e l a y s on a r e a l network. I t was  concluded  t h a t although  these r e s u l t s s e r v e d to h i g h l i g h t  the weakness of the system, a more r e a l i s t i c network s h o u l d be  developed  w i t h the t e s t network the system of models produced r e s u l t s which were reasonable.  The  first  a mode were reduced  c r i t e r i a was  s a t i s f i e d i n t h a t when t r a v e l times  the use of t h a t mode i n c r e a s e d and when the  of  parking  c o s t s i n c r e a s e d the use of the automobile dropped. I t appeared a l s o , t h a t a l l changes i n l e v e l s of s e r v i c e were p r o p o r t i o n a t e to changes i n demand and v i c e v e r s a except  i n the case of the p a r k i n g a l l o c a t i o n model. In  case a l a r g e change i n the p a r k i n g a l l o c a t i o n o c c u r r e d due i n p r i c e . I t was  to a s m a l l change  thought t h a t t h i s o c c u r r e d because the p a r k i n g model  o p t i m i z e d the t r a d e - o f f between p a r k i n g c o s t s and w a l k i n g system, not  this  the i n d i v i d u a l  user.  Some problems were noted  i n the e q u i l i b r i u m a l g o r i t h m . The  not converge a s y m p t o t i c a l l y as expected. d e c r e a s i n g amplitude  appeared t h a t the number of systems i n t e r a c t i n g and another  system d i d  I t converged by o s i l l a t i n g  about a v a l u e . The problem was  the sub-systems from one  time f o r the whole  seen to be  two-fold. I t  the independence of  caused the problem. I t was  the independence of the sub-models c o u l d be reduced  with  thought t h a t  by m o d i f y i n g  the  equili-  b r i u m a l g o r i t h m so t h a t i t would a l l o w s m a l l e r i n c r e m e n t a l changes i n the mode s p l i t when l a r g e changes i n t r a v e l time between i t e r a t i o n s were detected. I t was  noted  t h a t the computation of the automobile j o u r n e y  times  for  the mode s p l i t u s i n g a minimum path a l g o r i t h m produced low t r a v e l times f o r  104  the auto mode., T h i s was  l a r g e l y a t t r i b u t e d t o the f a c t t h a t the d e l a y s on  the l i n k s on t h i s p a r t i c u l a r network v a r i e d from tens of seconds of  seconds.  I t was  thought  to  thousands  t h a t i n a r e a l i s t i c network such v a r i a t i o n s would  not occur and the minimum path a l g o r i t h m would compute t r a v e l times r e p r e s e n t a t i v e of r e a l  times.  D e s p i t e the problems w i t h the network, the a n a l y s i s of the two p a r k i n g p o l i c i e s t e s t e d g e n e r a l l y confirmed the e x p e r i e n c e w i t h p a r k i n g p r i c e increases.  The r e s u l t s suggests t h a t f o r p a r k i n g p o l i c i e s  i n r e d u c i n g c o n g e s t i o n and  to be  effective  i n c r e a s i n g t r a n s i t r i d e r s h i p , i t i s n e c e s s a r y to  control a l l parking. At  the b e g i n n i n g of t h i s demonstration i t was  be shown to be p r a c t i c a l , r e l i a b l e and economical. demonstration was  to show t h a t the model was  r e s u l t s . . • The remaining c r i t e r i a mentioned The demonstration was of  the r e s u l t s .  accurate.  noted t h a t a model must The o b j e c t i v e of the  p r a c t i c a l and produced  above c o u l d be addressed by o t h e r s .  s u c c e s s f u l i n showing the .reasonableness and  practicality  I t i s not p o s s i b l e a t t h i s p o i n t to s t a t e t h a t the model i s  I t i s p o s s i b l e to say t h a t i n g e n e r a l i t produces  expected, g i v e n the t e s t i n g network.  results  as  The demonstration d i d succeed i n p i n -  p o i n t i n g s e v e r a l weaknesses and p r o v i d i n g i n s i g h t s i n t o how behaves.  reasonable  the  system  FOOTNOTES T. J. Atherton, J , H, Suhrbier, and W A,. Jessiman, "Use of Disaggregate Travel Demand Models to Analyse Car Pooling Policy Incentives", Transportation Research Board, 599., 1976, p.35. r  106^ CHAPTER 8 8.0  RECOMMENDATIONS  A s e t o f recommendations arose out o f the a n a l y s i s o f the t e s t network. Before any o f the f o l l o w i n g s u g g e s t i o n s a r e c a r r i e d out i t i s recommended t h a t an unmodified  v e r s i o n o f the m o d e l l i n g system developed  i n this  paper be t e s t e d on a more r e a l i s t i c network. T h i s may r e s u l t i n the c l a r i f i c a t i o n o f the doubts which gave r i s e t o some o f the f o l l o w i n g recommendations. Two d e f i c i e n c i e s were noted  i n the p a r k i n g a l l o c a t i o n model. The model  c o n s i d e r s a t r a d e - o f f between p a r k i n g c o s t s and w a l k i n g the d e c i s i o n made by the commuter. I t was thought  time i n r e p r e s e n t i n g  t h a t the model would be  improved i f the i n v e h i c l e t r a v e l times on a congested  network were a l s o  c o n s i d e r e d i n the model. T h i s s u g g e s t i o n was made because the c h o i c e o f a parking l o t not only a f f e c t s walking h e a v i l y congested  time and p a r k i n g c o s t s but on a  road system i n the C.B.D. the c h o i c e c o u l d have a s i g n i -  f i c a n t e f f e c t on i n v e h i c l e t r a v e l  time.  I t was thought  t h a t t h e r e may be a problem i n the way the p a r k i n g  a l l o c a t i o n modelled  the t r a d e - o f f between the two v a r i a b l e s . The model  minimizes  the sum o f the p a r k i n g c o s t s and w a l k i n g  costs f o r a l l users.  T h i s r e s u l t e d i n l a r g e s h i f t s i n p a r k i n g demand due t o s m a l l changes i n p a r k i n g p r i c e s . I t was thought a c o n c l u s i v e statement  t h a t t h i s behaviour was n o t r e a l i s t i c . However,  cannot be made due t o the l a c k o f e m p i r i c a l data  c o n c e r n i n g p a r k i n g behaviour.. A model which o p t i m i z e s t h e t r a d e - o f f s •: f o r the i n d i v i d u a l r a t h e r than a l l o f the d r i v e r s would r e p r e s e n t the c h o i c e p r o c e s s b e t t e r . I t i s recommended t h a t r e s e a r c h be undertaken i n o r d e r t o more f u l l y understand  the behaviour  o f commuter p a r k i n g i n the C.B.D.. With  t h i s knowledge the model may be m o d i f i e d so t h a t i t a c c u r a t e l y r e f l e c t s behaviour.  that  107  Appendix A i l l u s t r a t e s the reasoning behind the choice of a modifier for the mode s p l i t i n the equilibrium algorithm. The mode s p l i t i t s e l f was selected as a modifier because i t was the most e f f i c i e n t i n bringing the system to convergence.  Under a test model and network i n Appendix A the  system reached convergence through an asymptotic approach i n three or four i t e r a t i o n s . The results produced by the larger framework were d i f f e r e n t . Equilibrium was obtained by o s i l l a t i n g with decreasing amplitude about a value and four to f i v e i t e r a t i o n s were required f o r convergence.  Two factors  were seen to contribute to the difference. F i r s t there are four sub-models in the larger system whereas there were only three i n the test system of Appendix A. Secondly, the sub-systems operate r e l a t i v e l y independently from one another. One recommendation has already been made to include invehicle travel time i n the parking a l l o c a t i o n . This would serve to reduce the independence between the parking a l l o c a t i o n and vehicle assignment models. It i s also recommended that the influence of the modifier i n the equilibrium algorithm be examined more thoroughly. The testing should be done on the f u l l size modelling system. Research i n this area may provide a better understanding of the mechanisms involved i n the convergence to equilibrium and lead to improvements i n the modifier. The automobile journey time for the mode s p l i t model i s computed by a minimum path algorithm after the network has been loaded. Due to the large variations of t r a v e l times on the links (from tens of seconds to thousands of seconds) the minimum path algorithm computed low journey times, ( i . e . i t selected l i n k s with low volumes and small delays). I t i s recommended that the s e n s i t i v i t y of the results to the use of a minimum path algorithm to obtain auto journey times be examined using a r e a l i s t i c network. The mode s p l i t model used was developed and calibrated i n 1964 for a  108  study i n Toronto"'". I t was  satisfactory  f o r the purposes o f t e s t i n g  and  demonstration i n t h i s paper. However, i t i s recommended that i f a study i s to be undertaken  on a r e a l network, the l o g i t model s h o u l d be c a l i b r a t e d  to  the c o n d i t i o n s of the a r e a b e i n g s t u d i e d . The development of a m o d e l l i n g system proceeds i n s e v e r a l s t a g e s . The t h e o r y and a m o d e l l i n g system have been developed. The system has been t e s t ed on a s m a l l network and has been shown to produce  reasonable r e s u l t s . I t  has been recommended that a more r e a l i s t i c network be used f o r f u r t h e r t e s t i n g . S u b j e c t to the outcome of those t e s t s a s e t of r e f i n e m e n t s and sensitivity  t e s t s were recommended. Once these have been completed  f i n a l t a s k i s to show t h a t the system i s p r a c t i c a l , r e l i a b l e and Upon s a t i s f a c t o r y  the  economical.  completion of the recommendations above the system would  be ready f o r a p r a c t i c a l  application.  109  FOOTNOTES  D. W. G i l l e n , "Effects of Changes i n Parking Prices and Urban Restrict-- . ion on. Urban Transport Demands and Congestion Levels", University of Toronto-York University, Joint Program i n Transportation, 1975, pp. 28 - 35.  110 SELECTED-BIBLIOGRAPHY  Atherton, T.J., J.H. Suhrbier and W.A. Jessiman, "Use of Disaggregate Travel Demand Models to Analyze Car Pooling Policy Incentives," Transportation Research Record 599, 1976. Austin, T.W., "Allocation of Parking Demand i n a C.B.D.," Research Record 444, 1973.  Highway  B u r r e l l , J.E., M.A. F l o r i a n (ed) "Multiple Route Assignment: A Comparison of Two Methods," T r a f f i c Equilibrium Methods, Proceedings of the International Symposium Held at the Universite de Montreal, ApringerVerlag. New York, 1976. Button, K.J., "The Use of Economics i n Urban Travel Demand Modelling: A Survey," Socio-Economic Planning Science, Vol. 10, 1976. Chapman, R.A., H.E. Gault and S.A. Jenkins, "The Operation of Urban Bus Routes," T r a f f i c Engineerings and Control, June 1977. Chriqui, C., and P. Robillard, Vol. 9, No.2, 1976.  "Common Bus Lines,"  Transportation Science,  Culham, T.E., "An Examination of the Costs and Benefits of Various Parking P r i c i n g P o l i c i e s i n the C.B.D.," Student Paper Number 21, Centre for Transportation Studies, University of B r i t i s h Columbia, 1977. D i a l , R.B. and R.E. Bunyan, "Public Transit Planning System," Economic Planning Science, Vol. 1, 1968.  Socio-  D i a l , R.B., and A.M. Voorhus & Associates, Inc. "Transit Pathfinder Algorithm," Prepared for Presentation at Highway Research Board 46th Annual Meeting, Washington, D.C, January 1967. D i a l , R.B., "A P r o b a b l i s t i c Multipath T r a f f i c Assignment Model. Path Enumeration," Transportation Research, Vol. 5, 1971.  Which obviates  Fisk, C., "A Transportation Planning Model f o r Detailed T r a f f i c Analyses," Transportation Research Series, Report No. 11, Department of C i v i l Engineering, University of B r i t i s h Columbia, 1977. F l o r i a n , M., "A T r a f f i c Equilibrium Model of Travel by Car and Public Transit Modes," Transportation Science, Vol. 11, No. 2, May 1977. F l o r i a n , M. and S. Nguyen^ . "A Method for Computing Network Equilibrium with E l a s t i c Demands," Transportation Science, Vol. 8, No. 3, 1974. F l o r i a n , M., S. Nguyen, and J. Ferland, "On the Combined D i s t r i b u t i o n Assignment of T r a f f i c " Transportation Science, Vol. 9, No. 1, 1975. F l o r i a n , M., et a l , "A Planning Method for Multi-Model Urban Transportation Systems," Universite de Montreal Publication 62, Centre de recherche sur les transports, Mar 1977.  Ill  Florian, M., and S. Nguyen, "An Application and Validation of Equilibrium. Trip Assignment Methods," Universite de Montreal, Publication 28. Centre de recherche sur les transports, Aug 1975. G i l l e n , D.W., "Effects of Changes i n Parking Prices and Parking Restrictions on Urban Transport Demands and Congestion Levels," Research Report No. 25. University of Toronto, York University Joint Program i n Transportation, 1975. G i l l e n , D.W., "The E f f e c t s of Parking Costs on Mode Choice," Research Paper No. 23, The Department of Economics, The University of Alberta, 1975. Heggie, I.G., "Consumer Response to Public Transport Improvements and Car Restraint: Some P r a c t i c a l Findings," Working Paper No. 2(Revised) Transport Studies Unit, University of Oxford, 1976. Hoel, L.A., et a l , "Latent Demand for Urban Transportation", Transportation Research I n s t i t u t e , Carnegie-Millon University Pittsburgh, Pennsylvania, 1968. Hutchinson, B.G., " P r i n c i p l e s of Urban Transport Systems Planning," McGraw H i l l Book Co., 1974. Hutchinson, B.G. "A Framework for Short Run Transport.Policies," Roads and Transportation Association of Canada, Annual Conference, Planning Technical Sessions and Workshops, 1977. Irwin, N.A., and H.G. Van Cube, "Capacity Restraint i n Multi-Travel Mode Assignment Programs," Highway Research Board B u l l e t i n , 347. J o l l i f f e , J.K., and T.P. Hutchinson, "A Behavioural Explanation Association Between Bus and Passenger A r r i v a l s at a Bus Stop," Transportation Science, No. 3, Vol. 9, 1975.  of the  King, D.J., "Control of Congestion i n the C i t y of Vancouver: An Investigation of Parking Charges," A Study prepared for the City of Vancouver, 1974. Kulash, D., "Parking Taxes for Congestion R e l i e f : A Survey of Related Experience," The Urban I n s t i t u t e , Washington, D.C, 1974. Kulash, D., "A Transportation Washington, D.C, 1971  Equilibrium Model,"  The Urban I n s t i t u t e ,  Leblanc, L.J., "An Accurate and E f f i c i e n t Approach to Equilibrium T r a f f i c Assignment on Congested Networks," Transportation Research Board 491, 1974. Manhiem, M.L., " P r a c t i c a l Implications of Some Fundamental Properties of Travel Demand Models," Highway Research Record, 422, 1973. Navin, F.P.D., C. Fisk, and Engineering Department, City of Vancouver, "A Downtown T r a f f i c Management System," A paper prepared f o r the Canadian Transportation Research Form Annual Meeting, 1977. Ruiter, E.R., Transportation  "Implementation of Operational Network Equilibrium Proceedures," Research Board, 491, 1974.  Ruiter, E.R., M.A. F l o r i a n (ed) "Network Equilibrium C a p a b i l i t i e s f o r the UMTA Transportation Planning System," T r a f f i c Equilibrium Methods,' Proceedings of the International Symposium Held at the Universite de Montreal, Springer-Verlag, New York, 1976.  112  Shortreed, J.H. (ed) Urban Bus Transit: A Planning Guide, The Transport Group, Department of C i v i l Engineering, University of Waterloo, Waterloo, Ontario, 1974. Wardrop, J.G., "Some Theoretical Aspects of Road T r a f f i c Research," Proceedings, Institute of C i v i l Engineering, Part I I , 1952. Whitlock, E.M., "Use of Linear Programming to Evaluate Alternate Parking S i t e s , " Highway Research Board, 444, 1973. Wigan, M.R., (M.A. F l o r i a n (ed)), "Equilibrium Models i n Use: Practical Problems and Proposals for Transport Planning," T r a f f i c Equilibrium Methods, Proceedings of the International Symposium Held at the Universite de Montreal, Springer-Verlag, New York, 1976.  APPENDIX  A  DEVELOPMENT OF A MODE SPLIT MODIFIER  114  "  APPENDIX A  The f o l l o w i n g i s a d i s c u s s i o n on t h e development mode s p l i t .  The computation o f t h e t r i a l mode s p l i t  the methodology  of a modifier  of the  i s the p i v o t a l point of  s e t out i n the main t e x t . The t r i a l mode s p l i t  computes  the new t r a n s i t - a u t o demands f o r the next i t e r a t i o n . T h e o r e t i c a l l y t h e t r i a l mode s p l i t  can range from t h e o l d mode s p l i t  mode s p l i t  i n f a c t i s the t r i a l  mode s p l i t  i s computed based on the l e v e l o f s e r v i c e and s e r v i c e a t t r i b u t e s  of t h e p r e s e n t i t e r a t i o n . s p l i t within  split  t o t h e new mode s p l i t .  The o l d  o f t h e p r e v i o u s i t e r a t i o n . T:he new  I t was found t h a t t h e v a l u e o f t h e t r i a l mode  t h i s range had a s i g n i f i c a n t i n f l u e n c e on t h e convergence o f  the s o l u t i o n . F i g u r e s  17 a to b i l l u s t r a t e the e f f e c t o f d i f f e r e n t m o d i f i e r s  on t h e convergence o f t h e s o l u t i o n . The purpose o f t h i s appendix was t o develop a m o d i f i e r  o f t h e new mode s p l i t  such t h a t t h e t r i a l mode s p l i t  would produce a s w i f t convergence to t h e s o l u t i o n . I t was n o t p o s s i b l e  t o develop such a m o d i f i e r m a t h e m a t i c a l l y and  a c c u r a t e l y p r e d i c t i t s e f f e c t s . T h i s was due to t h e i n d i r e c t n a t u r e o f obtaining  t h e e q u i l i b r i u m s o l u t i o n ; see Chapter 3 s e c t i o n 3.1. I t was  n e c e s s a r y t o determine the f u n c t i o n o f t h e m o d i f i e r  e m p i r i c a l l y . Two  approaches c o u l d have been taken i n o r d e r t o s o l v e t h i s problem. The f u l l set o f computer functions  programs  c o u l d have been w r i t t e n and r u n u s i n g d i f f e r e n t  t o compute t h e m o d i f i e r .  i s o l a t e the e s s e n t i a l functions  T'he second approach would have been t o  i n t h e l a r g e r framework and b u i l d them i n t o  a small, system which r e p l i c a t e s t h e l a r g e r system. I t was d e c i d e d t o take the second approach because i t was thought to be more f l e x i b l e and amenable to e x p e r i m e n t a t i o n . I t was a l s o l e s s c o s t l y and time consuming first  than t h e  approach. The draw-back o f t h e second approach would be t h e l o s s o f  an u n d e r s t a n d i n g o f t h e exact b e h a v i o u r o f t h e l a r g e r system.  FIGURE  17  PARKING PRICE INCREASE FROM $1.50 TO $2.50  (a)  (b)  m o d i f i e r = .25  timei min.  timei min. 50 h  50 h  40  40  30  X  X  X  X  X  1 2 3 4 5 6 7 8 9  10  30  X  X  X  X  2 3 4 5 6 7 8 9  10  iterations  iterations  (c)  m o d i f i e r = .50  (d)  m o d i f i e r = .75  m o d i f i e r = 1.00  timei min. 50 h  40 h  30 h X  X  X  X  1 2 3 4 5 6 7 8 9 iterations  10  1 2 3 4 5 6:i7 8 9 10 iterations  116  FIGURE  18  AUTO TRAVEL TIME VERSUS NUMBER OF ITERATIONS (a) m o d i f i e r = f ( l o g i t f u n c t i o n )  (b) m o d i f i e r  t ime min.  time min.  50  50  40  40  30  J  L  J  30  L  ] _ f|Z(logit dx  JL  •  I  I  function)  L  1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 iterations iterations ORIGINAL PARKING CHARGE = $1.50 INCREASE PARKING CHARGE TO $2.50 (b) m o d i f i e r = (c) m o d i f i e r = f ( l o g i t f u n c t i o n ) time min.  time min. 50  50  40  40  30  30  1 2 3 4 5 6 7 8 9  10  1 _ f^(logit dx v  function)  -L  1 2 3 4 5 6 7 8 9  iterations iterations ORIGINAL PARKING CHARGE = $0.00 INCREASE PARKING CHARGE TO $1.00  10  117  The c o m p o s i t i o n o f the t e s t framework was d i c t a t e d r e q u i r e d by the l o g i t larger  model and the c r i t e r i a  framework as much as p o s s i b l e .  that  by the i n p u t s  i t s h o u l d resemble t h e  The e s s e n t i a l  elements o f the l a r g e r  system a r e the p a r k i n g a l l o c a t i o n , auto assignment, t r a n s i t passenger assignment, mode s p l i t models and e q u i l i b r i u m Chapter 3 s e c t i o n  3.2.. The i n p u t s t o t h e l o g i t  a l g o r i t h m ; r e f e r t o F i g u r e 7, model a r e , t h e t r a n s i t  travel  time, auto t r a v e l time, number o f m i l e s t r a v e l l e d by auto and the p a r k i n g costs;  r e f e r to Chapter 5 s e c t i o n  5.6 e q u a t i o n 23.  The p a r k i n g a l l o c a t i o n model was not i n c l u d e d i n the t e s t f o r the f o l l o w i n g  framework  reasons:  (1)  I t d i d not have d i r e c t i n p u t t o t h e l o g i t  (2)  The network to be run on the t e s t framework was such that not  be a f f e c t e d  model; r e f e r  to F i g u r e 7. i t would  by t h e p a r k i n g a l l o c a t i o n model.  The t e s t system i s shown i n F i g u r e 19 below; r e f e r t o F i g u r e 7 f o r a comparison w i t h the f u l l s c a l e  FIGURE 19  transit person t r i p demand  system.  MODE SPLIT MODIFIER TEST SYSTEM  transit t r a v e l time computation  auto t r a v e l time computation  l o g i t model mode s p l i t  revised transit demands  equilibrium algorithm auto-transit demand  revised auto demands  auto person t r i p demand  118  The important aspect to be considered i n the choice or development of the functions to compute transit and auto t r a v e l times was not that they be exact or extremely accurate; they must be responsive to changes i n demand and representative of the subsystems being modelled. The test network was simply a 6 mile long road with a free flow v e l o c i t y of 25 mph. I t was assumed to carry buses as well as cars. One end of the l i n k was assumed to originate i n the suburbs and the other i n the C.B.D.. It was assumed that there was a parking l o t i n the C.B.D. which would accomodate any s i z e demand. The demand for both bus and auto t r a v e l was assumed to be distributed uniformly over the length of the l i n k . The functions f o r each of the stops i n the test framework are given below: 1.  Auto Travel Time K = PD / (AO x M)  26  , 1.8 .,• V = VF (1-K/KJ) .  27  T = V /M where:  —  28  V = velocity VF = free flow v e l o c i t y K = density of cars on the road KJ = the jam density M = the number of miles PD = person t r i p demand by auto AO = auto occupancy  Equation 27 was developed by May - K e l l e r ^ and computes the average v e l o c i t y on a l i n k as a function of the free flow v e l o c i t y , jam density (200 cars per mile) and actual density. The actual density i s a function of the demand f o r t r a v e l by car. In order to compute the average v e l o c i t y the auto person t r i p demand was translated into vehicle demand by assuming  119  t h e r e were 1.2 p e r s o n s per c a r . T h i s demand was t h e n a s s i g n e d t o t h e r o u t e as a u n i f o r m d e n s i t y over t h e l e n g t h o f t h e l i n k . T h i s d e n s i t y i s t h e n used i n e q u a t i o n 27 to determine the average v e l o c i t y and e q u a t i o n 28 computes the a c t u a l auto t r a v e l t i m e o v e r the l i n k . 2.  Bus T r a v e l Time BT = AT x 1.15 + BP x LT  where:  29  BT = t h e bus t r a v e l t i m e over the r o u t e AT = t h e t o t a l auto t r a v e l t i m e o v e r t h e r o u t e BP = t h e number o f bus  passengers  LT = t h e l o a d i n g t i m e p e r passenger The bus t r a v e l time i s computed as a f u n c t i o n of the auto t r a v e l t i m e and the number o f passengers u s i n g t h e bus. The 1.15  f a c t o r a c c o u n t s f o r the  s l o w e r average speed o f t h e bus due /to s l o w i n g down f o r bus s t o p s . The number o f passengers and l o a d i n g time per passenger account f o r t h e stopped t i m e o f the bus. 3.  The L o g i t Model  The l o g i t model i s the same as d e f i n e d i n e q u a t i o n 24 and 25 i n t h e main r e p o r t and a r e r e p e a t e d here f o r c l a r i t y P  c  =  e  GC*)  /  ( 1  +  e  G(x)  sake.  )  £.:..= -.83 + 1.27TJT; / TC + .095  2 4  (.35  / MILES x  - .615 EPC where:  .08) 25  P^ = t h e p r o b a b i l i t y of u s i n g t h e c a r ITT = t r a n s i t t r a v e l time i n c l u d i n g out o f v e h i c l e t i m e TC = auto t r a v e l t i m e i n c l u d i n g out of v e h i c l e t i m e MILES = l e n g t h of t r i p i n m i l e s EPC = t h e c o s t of p a r k i n g the c a r  120  The Development of the Modifier Function As noted e a r l i e r the value of the modifier function must l i e between the values zero and one. Also as noted e a r l i e r the t r i a l mode s p l i t i s a sfunction of the old mode s p l i t , new mode s p l i t and the modifier.  Equation  30 shows this function. M  T  where: M  =  M  x  = the modifier  Q  + ''xC M  N  - M  Q  )  30  = the mode s p l i t and the subscripts N = new 0 = old T = trial  A two step approach was taken i n defining the modifier. F i r s t an optimal range of the function was defined. T h e o r e t i c a l l y i t was known that the value l i e d between zero and one but i t was. hoped to narrow the range by t e s t i n g the system with d i f f e r e n t values i n that i n t e r v a l . The second step a f t e r an optimal i n t e r v a l was defined was the testing of several functions which produced values within the optimal range. Four values were selected for the i n i t i a l test. They were .25, .5,  ,75,  and 1.0. A heavily congested network and mode s p l i t values between ,4 and .6 were used for this experiment. These conditions were selected because (1) the t r a v e l times on a heavily congested network are s e n s i t i v e to small changes i n demand and (2) the slope of the l o g i t function i s at i t s greatest within the values defined above and hence i s also most sensitive to changes i n input paramet-^ ers. The convergence of the system can be determined by examining any of the following values: the auto t r a v e l time, the transit t r a v e l time and the ......  121  a u t o - t r a n s i t t r a v e l demands. When the d i f f e r e n c e between any one of these values from one i t e r a t i o n t o the next i s equal to zero or i s small then the system i s s a i d to have converged to a s o l u t i o n . The auto t r a v e l time was selected as the parameter to be used t o t e s t f o r convergence. Figures 18 (a) (b) (c) (d) show the auto t r a v e l time versus the number of i t e r a t i o n s f o r each modifier. Table 10 shows the values f o r a l l of the . parameters through the i t e r a t i v e process f o r each of the modifiers. I t can be seen that the system converges to a s o l u t i o n f a s t e s t when the modifier . i s equal t o 0.50. I t appears then, that the optimal range f o r the modifiers when the mode s p l i t i s between ,4 and .6 i s the i n t e r v a l from .25 to .75. Further, i t appears that i n t h i s case i t would not be p o s s i b l e to improve upon the r e s u l t s produced by the .5 modifier. Table l^'tb^sRows that a s o l u t i o n was reached i n 3 to 4 i t e r a t i o n s . I f t h i s was reduced to 2 to 3 i t e r a t i o n s then that would be close to achieving a d i r e c t s o l u t i o n . The f i r s t i t e r a t i o n i s r e a l l y the conditions associated with the $1.50 parking p r i c e . The ultimate then would be t o achieve convergence i n the t h i r d , p o s s i b l y the fourth i t e r a t i o n . The l o g i t function ranged between .54 and ,46 f o r these experiments and the modifier selected was .5, approximately the value of the l o g i t function. I t was thought that the l o g i t function i t s e l f could be used as a modifier. In other words when the mode s p l i t of the previous i t e r a t i o n i s .8 and the mode s p l i t of the current i t e r a t i o n i s .7 the modifier would be equal to .8. T h e o r e t i c a l l y t h i s was thought t o make sense because the slope of the l o g i t function approaches zero as i t s value approaches the l i m i t s of zero and one. Greater changes are allowed where the f u n c t i o n i s l e s s s e n s i t i v e to changes. The t r i a l mode s p l i t then i s computed as f o l l o w s : when  M  ^  .5  122  M = M„ + M„ (M - M j T 0 O N 0 m  when  T  MQ  ^  .5  M_ = M. + ( 1 - M_ ) ( M. - M. ) T 0 O N 0 T  The variables and subscripts are as defined e a r l i e r . A second modifier function was developed for comparison purposes. This function was based on the slope of the mode s p l i t . The derivative of the l o g i t function was taken and i s shown below: S = e - / (1 + 2 e ' :X  X  + e ' 2  )  X  31  where S = the slope of the l o g i t function -X-' = generalized cost difference between modes S MAX  s  M T M  MIN  = .25  @  '' = 0 x  L  = 0  @ V-= ±  The maximum value of the slope occurs when the generalized cost difference between the two modes equals zero and i s equal to .25. The minimum occurs when the generalized cost difference i s p o s i t i v e or negative  i n f i n i t y and  i s equal to zero. The purpose of the modifier i s to reduce s h i f t s i n the t r i a l mode s p l i t . I t i  s  not possible to use the slope d i r e c t l y for this  purpose but the residual function, ( 1 - S. ) s u f f i c e s . The value of this function when the generalized cost difference i s zero i s equal to .75. The t r i a l mode s p l i t using the slope residual i s computed as follows: M  T  = M  Q  + ( 1 - S ) (  - M  )  Q  32  A l l variables are defined previously. Four scenarios were tested i n order to determine the performance of the modifier functions. These scenarios were divided into two,groupings. The f i r s t entailed parking p r i c i n g changes on a heavily loaded network when, r  the mode s p l i t was i n the range of .4 to .6. The second was performed on a heavily loaded network when the mode s p l i t was i n the range of .7 to .8.  123  One p a r k i n g p r i c e i n c r e a s e o f $1.00 was considered;' The base p a r k i n g p r i c e f o r the mode s p l i t  range o f .4 t o .6 was $1.50 and f o r the .6 t o .75  range was $0.00. A t these base p r i c e s the average  auto speed on t h e r o u t e  was a p p r o x i m a t e l y 7 m i l e s p e r hour. A f t e r the p r i c e i n c r e a s e s i t was approximately 1081  9 m i l e s p e r hour. The demand a t the $1.50 base p r i c e was  persons by c a r and 918 by t r a n s i t and a t the $0.00 base p r i c e was 1083  by c a r and 446 by t r a n s i t . The auto demand was m a i n t a i n e d e q u a l i n both cases so t h a t the t e s t s would be performed  approximately on the r o u t e s w i t h  the same l e v e l o f c o n g e s t i o n . The  t e s t showed t h a t the l o g i t f u n c t i o n m o d i f i e r was s u p e r i o r t o the  d e r i v a t i v e o f the l o g i t  f u n c t i o n . In f a c t i n each t e s t case the e q u i l i b r i u m  s o l u t i o n i s a t t a i n e d a f t e r 4 i t e r a t i o n s and i s v e r y c l o s e a t the t h i r d i t e r a t i o n when the l o g i t graphs  f u n c t i o n m o d i f i e r i s used. F i g u r e 18 shows the  o f t h e auto t r a v e l times v e r s u s the number o f i t e r a t i o n s . T a b l e 12  i l l u s t r a t e s a l l o f the parameters  in detail.  S e v e r a l more t e s t s were con-  ducted w i t h the l o g i t m o d i f i e r under d i f f e r e n t c o n d i t i o n s .  In a l l s i t u a t i o n s  a s o l u t i o n was a t t a i n e d a f t e r 3 t o 4 i t e r a t i o n s . T a b l e 13 shows the r e s u l t s of these t e s t s . be  used.  I t was d e c i d e d a t t h i s p o i n t t h a t the l o g i t m o d i f i e r would  124  TABLE I I  THE ITERATIVE PROCESS USING FOUR CONSTANT MODIFIERS PARKING PRICE INCREASE FROM..$1.50 TO $2.50  (a) modifier = .25 ITERATION NO. 1 2 3 4 5 6 7 8  .. AUTO ..... BUS TIME TIME 54 54 45 41 39 38 38 38  AUTO TRIAL NEW MODE SPLIT MODE SPLIT DEMAND  BUS DEMAND  79 79 70 66 64 63 63 63  .54 .39 .42 .43 .44 .45 .45 .46  .54 .50 .48 .47 .46 .46 .46 .46  ...1081 1005 962 938 926 920 917 915  918 994 1037 1061 1073 1079 1082 1084  79 79 63 63 63  .54 .39 .46 .46 .46  .54 .46 .46 .46 .46  1081 916 913 913 913  918 1082 1086 1086 1086  79 79 58 65 62 63 62 63  .54 .39 .49 .44 .46 .45 .46 .46  .54 .43 .47 .45 .46 .46 .46 .46  1081 853 945 899 920 909 915 913  918 1145 1053 1100 1078 1089 1083 1086  79 79 55 77 55 76 56 75  .54 .39 .53 .39 .53 .40 .52 .40  .54 .39 .53 .39 .53 .40 .52 .40  1081 778 1066 787 1054 796 1044 802  918 1221 933 1211 944 1203 956 1196  (b) modifiei- = .50 1 2 3 4 5  54 54 38 37 37  (c) modifiei: = .75 1 2 3 4 5 6 7 8  54 54 33 40 36 38 37 37  (d) modifieic = 1.0  1 2 3 4 5 6 7 8  54 54 28 53 29 51 30 50  . ALL TIMES ARE IN MINUTES DEMANDS ARE IN PERSONS  125  TABLE 12- THE ITERATIVE PROCESS USING TWO MODIFIER FUNCTIONS (a)  PARKING INCREASE $1.50 t o $2.50  ITERATION NO. 1 2 3 4 5  (b)  54 54 38 37 37  79 79 63 63 63  .54 .39 .46 .46 .46  54 54 33 40 36 38 37 38  79 79 59 65 61 63 62 63  .54 .39 .49 .44 .46 .45 .46 .45  55 55 39 39 39  71 71 55 55 55  .71 .57 .61 .61 .61  PARKING INCREASE $0 .00 t o $1. 00  1 2 3 4 5  TRIAL MODE SPLIT  function)  AUTO DEMAND  BUS DEMAND  1081 916 914 913 913  918 1082 1085 1085 1085  i  PARKING INCREASE $0 .00 t o $1. 00  1 2 3 4 5  Cd)  NEW MODE SPLIT  BUS TIME  PARKING INCREASE $1.50 t o $2.50  1 2 3 4 5 6 7 8  (c)  AUTO TIME  modifier = f ( l o g i t  55 55 38 39 39  TIMES ARE IN MINUTES DEMANDS ARE IN PERSONS  71 71 55 55 55  .71 .57 .61 .61 .61  .54 .46 .46 .46 .46  m o d i f i e r = 1 - f --f- ( l o g i t  .54 .42 .47 .45 .46 .45 .46 .46  function)  918 1150 1052 1102 1078 1090 1080 1088  1081 849 947 897 921 909 919 910  modifier = f ( l o g i t function)  .71 .61 .61 .61 .61  m o d i f i e r = 1-  .71 .60 .61 .61 .61  1083 930 929 929 929  (logit  1083 920 931 930 930  446 598 599 599 599  function)  446 608 598 599 599  126  TABLE 13'  (a)  VARIOUS PARKING INCREASES AND CONGESTION LEVELS USING THE LOGIT FUNCTION MODIFIER  PARKING PRICE INCREASE $2.50 to $2.75  ITERATION NO. 1 2 3 4 (b)  AUTO TIME  BUS TIME  37 37 35 34  63 63 60 60  NEW MODE SPLIT .46 .42 .44 .44  PARKING PRICE INCREASE $2.50 to $2.75  1 2 3 4 (c)  17 17 16 16  29 29 28 28  .47 .43 .45 .45  PARKING PRICE INCREASE $2.50 to $3.50  1 2 3 4  Cd)  1 2 3 4 5  37 37 29 28  63 63 55 55  .46 .31 .38 .39  PARKING PRICE INCREASE $2.50 to $3.50  17 17 15 14 14  29 29 28 28 28  TIMES ARE IN MINUTES DEMANDS ARE IN PERSONS  .47 .33 .37 .38 . 38  MODERATELY CONGESTED  TRIAL . AUTO MODE SPLIT ': DEMAND .46 .44 .44 .44  914 879 876 876  BUS DEMAND 1086 1120 1123 1123  LIGHTLY CONGESTED  .47 .45 .45 .45  471 453 449 449  528 546 551 551  MODERATELY CONGESTED  .46 .39 .39 .39  914 782 773 772  1086 1218 1227 1228  LIGHTLY CONGESTED  .47 .40 .39 .39 .38  471 402 389 386 386  528 597 609 612 612  127  FOOTNOTES  1.  A.D. May, H.E. K e l l e r . , "Non-Integer Car Following Models," Highway Research Record, 199, 1967, pp. 19-32.  APPENDIX  B  THE COMPUTER PROGRAM BUS  (SHIN '1=1' ( i ) n a H i N ) (s's) 3V33  ( 8 d O N ' L = l ' (I) d X S 3 N ) * * * * * * * * * * * * * * * * * * sit * * * * * * * * * * * * * * * * * * *  (S'S)aVld  3 S N O i i V H i x s a a NV S N I 9 I H O I I S H V B I QNV a i n v NT a v 3 a 3 3 ******************************************* ********************3 0=IZT 3?nZN*3 = XXI o*o=aowi  0 '0=1113  * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * **********°jr*<i<*:****#*3 3  XXT3 3HX H31N3 S3 NIT' S03 353 HM S3GON 3HX =uHHIN vaav xanxs 3HX a a x o s a w n sna SHSHK SSGON 3 0 OR 3 H i =HHXN xno  SI  swiaa  aaiKiaa  HDIBM SX3VXS 3NI*I SO0 V H3II1M XV SOON. 3HX =dIS3N XQO a a X N I H d 3 3 OX S3 N i l Su3 30 *0N 33X =dS3N SHXVd EOWTNIH 3HX 30 S300N N 0 I I V N I X S 3 G 3HI =CiIdON NISiaO 3 H X Id01 * HUM <33XNiad 33 OX SHXV3 WnWIWIW 30 "OH 3HI =GdON QSLNIHd 33 OX HXVd UOWIKIW 3HX 30 NI9IH0 3HX =X30I s N o i x v a a x i XNanOasans GNV anz=i N o i x v a a x x XSL=O xaaur MOIXVS3XI aex =aoi  3 3 3 3  D 3 3 3 3  3 3 3  * ******** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ***** D 3 3  L566 OX 09 (NDiaON *3N * 3 3 S I l ) 31 saos ' a a o R ' x a o i ' a s i ' a o i a s a ' s i * a n o s 9 W ' 2 N o z N ' x x 3 N ' M N i T N ' i s 3 G N + 'NSIHON'XSIN ' 3 3SXR ' 3 3 V 3 33 '(IHV03 'dOXSR ' 3 N I T T ( S 3 ' 9 ) 3 1 i a M '  "• '  .  aaoN'eaoN'+  U ' S ) 3V33 (3L)GV3a 3 M i l l (EL) 3V33 HX'SV7.3Nl'lX3N'anOHSN'SROZrc (8L)aV33  i a O l ' a 9 l ' a H I N ' d O X S N ' 2 S I N ' 3 3 S X N '3HV03 XS*3GN'N9iaON'3(IONH'MITN'XSVI ' G 0 I H 3 d ' 3  3  V  3  3  G  D  ***************************************************************3 D  S 3 3 I 3 E V H Y d KVH90S3 NT dVIH  3 3 ***************************************************************3  (XSI ' l ' 0 0 8 ' 0 t ? 3 ) «/ 3113 3NI33Q • (OOL) 3' (OOty)MMISaK' ( S L ) 3 N ' ( 0 S L ' 0 S L ) d t t ' + (OOL'OOL'E) GOX' (OSL ) 3 ' (OE) 3N0ZW' ( O S L ' O S L ) « ' (0S3> A V X V + (0S3) SNISAN ' ( 053) SIGV (0S3> AVI' (0S3) AVX3 ' (OE) 3 K 0 Z T ' + (SL) 3 W (SL) S f ' (OOL 'OOL ' £ ) O ' (OOL'OOL) RIO /JIHVaYNOHWOD (OOSD 3 V X I ' (OOSL ) RN' (OOSE) 03 3 d l /SStfV SOW MOD 0 3 3 3 T 1 3 ' (OOSL ) 3 0 S 3 3 d ' +  6 Z l  s H r i V i a ? oa'+ DOV030' (S'OOSL) NNN' (005 L ) N 0 S H 3 d ' (000L)GV3H/3WX/N0WW0D (OOSL) S333' (OOL3) ON' (OOL Z) XSIQ * (OE' OOL3) Sf!3N + ' (0 0L3)X3N' ( 0 0 L 3 ) a N ' 3 a O N N ' X S V 3 ' M M I 3 N ' (OOSL)IHI' + (os*OOSL) IN' (OOSL) AVH'I' (ooie) M u n i ' (OL 'oost) a a n H n + '(OOSL)aaawnN'(OOSL)IQN*(OS'OOSDOXX /NIZW/KORWDD (os) a x a o N ' (os i) A v i a ' (OSL) XXND' + (001?) ON' ( f t ' O O L 2 ) M3 ' (f7 'OOL Z) SN ' (83 'OOSL) 3 X R ' (OOSL) U N ' + (OOL) a x a o N ' ( OE) P.HHXN ' ( o o t ) HI a * (oo L) a x s a N ' (OOL ) SON * + (OSL) A v a x V (os3) w n a ' (0S3) a x v w ' (0S3) o x v w N D i s M i w i a (053) OXXW' (0S3)QXXW' ( 0 3 ' 0 0 O L ) HKVR ' (053) SIG R0ISN3WICI  i+(NW)aaawnN= (NU)diawnN N W = (I) 0 N N = (I)GM (E'L=W ( W ' N ) » 3 ) ' (E'l=W (H'NW) M 3 ) ' (C't=W' (M *N> 3S) ' + (E' i=w'(w 'NH) SN ) M i ) M m ' ( i ) i s i a 'N 'NW ( c H ) a v 3 3 xi=-(i) IHH (XT 'L = M' (M 'I) SOON) 'XI ( E l ) a ? 3 S MKI1N'L=I 031 OQ sq^buax  5 saffiiq.  TSAEI;  MUTT  'seavu  ;eei^s  pp^H /  D D O  (EE ' 9 ) 3 1 1 3 * SflNIIMOD 5 3 1 H R= (I)ON a if 3HT= (WM.) a van ( 8 L ' I =M ' (M * W N ) 3 W VM) * Q^3III' MN (Ct)aVlH a n m ' i = i 5cU oa 3 sAEtfpeaq  put;  seuxx  D  snq p^eg  D  3 DM U N 03 t = (ww) im WW  091  1 V I 3  <JOISN*l=I DEL Oa s d o ^ s s n q ppsa aOMIIMOD 0 = (I) U N ' 0=(T)ttN o=(i)xas o "0= ( i ) i o s a g d 0'C = ( D N DS 333  D D Sll  0 = ( I > 1 S N  0= (I) d3IWriM X S V T ' L = I 511 oa (c"E'9> 31IHM 0t?l ***************************************************************3 0  smm.  N O S3NH  sne O N ? S M N i i ' s a a o N a - o N T a t f i s  D  D * ** ** * * * * * * * * * * * * * * * * * * * * * *************************************D anNiLNoa o o i (6666=aa3 LD a\fia M I = (MM) i » r ( M T ' L - N ' ( N ' H M ) I L N ) 'MM'HI (0i7l=ati5 ' L l ) 3 V 3 3 OOOE'I=I o o i oa ***************************************************************o ( I'L=N' (N'M^)OiLi) V  J  0  SdOIS SOB W08J QMV 01 S3KIX  ST 3tf33  3 0  * * * * * * * * * * * * * * * ************************************************D (L t *9> 3 I I H M ' l =1' (I) M T S A N ' (I) Q.LVW) ( 9 ' S l ) a V 3 3 (NOItfON. ' l = l ' (I) oivw) (s'siJavaa (0E'9> 3II3M (MS1N ' 1=1' (I) MNISdK ' (I) a i l W ) (9'S)aV33 (3 DSIN * L =1 * (I) 01IW) (Z'9) Jtflff • (adON' i = i ' ( i ) aidON) ( s ' s ) a v i a (adON'l=I* (I) 0X3ON) ( 5 ' S ) a V 3 B  (IS3CIN  OCT  JJ=NUMDEP (Mitf) LINKDP (MN,JJ)=-I 120  C C C  150 C C C 155 160  161 C C C 164  165 C C  c 170  1  3  1  CGNHNDE  WFITE(6,34) Read i n e l a s t i c auto demand IF (IN£L AS. N E. 1) GO TO 155 DO 150 I=1,N0RIGN EEAE (19,7) (CIN(I,K) , K= 1 , NZON E) CON 1IN U E Read e l a s t i c a u t c demand DO 160 M=1,NGROUP DC 160 I=1,NOBIGN BEAD (19,7) (0(M,.I,K) ,K=1 ,KZON£) CONTINUE WKITE{6,35) If(NEXT.EQ.0) GO TO 16U DO 161 I=1,NORIGN RI AI (19,4) F Read t r a n s i t demand DC  16 5  fl=1,NGBOUP  DO 165 I=1,NOBIGN BEAL (19,7) (TOD(H,I,K) ,K= 1,NZONE) CONTINUE WRITE (6,36) Read parking data  .  DC 170 K=1,NZONE REAC(18) J5 (K) , MR (K) ,LZCNE(K),HZCNE(K) ,C (K) CCMUMUE  WRITE (6, 37) C C C  Read walk t r a v e l  times  READ (18) ( (W ( 1 , K) ,L=1 , NZCNE) ,K=1 ,NZGNE) BEAD (18) ( (WP (L, K) , L= 1, NZCNE) ,K= 1 ,NZONE) WBITE(6,.38) C C 180.  DC 180 1=1, NZCNE MC(I)=0 CONTINUE DC  190 C C C C  190  M=1,N1SK  LL= NPSINK (t'i) L=M ZO N E(LL) NC (I)=NC (L) +1 CONTINUE F i r s t e x e c u t i o n cf minpth witout passenger l o a d i n q DC 300 Assignment I=1,NTSCii of passengers t c bus l i n e s and stops N HO ME = M TTO (I) CALI MINPTH (MHOf-lE, MTTD, NTSK,0,NS , EW , NTHR, NTHRU, NOPTD , NOPD)  300  r  CALL ASSN (FJTTD, N HOME, NTSK , NZONE, NG ROUP ,I,TOD ,NC , NPSINK +,MZCNE,PERIOD) CONTINUE  C C  I n i t i a l i z e scalars  f o r manaqeinent o f s e q u e n t i a l  132  file  II=NEXT+1 IXT=2*NZONE+3 IXXT=NZCNE+1 IZT = 0 C C C  C C C C C C C  470 C C C  480 C C C 320 C C C  Read t o t a l t r i p t i t c e and l e n q t h  from u n i t  12  passenqer  loading  K B I T E ( 6 , 19) DC 400 I=1,NTSCE NHOME=MTTO(I) READ (12) (DIS (J) ,J=1,N DEST) REAC(12) (ATRAV (J) ,J=1,NDEST) Second e x e c u t i o n CALL  c f minpth  with  MINPTH(NHOME,MTTD,NTSK,IOPT,NS,EW,NTHB,NTHRU,NOPTD,NOPD) " I n i t i a l i z a t i o n of v e c t o r s i n p r e p a r a t i o n f o r s u b r o u t i n e SPLIT  DG 470 L=1,NZONE TAV(L)=0.0 ETAV(L)=0.0 ADIS(L)=C0 ATAV{l)-0.0. 'CNT1 (L) =0.0 I F (NC (L) . EG. 0) TAV (L) = 9 9 9 9 9 9 . I F ( J S ( L ) .EQ.0) A D I S ( L ) = 9 9 S 9 9 9 . 'CONTINUE Aggregate data  f r o m node l e v e l  t o zone l e v e l  f o r SPLIT  DO 480 M=IL,NDEST LL=NVSINK (M) L=MZCNE ( I I ) I F ( J S (L) . EQ. 0) GO TO 480 ADIS (L) = ADIS (L) +EIS { M J / I L O A T (JS (L) ) A l A V (L) = ATAV (L) + ATRAV (H) /FLOAT (JS (L) ) CONTINUE Bead w r i t e I F (IGE. EQ. 0) GO TO 340 / I2T=IZT+1 IS1=IZT  auto t r a v e l  times to seguential  GO TO 320  First iteration  write  to sequential  • WRITE (4'1ST) (ATAV (J) ,J= 1 ,NZONE) IXXT=IXXT+1 IST=IXXT . WRITE.(U 1ST) (ATAV(J) ,J=1,NZCNE) 3 4 0 ' I F ( I G D . G E . I ) GO TO 350 1  file  file  1 3 3  350  GO 10 360 IXXT=IXXT+1 IST-IXXT  C  C  2nd 3 r d 4 t h . . . i t e r a t i o n  read  of previous  travel  time  of c u r r e n t  travel  time  C  READ (4'1ST) (BTAV(J) , J= 1 , NZONE) IST=IXXT C  C  2nd 3 r d 4 t h . . . i t e r a t i o n  write  C  WRITE (4'IST)  (ATAV (J) ,J-= 1,NZCNE)  C  C  Preparation  of data  f o r write  of equilibrium  statistics  C  360  4 90  370  TCTALT=0.0 '101 ALE-O.0 TOTALA=0.0 TOTALB=0.0 CCUNT=0.0 DC 490 M=1,NTSK M M- KTTD ( M) KK=NPSINK (fl) K=MZCNE(KK) IF (TRAV (MM) . GT. S99990) GO TO 490 TAV (K) = T5V (K) +TRAV (MM) ETAV (K) = ET A V (K) +ECES (MM) TOTAIT= TOT ALT +T R AV (MM) - EC ES{ MM) TOTALE=TGTALE+ECES(MM) CCUKT=CCUNT+1 CNTT (K) =CNTT (K) + 1 CONTINUE 1GTALE=T0TALE/(CCUNT*60) .TCTAIT=TCTALT/(CCUNT*60) DC 370 J=1,NZONE I f (-1GD.LT. 1) ETAV ( • J) =0.0 TOT AI A= TOTAL A + AT A V (J) TOTAL B= TO TALB + .BTAV(J) TAV (J)=T AV (J)/CNTT (J) ETAV (J) =ETAV (J) /CNTT (J) CONTINUE TOTA LA=TOTALA/(NZONE*60) TOT AlB=T CT ALB/(NZGNE*60)  .  C  C  Write  equilibrium  data  c  WHITE (6 ,21) WRITE (6, 29) WEITE(6,22) WHITE{6,23) WRITE (6,20) (NS (NH0ME,M) ,M=1,3), ( E3 (NHOME, N) ,M=1,3) +,TC1 ALA,TOT ALB,TOTALT,TCTAIE C C C C 400  C a l l SPLIT demands  compute  mode s p l i t  and new  auto-transit  CALL SPLIT (I,NHOME,N GRUU P,NZONE, IG E,IXT,DIFr,IMOD,TMA X) CONTINUE  C  C  Write  eguiliorium  statistics  produced  b y SPLIT  134  c  455  450  460 C c c 510 C C C 550  C C C  REWIND 19 WRITE (6,24) KRITE(6,26) WRIT£(6,27) DO 450 H=1,NGROTJP DO 450 I=1,NOEIGN TTOIAL=0.0 A1G1AL=0.0 DC 455 K=1,NZONE TTOTAL=TTOTAL+TOC (H, I , K) A101AL=ATOIAL+0 (M , I , K) CONTINUE S P L l = ATOTAL/(ATO-TAL + TTOTAL) NHC HE=MT'TC (I) WBITE(6,12) (NS(NHOME,!) ,1=1 ,3) . {EW(NHOME,L) ,L=1,3) *, ATOTA; ,TT OTA L, SPIT WRITE (19,7) (0 (M,I,K) ,K= 1 ,NZONE) CONTINUE DO 460 M=1,NGROUP DO 460 I=1,NOFIGN K R I T E ( 1 9 , 7 ) (IOD(M,I,K) , K= 1 ,NZONE) CONTINUE  I F (IGD. GT. 0) GO TO 510 GO TO 550 ER R C R= DI FF/TMGD WHITE ( 6 , 11) ERROR \  Print  option  f o r s t a t i s t i c s on b u s l i n e s  I F (NOPB.EQ.0) GO TO 999 8 DC 600 JJ=1,NOPB LIN=NOPTB(JJ) KM=NBSTP(JJ) Call  BNET p r e p a r e  bus l i n e  data  f o rprint out  CALL BN ET{NO B,N B3TP,LIN,N fl,IBT,BT K,NTT,N TR,N U,SP ED) WRITE ( 6 , 13) WRITE (6,14) WRITE (6,15) HEAD (LI N) , L I N , (NAME(LIN,K) , K—1,18) WRITE(6,16) WRITE (6 , 17) DO 650 K=1,IBT NK=NGG(K) B1& (K) = BTM (K) /6 0 I X T - K T T (NM) WEITE{6, 18) (NS (NM,N) ,M=1,3) , (EW (K.H,M) ,M=1 ,3) ,PERSON (NM) , + PEESCF(NM). , ETM ( K) , (NTR{NM,II) , 11=1,IXT) 6 50 CONTINUE - - WRITE (6,28) SPED 600 CONTINUE C C C 1 fCHHA1 (3F8. 2, 1414) 2 FORMAT 114)  3 4 5 6 7 8 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25  26 27 28 29 30 31 32 33 34 35 36  FORMAT ( I 4 , 8 X , I 4 ) 135 FORMAT (F20.0) FORMAT (2014) FORMAT (214) FORMAT(8F10.0) FORMAT (8F10. 0) FORMAT (/10X,'THE P E R C E N T CHANGE IN TRAVEL TIME FROM ONE C I TER AT ICN TO THE NEXT I S ' , F 1 0 . 5 ) FORM AT (1 OX,2 (3A4) , 5 X , f 6 . 0 , 5 X , F 6 . 0 , 1 0 X , F 4 . 3 ) FOEMATf1',10X,» BUSLINE BUSLINE*) FCBMAT (10X, • HEADWAY NUMEER NAME') FORMAT(/10X,F3.0,' MIN•,3X,12,6X , 20A4) F O R M A T ( / 1 8 X , » E U S STOP',14X,* PEOPLE',11X,'PEOPLE' ,11X + ,'LINK,TIME',11X,'BUS LINES') FORM A T ( 1 6 X , ' I N T E R S E C T I O N ' ,10X,•CN THE BUS',7X,'AT T H E S T O P ' + ,7X,'S T CT AL T i a E ' , 8 X , ' A T T E E STOP*) FORMAT(10X,2(3A4) ,8X ,F3.0,14X,F3.0,12X,F5. 1, 10X,1014/89X,1014 +/89X,10I4) FORMAT(////50X, 'EQUILIBRIUM S T A T I S T I C S ») FORMAT (1 OX ,2 (3 A4) ,7X , F6. 1, 5X, F6. 1 , 1 OX , F6 . 1 , 8X, F 6 . 1) FORMAT (///10X,'TRAVEL TIMES FROM THE GIVEN INTERSECTION', +» TO ALL DESTINATIONS') FORMAT (/18X, ' INT ERS ECT IC N ' , 1 1X, » CURRENT' , &X, 'PREVIOUS' + ,6X,'IN VEHICLE ' ,7X, 'EXCESS') FORMAT(34X,2 (4X,'TRAVEL TIME»,4X,'TRAVEL TIME»)} FOR MAT {////10X,'CAR AND BUS S P L I T S FOR THE GIVEN ' +,'INTERSECTION TO ALL DESTINATIONS') FORMAT (/ 10X , ' NUMBER OF BUS L I N E S = ' , I 4 , +/1GX, NUMBER OF BUS ST0PS=',I4, +/10X, BOARDING TIME FOR THE BUS (SEC PER P ER SON ) =' , F4. 1 , +/10X, BUS A C C E L E R A T I O N ( F T / S E C / S E C ) - ' , F 4 . 1 , +/10X, BUS D E C E L E R A T I O N ( F T / S E C / S E C ) = ' , F 4 . 1 , + /1 0 X , NUMEER C F T R A N S I T 0 B 1 G I N S = ' , 1 4 , +/10X, NUMBER OF TRANSIT D E S T I N A T I O N S = ' , 1 4 , +/10X, NU M E ER OF VEHICLE O R I G I N S = » , 1 4 , +/10X, NUM E ER OF VEHICLE D E S T I N A T I O N S ^ ' , 1 4 , +/10X, NUMBER OF LINKS=' , 1 4 , +/10X, NUMBER OF EXTERNAL VEHICLE ORIGINS^' 1 4 , +/10X, NUMBER OF 2 0 N E S = » , I 4 , +/10X, NUMBER C F SOCIOECONOMIC GROUPS=',I4, +/ 10 X , MAXIMUM WALKING TIME='>F 10.0, +/1CX, PERIOD OF ASSIGNMENT^' ,F5.0 , +/10X, ITERATION INDEX=',I4, +/10X, ORIGIN NODE FOR MINIMUM PATH PRINT OUT IS=',.I4, +/10X, NUMBER CF PATHS PRINTED I S = » , I 4 , +/10X, NUMBER OF 1US LINES TO BE PRINTED OUT I S = » , I 4 ) FORMAT(/16 X, ' INTERSECTION' ,11X,'PERSONS',5X, 'PERSONS' ,5X, +'AUTG SPLIT') FORM AT (4OX,'BY CAR',6X,'BY BUS') FCRKAT(///10X,'THE AVERAGE SPEED OF THE BUS IS ' , F 4 . 1 , « MPH. *) FORMAT (/4 7X,'AUTO',2 4X, * BUS') FORMAT(//10X,'DATA FROM UNIT 5 READ IN') FORMAT(//10X, 'VEHICLE ORIGINS & DESTINATIONS FROM * +'UNIT 15 READ IN') FORMAT(//10X,'PEDESTRIAN WALK TIMES FOR TRANSIT READ +'IN FFOM UNIT 11') FORMAT(//10X, ' BUS NETWORK DATA READ IN FROM UNITS 17S13') FORMAT (// "I 0 X ,'VEHICLE S BUS NETWORK READ IN FROM UNIT 12') FORMAT (//10 X, 'AUTO T R I P S READ IN FROM UNIT 19») F C R f A T ( / / 1 0 X , ' T R A N S I T T R I P S READ IN FRCM U N I T 1 9 ' )  37 38  FOB M AT{//10 X , P AE KlNG C AT A READ IN FROM UNIT 18') FORMAT (//10X,'ZONE TO ZONE WALKING TIMES FOR AUTO DRIVERS * +,'BEAD I S FRCM UNIT 18') 50 FORMAT (10X,'IMPROPER REAC IN ON UNIT 11«) 52 FORM AT{'THE NO OF AUTO ORIGINS ',14, 'IS NOT EQUAL TRANSIT ' +,'CBIGINS',14) GC TO 9998 9999 WBITE(6,50) 9997 WRITE{6,52) NORIGN,N TSC E 9 99 8 RETURN END 1  C C  c c  C C  c  C C  c j  SUBROUTINE MINPTH (NHOME,MTTD,NTSK,IOPT,NS,EW,NTHR,NTHRU,NOPTD + ,NOFD) CCMMCN/MEIN/ TTO ( 1 5 0 0 , 5 0 ) , N B L (1500) ,NUMDEP (1500) , + LINK DP ( 1 5 0 0 , 10) , T L I NK (2100) ,TRAV(150 0) ,NT (1500,50) + , I K T ( 1 5 0 0 ) ,NLINK,LAST,NNODE,ND (2100) ,M8T(2100) , *• N BUS (2100, 30) , DIST (2 100) , NO (2 1 00) , EC ES (1 50 0) COMMON/TME/HEAD(1000) ,PERSON (1500) , NNN (1500,5) ,DEC,ACC,LLINE +,£CAEC + ,PERSOF (1500) ,FEEFLO DIMENSION NBU (1500) , I P E D ( 3 5 0 0 ) ,NCUM ( 1500) , TCUM ( 1500) +, ETT D (1500) ,KEEP (5) , TCM (5} , E SE (5) ,NS (2100,4) , EW ( 2 1 0 0 , 4) + ,NTHBU(30) ,NOPTD (50) ,ECUM (1500) COMMON / A S S / I P E E O ( 3 5 0 0 ) ,NN< 1500) ,ITAC(1500) C  C  Initialize  vectors  C  100 105  DC 100 1=1,LAST TRAV (I) =999999. ITAC(I)=0 NN(I)=0 ECES(I) = 0 DO 105 1=1,LAST DC 105 J=1,5 NNN ( I , J ) = 0 N T E E E- 1 N N ( NHCM E) =0 KCM=0 KZZ=0 NK=NKCME / II=NLINK '  C  C C  D e t e r m i n e w h e t h e r niicme i s on a t h r u b u s l i n e  or not  -  110  DC 1 1 0 1=1,NTHR I F ( NHCME.EQ.NTHRU (I) ) GO TO 129 CONTINUE  Q*****************************************************  c  C.  DETERMINE WALK TIMES TC BUS STOP & WAIT TIME FOR  BUS  C C  :SECTION #1  C**************** C C C  i J /  ***********************************************  F i n d walk l i n k s & t i m e s  t o bus s t o p s  IK= IKT (N fl) DC 120 J=1,IK K=N3(NM,J) I F (NBL ( K ) . EQ.O) GO TO 120 SUM = 0 N=0 ECE=0.0 IN= NUMDEP(K) I F ( I N . E Q . O ) GO TO 120  C C C  F i n d bus l i n e s  passinq  bus stop  DO 125 L=1,IN 1 = 11 N KDP (K , L) I f ( N B U S ( I , 1 ) .EQ.O) GO TO 125 IT-NET ( I ) C C C  Compute w a i t t i m e  f o r bus  DC 126 I A = 1 , I T IS=NB0S(I,IA) N=N + 1 SUH=S0M + HEAD (IS) *60.0 126 CONTINUE 125 CONTINUE I F (N. EQ. 0) GO TO 127 EC£=SUM/ (N*2) I F (ECE.GT.210) ECE=. 13*SUM+ 2.3 • I F (PERSON (K) .GT.60) ECE=ECE+SUM C C Enter times S l i n k s into the l i s t C 127 NCM=NCM+1 TCUM (NCM) = TTO (NM, J) + ECE ECUM (NCM) =ECES (NM) +TTO (NM, J) + ECE 11=11+1 NEU(NCM)=2 NCUK (NCM)=11 IPF.B(II)=K I F F DC ( I I ) = NM 120 CONTINUE 1FLAG=0 GC TO 180 r j * * * ************************************* ******** ************ ** * C C C C  DETERMINE TRAVEL TIME -.SECTION #2  EPCM NODE TO NODE BY BUS  r j * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  129  NTH fE-2 NM=NHCME TRAV (NM) =0.0 11=11+1 NN (MS) =11  ,  >  138  C  C C 130  find  vehicle links  d e p a r t i n g t h e bus s t o p  IN= NUMDEP (Nil) NTB=0 I F ( I N . EQ.O) GO TO 180 DO 150 L=1,IN I^LINKDP(NM,L) K=ND (I)  C  C  Determine i f t h e r e a r e buses running  on t h e l i n k  c  145 140  I F (NBUS ( I , 1 ) .EQ.C) GO TO 150 I f (TRAV ( K ) - 9 9 9 9 9 9 . ) 145,140,145 I F ( NN (K) .LE. NLINK) GO TO 150 NCK=NCM+1 KZZ=K2Z+1  C  C C c  For l i n k s on l i n k  w i t h bus l i n e s  call  TIM f i n d  travel  time  C A L I TIM (KM,K,I,TIME, NTREE, EC£,LINK)  C  C  Enter l i n k & times into  list  C  C  C  TCUM |NCH)=TRAV ( N M) +TIME ECUM (NCM)= ECES(NM) + ECE NCUK (NCM) =1 NBU(NCM)=0 I T A C (K) = 1 NZZ = K i I F (NBL (K) . EQ. 1) GO TO 147 GO TO 150 Determine  i fdestination  node i s a b u s s t o p  C  147  150  RTB=NTB+1 KEEP (NTB) = K TCM (NIB) =TCUM (NCM) ESE (NTB) = ECUM (NCM) CONTINUE I F L A G= 1 ICOUNT=0 NM=NZZ I F ( NTB.Gl.0) GO TO 155  C  C C  I f destination  node i s a b u s s t o p qo t o s e c t i o n  3  GO TO 180  r***************************************************************  C  C C C C  '  DETERMINE TRAVEL TIME FBOM LAST BUS STOP TO F I N A L DESTINATION :SECTION #3  rj * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  155  DO 167 J J J = 1 , N T B NQ=KEEP ( J J J ) 'IFLAG=1 ICGUNT=ICCUNT+1  IK=IKT(NQ) C C C  Find  -L walk, l i n k s  from bus s t o p s  DO 160 J = 1 , I K K= N T (NO,J) IZ= 1 I F (TRAV ( K ) - 9 9 9 9 9 9 . )  170 165 C C C C  170, 165, 170  ABC=TRAV (K) AE-TRAV (NG) +TTO (NQ, J ) I F ( A E . G 1 . A B C ) GO TO 160 KCM=NCM+1 I f t o t a l time t o d e s t i n a t i o n a l r e a d y s t o r e d add t o l i s t .  i s l e s s t h a n minimum  TCOM (NCM) = TCM (JJJ) + TTO (NQ,J) •ECUK JNCH) = E S E ( J J J ) +TTO(NQ,J) 11=11+1  NCUM (NCM) = 1 1 'NBU(HCM)=1 ITAC(K) = 1 IPEC(II)=K IFF DC (II) =NQ 160 CONTINUE 167 CONTINUE C*************************************************************** C C DETERMINE MINIMUM TRAVEL TIME IO THE NODES WHICH HAVE C EIEN COMPUTED C C ' C************************************************ *************** 180 THIN=999999. IF (NCM.EQ.O) GO TO 270 EC 2 00 K=1,NCK C C C o n s i d e r i n v e h i c l e bus l i n k s o n l y u n t i l t h e y have a l l C been removed f r o m t h e l i s t . Then c o n s i d e r w a l k l i n k s . C IF (NBU (K) .SQ.1.AND.KZZ.GI.0) ' GO TO 200 IF (T HIN-ICU M ( K) ) 2 0 0 , 2 0 0 , 190 190 TBIN = TCUH (K) EX=ECUK(K) L=NCUM(K) 11= K IF (NBU (K) .EQ.0) LINK = L I F AG= tJEU (NCM) 200 CONTINUE C C IF ( I . GT. NLINK) GC TO 20 5 K=ND(L) GO TC 20 6 205 K=IPFB(L) 206 I F ( N N (K) ,LE. NLINK. ANC.NN (K) . GT.0. AND,L.GT.NLINK) GO TO 210 IF (TRAV (K)-TMIN) 210,210,220 C C I f t r a v e l time found above i s l e s s t h a n t h a t a l r e a d y C s t o r e d t h e n c h a n q e s t o r e d v a l u e t o new v a l u e .  c  1 4 0  210 C C C  1-1 I f t r a v e l time i s q r e a t e r than t h a t don't chanqe s t c r e d v a l u e .  already stored  C  220  GO 10 230 TEAV(K)=TMIN ECES (K) = EX NN(K)=L 1=0 NT B E E= NT B EE+1 IF{NTEEE-NNODE)230,270,230  C  C  Remove l i n k  & times frcm  list  C  230  240  I F (M.EQ. NC.M) GO TO 2 50 . CO 240 MM=M, NCM TCUM (MM) =TCUM (MM + 1) NCO M (MM) =NCUM (MM + 1) ECUM (MM) =ECUM (Mtf + 1) NBU (MM) = NBU (MM+1) IF(MM+1-NCM) 2 4 0 , 2 5 0 , 2 4 0 CONTINUE  C  250  NCM=NCM-1 IF(L.LT.MLINK)  KZZ=KZZ-1  C  C  I f stored  v a l u e was n o t c h a n q e d qo t c 180  C  260  I F ( I ) 180,260, 180 '[II (NN (K) . GT. NLINK. AND. I f AG. NE. 2) GO TO  130  C  C C C  I f l a s t l i n k was a w a l k l i n k qo t o 130 S u s e o r i q i n node (bus s t o p ) o f l i n k a s t h e new o r i q i n node f o r t h e n e x t bus l i n k .  C  NM=K GO 10 130 C  C  Print  o p t i o n o f minimum  transit  path. .  C  270  IF(IOPT.NE.NHOME) GO TO 320 WRITE (6 , 9) { NS ( N HCM E, M) , 11= 1, 3) , ( FW (N HOME, M ) , M = 1 , 3) DC 510 J=1,NOPD KK= NOPTD (J) IF(KK.EQ.NHOME) GO TO 310 I F ( T R A V (KK) .GT. 999990.) GO TO 312 WRITE (6,4) , TRAV (KK) , ECES (KK) WRITE (6,7) W E I 1 E ( 6 , 8) 1.1= NN (KK)  DO  5C5 J J = 1 , N L I N K NET (LL) WRITE(6,6) (N5(KK,M) ,M=1,3) , (EW(KK,M) ,M= 1 , 3) , NN (KK)  1X1=  + , P E F S C N { K K) , ( N B U S {LL , 11) ,11=1, IX T)  290  GC TO 290 I F ( L L . G T . N L I M K ) K K=.I P EDC (LL) I F ( I L . L E . NLINK) KK-NO(LL) IM = L L  L L = » N (KK)  I F (LL.GT,NLINK) GO TO 3 11 IF (KK. EQ. NliCME) GO TO 3 1 1 305 CONTINUE 311 WHITE ( 6 , 6) (NS(KK,M) , H= 1 , 3) , (E U { K K , M) , M= 1 , 3) ,NN (KK) +,F£FSCF(KK) , (NBUS ( L M , I I ) ,11= 1, IXT) GC TO 310 312 WRITE (6,5) KK 310 CONTINUE 320 RETURN 4 FORMAT (///1 OX,'TOTAL TRAVEL TIME (SECS) ' , F 1 0 . 0 , + / 1 G X , « T R A N S F E R , WAIT AND WALK TIME (SECS) ' ,F 1 0 . 0 ) 5 FORMAT(///'TEE MINIMUM PATH FOR DESTINATION NODE*,15,* + WAS NCT COMPUTED') 6 FOSMAT(10X,2(3A4) , 1 1 0 , F 1 0 . 0 , 5 X , 1 4 1 4 / 5 9 X , 1 4 1 4 ) 7 FORM AT(/13X,'INTERSECTION',15X,'LINK',3X,'PERSONS ON' + ,3X,'BUS L I N E S ' ) 8 FORM AT(48X,'THE EUS',5X,'AT THE NODE'). 9 FORMAT(////10X,'MINIMUM PATH TREE FROM I N T E R S E C T I O N ' , 2 ( 3 A 4 ) ) END C  c c C C  c c c C C  SUBROUTINE TIM (NM,K, I,'TIME,NTREE, ECE, L INK) COM MC N/M EI N/ TTO (1 5 00 , 50) , NBL ( 1500) , NU MDEP (1 5 0 0 ) ,' + LINKUP ( 1 5 0 0 , 1 0 ) , TL1N K (2100) ,TL(AV (150 0) , NT ( 1 5 0 0 , 5 0 ) + , I K T ( 1500) , NLINK, LAST, NNODF , ND ( 2 1 0 0 ) ,NBT(2100) , + NBUS(21C0,30) ,DIST (2100) ,NO (2100) ,ECES (1500) CCMMCN/TME/HEAD { 1 0 0 0 ) ,PERSON (150G) ,NNN ( 1 5 0 0 , 5 ) , D E C , A C C , L L I N E +,BOARD +,PERSOF(1500),FREFLO DIMENSION NN (1500) C********************************************** *****************  c  C TRAVEL TIME FOR PASSENGERS JUST EOARDING THE BUS C £************ ********************************** ***************** ECE=0.0 I F (NTREE.EQ.2) GO TO 1 0 0 GC TO 120 100 I T= N ET (I) SUM = 0 C C S t o r e t h e b u s l i n e s w h i c h use l i n k ' I * . C DC 110 M 1=1, IT 11= NEliS (I,MT) NNN (I,MT) = NBUS (I,MT) 110 CONTINUE C N N ( I ) =IT I F (TLINK (I.) . EQ. 0) GO TO 115  VEL-DIST (I) /TLINK (I) GC TO 117 C  C  Compute s t o p p e d  t i m e and l i n k  travel  time.  C  115 117  VE1=FEEF10 STGP=B0ARB*P£ESOF(NM) AT=V£I/ACC ET=V EL/DEC S=.5*ACC*AT**2 SS=DIST ( I ) - S TT=SS/VEL I F ( S S . L T . O ) TT=0 TIME=STOP+AT + .ET+TT GO TO 200  Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  c C C  TRAVEL TIME FOR PASSENGERS ON TfcE BUS WITH PROVISIONS FCR STOPS TO PICK UP PASSENGERS  C Q******************************************************  120  C C C  140 C 130  c C  * * * * * * * * *  N=0  IFLAG-O IT=NN (LINK) 1D=NBT ( I ) Determine  i f passenger  transfers.  DC 130 J = 1 , I T DC 130 MT=1,ID I F { N N N ( L I N K , J ) . E Q . N B U S ( I , M T ) ) GO TO 140 GC TO 130 • N=N+1 NNN ( I , N) =NBUS ( I , MT) WRITE(6,1) NN N ( I , MT) , N M , K , NT EE E ,1, TR AV (N M) , ECES (NM) , LINK IFLAG=1 CONTINUE NN(I)=N SUM = 0 Compute s t o p p e d t i i c e t o p i c k up p a s s e n g e r s  & link  time  C  I F ( T L I N K (I) .EQ.0) GO TO 155 VEL= EIST (I) /TLINK (I) GO TO 157 155 V£L= FREFLO 157 S10F=BOARD*PERSOF(NM) I F ( f ERSCN (NM) -PEESOH(K) . GT. 2 *P ER SO F(N H) ) STOP=(PERSON (Na) +-PEESON(K))*BOARC/2 I F (STOP. LT' 0. 1) GO TO 158 AT=VEL/ACC ET = V EL/DEC S=.5*ACC*AT#*2 • - • . SS=DIST (I) -S TT=SS/VEI I F ( S S . L T . O ) TT-0 TIME=STOF+AT+DT+TT C WRITE(6,2) TIME,STOP,AT,TT,SS,S,VEL,DIST (I) T L I N K (I) IF(1FLAG.EQ.C) GO TO 160 GO TO 200 r  TIME=1LINK(I) I F ( I F I A G . EQ. 0 ) GC TO 1 6 0 GO TO 2 0 0 C*************************************************************** 158  C C C  TRAVEL TIME FOR PASSENGERS  Q * * * * * * *  160  C 150  C C C 200  MAKING  TRANSFERS  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  *  DO 1 5 0 MT=1,ID 11= NEUS ( I , MT) SUM = SUM+fiEAD(II) * 6 0 . 0 NNN (I,MT) = NEUS(I,MT) WRITE ( 6 , 1 ) NNN (I,MT) , Ntl, K , NTREE,!, TRAV (NM) ,ECES(NM) ,LINK CONTINUE NN(I)=ID ECE=SUM/ ( I D * 2 ) IF(ECE.GT.300) ECE=300 Compute t r a n s f e r  time  TIME=TItfE+ECE RETURN END  C C c c c c c c C c  .  .  SUBROUTINE ASSN (MTTD , NHOME, NTSK, * ZC NE, NG ROUP , I , TOD ,.NC + , NP S I KK, MZO'NE, PERIOD) CCHHON/MEIN/ TTO ( 1 5 0 0 , 5 0 ) , N B L ( 1 5 0 0 ) ,NUMDEP ( 1 5 0 0 ) , + L I N K D P ( 1 5 0 0 , 1 0 ) ,TLINK ( 2 1 0 0 ) ,TRAV ( 1 5 0 0 ) ,NT ( 1 5 0 0 , 5 0 ) + ,.IKT ( 1 5 0 0 ) , NLINK, LAST, NNODE, ND ( 2 1 0 0 ) , NBT ( 2 10 0) , + NBUS ( 2 1 0 0 , 3 0 ) , DIST ( 2 1 0 0 ) , NO ( 2 1 0 0 ) , EC ES ( 1 5 0 0 ) CCBKGN/TME/HEAD ( 10 0 0 ) , PERSON ( 1 5 0 0) , NNN ( 1 5 0 0, 5) , DEC , ACC , L L I N E +,EOARC +,PEBSGF(1500),FREFLO CCMMON / A S S / IPEDO ( 3 5 0 0 ) ,NN ( 1 5 0 0 ) ,ITAC ( 1 5 0 0 ) DIMFNSIC N MTTD ( 2 5 0 ) , NQQ ( 1 0 ) , TOD ( 3 , 1 0 0 , 1 0 0 ) ,'TTT ( 1 0 0 ) ,NC ( 1 5 ) + ,NPSINK ( 4 0 0 ) ,MZONE ( 3 0 ) C C c  » DC 9 0 K=1,NZGNE TTT(K)=0.0 DC  90 C C C C  90 M=1,NG5CUP  T 1 T ( K ) = TTT(K) + TOD(M,I,K) CONTINUE Compute number o f p e r s o n s t r a v e l l i n q oriqin - destination pairs DO 1 0 0 J=1,NTSK NSTART=MTTD (J) KK=NPSIN.K ( J )  between  K=MZCNE (KK) T O T A L = T I T ( K ) / N C (K) I f { I T A C ( N S T A R T ) . E Q . 0 ) GO TO I=NN (NSTART) IF(L.GT,NLINK) GO TO 1 2 0  100  C C  110  C C 120  130  I T = SET (L) DC 1 1 0 MT-1 / I T NQQ (MT) = NBUS ( L , MT) NX=IT KH=H0(L) GC TO 1 4 0  N M= I EE DC (L) L=NN (NM) I T = N BT (L) I F ( I T . E Q . O ) GO TO 1 0 0 DC 1 3 0 M T = 1 , I T NQQ(MI)=NBUS(L M1) NM=NG(L) NX=IT #  C  c  140  DO 1 5 0 I I I I = 1 , N L I N K L = NN(NM) I F ( L . GT. NLINK) GO TO 1 3 5 T.T= NOT ( L ) I F ( I T . E Q . 0 ) GC TO 10 0 N=0 ,SUM=0.0  C C DC  DC  160 M1= 1 , I T 1 6 0 £10=1, NX  C C  Compute number  of people boardinq  bus.  C  160  I F (NCQ(MO) . N E . N B U S ( L , M T ) ) GO I I = N B U S ( L , MT) SUM = SUM+BEAD ( I I ) N=N+ 1 UQQ (N)=NBUS <L,HT) CONTINUE NX = N I F ( N . E Q . O ) GO TO 180 SUK=SUM/NX  TO  160  C C  C  Assiqn  people to buses.  '  FEB SCN ( NM) =PERSON (NM) + T C T A L * S U f l / ( P E R I O D * N X ) GO TO 1 5 0 180.. DC 190 M T = 1 , I T NQQ {MT) = NBUS (L,MT) 1 1 = NBUS(I,MT) 190 SUM=SUM + HEAD ( I I ) NX=IT SUM=SUM/NX C  C C 185  150 100  Assign  people  t o bus s t o p s  145  PERSOF(NM) =PERSOF(NM)+TOTAL*SUM/ (PERIOD*NX) P ER S C N(N M ) = PERSC N ( N M ) +T OT AL *SU M / (P ERIO D*NX) I F ( L . G T . N L I N K ) GO TO 100 IF (NO (L) . EQ. NFiOME) GO TO 100 NK=NC(L) CONTINUE RETURN END  C C C C c  C c  c c  C SUBROUTINE SPLIT(I,NHOME,NGRQUP,NZONE,IGD,IXI,DTFF,TMOD,TMAX) COMMON/PARK/ OI N (100,100) , 0 ( 3 , 1 0 0 , 1 0 0 ) JS (15 ) , M R (15) ,NC(15) +,LZCNE(30) , ET AV (250) ,TAV (250) ,ADIS (250) ,N VSIN'K (250) ,NPSINK (400) + ,ATAV (250) ,W (150,150) ,MZCNE( 30) , C(150) , TO D (3 , 10 0 , 1 00) , P (1 0 0) + ,WP ( 150, 150) f  Q******************* *****************************  C C C  1ST ITERATION  c * * * * * * * * * * * * * * * *  C C C C  *  *  *  *  *  *  *  ***************  COMPUTATIONS *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  I F ( I G D . G T . O ) GO TO 200 BC 100 K=1,NGROUF IXT=IXT+1 WRITE (6,121) I X T Initialize  v e c t o r s and s c a l a r s  DO 110 K=1,NZONE 1TTT=TAV (K) +ETAV (K) +1560 KK=0.0 CNT=0.0 ATTT=0.0 BIS-0.0 CT-0. 0 C C  Prepare data  f o r rocde s p l i t  computations  c  120  DO 120 L = 1 , NZONE I F (WP (K,L) . IT. .05) GO TO 120 ViiW (L, K) IF ( WT. GT. T.M A X) WT = T M AX •KK=WK+WT*WP (K,"L) ATTT = ATTT + AT A V ( L ) * W P ( K , L ) DIS = DIS + A D I S (1) * W P (K , L) CT=CT + C (L) *wP (K, I ) CNT=CNT+WP(K,L) CONTINUE WK=WK/CNT ATTT= ATTT/CNT + 1 2 0 0 B.1S= (D.IS/CNT + 3 0 0 0 0 ) / 5 2 8 0  .  *  *  *  *  *  *  *  *  ±40  CT=CT/CNT C C C  Compute mode  split  GX=-.83*1.27*(TTTT/ATTT)+.095*(.3 5/(DIS L*.08))-.615*CT I F (GX.GT. 170) GO TO 150 FA=EXP (Gl)/(1+EXP fGX) ) GC 10 160 150 PA=1.0 • 160 TCTAL-TOD (M, I,K) +0(M,I,K) C C Compute a u t o - t r a n s i t demands  c  110 C C C  0 (M,I,K)=TOTAL*PA TOD ( 8 , 1 , K)-TOTAL-0 (M , I , K) P(K)=PA CONTINUE IST=IXT W r i t e mode s p l i t  to sequential  file  WRITE ( 4 M S T ) (P (K) ,K=1, NZONE) CONTINUE 60 TO 1000 C*************************************************************** 100  c C MODE S P L I T COMPUTATIONS FOB SUBSEQUENT I T E R A T I O N S C C************************************ *************************** 2 00 DC 3CO M=1, NGEOUP iIXT=IXT+1 IS1=IXT C C Bead f r o m s e q u e n t i a l f i l e t h e p r e v i o u s i t e r a t i o n C mode s p l i t  c  R F A I ( 4 ' I ST) (P (K) ,K= 1 ,NZC NE) DC 310 K=1,NZONE C C C  Initialize  v e c t o r s and. s c a l a r s  TTTT-TAV (K) +ETAV (K) +1560 WK=0. 0  CNT=0.0 ATTT=0.0 DIS=0.0 C1=0.0  C C C  P r e p a r e d a t a f c r mcde s p l i t ' DO 315 L-1,NZONE I F ( W P (K , I ) . I T . . 0 5 ) GO TO 315 . . WT = W (L , K) IF(WT.GT.TMAX) RT=TMAX WK=WK + WT*WP (K,L) ATT T= ATTT+ AT AV ( L ) *WP (K, L ) DIS=DIS + ADIS (I) *WP (K , L) CT=CT + C (L) *WP (K , I ) CNT = CNT + WP (K,.L)  315  C  C  CONTINUE WK=WK/CNT A T T T= A T T1 /C N T + 1 2 0 0 EIS= (DIS/CNT + 3 0 0 0 0 ) / 5 2 8 0 C7 = CT/CNTCompute mode  147  split  C  GX=-.8 3+1.2 7 * ( T T T T / A T T T ) + . 0 9 5 * ( . 3 5 / ( D I S L*.08))615*CT IF (GX.G'I.170) GO TO 320 PA=FXP(GX) / ( 1 + EXP (GX)) GC TO 330 320 PA=1.0  C  C  M o d i f y mode s p l i t  b a s e d on p r e v i o u s mode  split  C  330  C  C C  310 C  C C  300 1000  DDD = P(K)-PA PP=P(K) I F ( F P . L T . 0 . 5 ) PP=1-PP FA= E (K) -PF*CID TMOD = TMOD + P (K) DIFF=AES (F ( K ) - P A ) P(K)=PA Compute a u t o - t r a n s i t demands TOTAL=TOD(M,I,K) +0 (M,I,K) 0 (M,I,K) =TOTAL*PA TOD(M,I,K)=IOTAL-0(M,I,K) CONTINUE 1 ST-1 XT Write WRITE (4* 1ST) CONTINUE RETURN END  new mode s p l i t  to sequential  tile  {P (K) , K= 1 , NZCNE)  C C  c c  C  c c c c c SUBROUTINE BNET (NOB,NBSTP,LIN,NK,IBT,BTM,NTT,NTR,NU,SPED) CCMf.CN/M EIN/ TTG (1500,50) ,NSL (1500) , NUKDEP (1 500) , + LINK DP ( 1 5 0 0 , 10) ,TLINK (2100) , TRAV (150 0) ,NT(1500,50) + ,1KT ( 1500) ,NLINK,LAST,NNODE ,ND (2100) ,NBT(2100) , + NEUS (2100 , 3 0) , DIST (2 100) ,NO (2100) ,ECES (1500) DIMENSION NBSTP (100) ,NOB (100) ,BTM (100) + ,NTT (150 0) , NT R (1500,28) ,NU{400) C  C  c  Initialize E T T = 0.0  vectors  SPED=0.0 DST=0.0 IET=1  148  11=0  NCB ( I B T ) = N M  120 C C C 400  C C C  DC 120 1=1,100 BTM(I)=0.0 Find  auto  links  with  bus l i n e  on i t  IN= N UMDEP (NM ) I F ( I N . E Q . O ) GO TO 100 IAT = 0 DO 200 L=1,IN I=LINKDP (NM,L) K=ND(I) IB=0 IXT=NET(I) Aqqreqate  auto l i n k s  between bus s t o p s i n t o  DO 300 KK=1,IXT N = NE US {I KK) KS= NTT(K) IF(KS.EQ.O) GO TO 340 DC 320 J J = i , K S IF(N.EQ.NTR ( K , J J ) ) GO TO 350 320 CONTINUE 340 NTT (K) = N 1 T (K)+1 KS= NTT (K) NTE(K,KS)=N '•IF ( I E T . GT. 1) GO TO 350 NTT (NM) =NTT (NM) + 1 KS=NTT(NM) • NT.R (NM,KS) =N 350 I F ( L I S , NE. N) GO TO 300 I K= 1 3 00 CONTINUE I F ( I H . E Q . O ) GO TO 200 I F ( I E T . E Q . I ) NT REE-2 I F ( I B T . G T . I ) NTREE=100 C C D e t e r m i n e t r a v e l t i m e s on l i n k s c C A L I TIM(NM,K,I,TIME,NTBEE,ECE L I N K ) LINK=I NM = K IT=IT+1 r  by b u s  r  C c C C C  Compute a q q r e q a t e  bus l i n k  travel  time  BT M (I ET) = ETM (I BT) +TIME Compute t o t a l  bus t r a v e l  E T T = E 1 T + TIM E £ S T - £ S T + D13 T (I) IF (NBI (K) . NE. 1) GO TO 400 IET=IBT+1 NOB (IET) =K  time 5 t r i p  lenqth  bus l i n k s  2 0 0 1 0 0  C C  c  4 5 0  470  GC TO 400 CONTINUE IF(IBT.EQ.O) GO TO 4 50 ETM (I ET) = ETT Compute  149  a v e r a g e s p e e d o f bus  SEED= (DS1/BTT) *. 6318 18 18 18 GC TO 4 7 C WRITE (6,1) NH  FOE AT(1 OX,'THE INPUT SPECIFIED + ,» WHICH HAS NO EXIT',14) RETURN END  A START NODE FOR A BUS L I N E '  

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