Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1978_A7 C84.pdf [ 7.29MB ]
Metadata
JSON: 831-1.0062868.json
JSON-LD: 831-1.0062868-ld.json
RDF/XML (Pretty): 831-1.0062868-rdf.xml
RDF/JSON: 831-1.0062868-rdf.json
Turtle: 831-1.0062868-turtle.txt
N-Triples: 831-1.0062868-rdf-ntriples.txt
Original Record: 831-1.0062868-source.json
Full Text
831-1.0062868-fulltext.txt
Citation
831-1.0062868.ris

Full Text

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 ' i n THE FACULTY OF GRADUATE STUDIES (Department of C i v i l Engineering) WE ACCEPT THIS THESIS AS CONFORMING TO THE REQUIRED STANDARD The University of British Columbia October, 1978 © Thomas Elwood Culham, 1978 In presenting t h i s thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make it f r e e l y available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for f i n a n c i a l gain shall not be allowed without my written permission. Department of CW«- //je&gft/G The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date Oct /973 i i ABSTRACT 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 short range p o l i c y questions. This type of framework i s needed because u n t i l recently most models dealt with long range c a p i t a l investment decisions while many urban transportation problems may be solved through low 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 indicated that equilibrium techniques were e s s e n t i a l i n providing solutions to short run p o l i c y questions. The features of equilibrium theory i n general were examined. The theory was then discussed i n terms of an ap p l i c a t i o n . It was found that the equilibrium state may be obtained through a d i r e c t or i n d i r e c t modelling approach. The d i r e c t approach u t i l i z e s a s i n g l e modelling step while the i n d i r e c t approach u t i l i z e s several sub-models. The state of the art i s such that i t appeared that the sequential i n d i r e c t approach was the best method to use. A computer modelling framework was developed which included modificat-ions and additions to a system produced at the University of B r i t i s h Columbia. The purpose of the U.B.C. system was to provide d e t a i l e d analysis 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 modelling contributions of t h i s paper were the de t a i l e d d e s c r i p t i o n of the t r a n s i t user through his t r i p from o r i g i n to destination and the assembly of an automobile assignment model, parking a l l o c a t i o n model, t r a n s i t assignment model and an auto-transit demand model into an equilibrium framework. The new system was tested on a small network. It produced "reasonable r e s u l t s " . Reasonable i n th i s case implied: (1) that any changes i n service l e v e l s or parking costs w i l l r e s u l t i n s h i f t s of demand i n the appropriate d i r e c t i o n and; i i i (2) that changes i n demand w i l l be i n proportion to the change i n l e v e l of s e r v i c e and v i c e versa. Two parking p o l i c i e s were analysed. The f i r s t p o l i c y approximated the case where a municipality decides to increase the rates i n i t s own parking l o t s . P rices were increased on one out of four l o t s i n the test network. The second p o l i c y approximated the case where the government i s able to levy a tax on a l l parking l o t s . P r i c e s were increased on a l l l o t s i n the test network. The outcome produced by the model confirmed the experience with parking p r i c e increases; that i s , 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 reducing congestion, i t i s necessary to co n t r o l a l l parking spaces i n the C.B.D.. A number of recommendations arose from the analysis of the r e s u l t s from the test network. It was recommended that f u r t h e r tests be c a r r i e d out on a more r e a l i s t i c network, and that a set of refinements and s e n s i t i v i t y tests be made on some of the sub-models i n the system. In general the model appeared to be s e n s i t i v e to changes i n a t t r i b u t e s of transportation a l t e r n a t i v e s . The development of t h i s system was a step to f i l l the gap i n the armoury of a n a l y t i c a l t o o l s . Further work and research may show i t to' be useful i n p r a c t i c a l a p p l i c a t i o n s . TABLE OF CONTENTS iv Page LIST OF TABLES v i ' LIST OF FIGURES v i i i ACKNOWLEDGEMENTS x CHAPTER ONE: Introduction 1 CHAPTER TWO: Theoretical Considerations 6 2.1 Transportation Systems in Equilibrium CHAPTER THREE: Criteria for the Development of a Short Run 16 Equilibrium Model 3.1 Approach to Equilibrium Solutions 3.2 The Modelling Framework CHAPTER FOUR: 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 Allocation Model 4.2.3 An Equilibrium Model for Vehicular Traffic 4.2.4 The Stochastic Vehicular Assignment Model 4.2.5 Vehicle Delay CHAPTER FIVE: The U.B.C. Framework Modified 43 5.1 An Equilibrium Model for 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 V TABLE OF CONTENTS (continued) CHAPTER SIX: An Application of the Modelling System 6.1 A Demonstration Using a Small Network 6.2 Capabilities of the Transit Program 6.3 An Illustration 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 v i LIST OF TABLES Page 1. Urban Scale Versus Planning Purpose 7 2. Subsystem Models Versus Level of Service and Service Attributes 28 & 101 2(a) Parking Policies Used to Illustrate the Program Capabilities 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 4. Travel Times From the Given Intersection to a l l Destinations 70 (a) For Parking Pricing Policy 2, Increment 3 70 (b) For Parking Pricing Policy 2, Increment 4 70 5(a) Car and Bus Splits for the Given Intersection to A l l Destinations Parking Policy A 71 (b) Car and Bus Splits for the Given Intersection to A l l Destinations Parking Policy B 71 6. Bus Statistics for Bus Line Number 3 74 (a) For Parking Pricing Policy 2, Increment 3 74 (b) For Parking Pricing Policy 2, Increment 4 74 7(a) Average Travel Times from Given Intersections to A l l Destinations for Each Iteration Between Policy 2, Increment 2 and 3 75 (b) Average Auto Mode Split From Given Intersections to A l l Destinations for Each Iteration Between Policy 2, Increment 2 and 3 75 8. Transition Parking Allocations for Each Iteration Between Policy 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 9. Parking Pricing Policies 93 10. Aggregate Statistics of the System for the Final State of Each Policy 96 v i i LIST OF TABLES (continued) Page 11. The I t e r a t i v e Process Using Four Constant M o d i f i e r s , Parking P r i c e Increase From $1.50 to $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 =1.0 124 12. The I t e r a t i v e Process Using Two M o d i f i e r Functions 125 (a) Parking Increase $1.50 to $2.50 M o d i f i e r = f ( l o g i t f u n c t i o n ) 125 (b) Parking Increase $1.50 to $2.50 M o d i f i e r = 1-f dy/dx ( l o g i t function)125 (c) Parking Increase $0.00 to $1.00 M o d i f i e r = f Q o g i t function) • 125 (d) Parking Increase $0.00 to $1.00 M o d i f i e r = f d y / d x ( l o g i t function) 125 13. Various Parking Increases and Congestion Levels Using the L o g i t Function M o d i f i e r 126 (a) Parking P r i c e Increase $2.50 to $2.75, Moderately Congested 126 (b) Parking P r i c e Increase $2.50 to $2.75, L i g h t l y Congested 126 (c) Parking P r i c e Increase $2.50 to $3.50, Moderately Congested 126 (d) Parking P r i c e Increase %2.50 to $3.50, L i g h t l y Congested 126 v i i i LIST OF FIGURES Page 1. A Flow Chart Showing the Major Activities of the Paper 3 2. A General Representation of a Transportation System in Equilibrium 11 3. The Effects of Shifts in the Demand and Supply on Equilibrium in a Transportation System 12 4. Transportation Demand and Fa 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 Analytical Framework 25 8. A Flow Chart of the U.B.C. Computer Framework 34 9. A Flow Chart of the Modified Framework 34 10. (a) 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 Split Subroutine: SPLIT 44 (f) Flow Chart of Bus Printout Subroutine: BNET 44 11. A Demonstration Network 62 12. (a) Transition Travel Times Policy 2, Increment 2 to 3 83 (b) Transition Mode Split Policy 2, Increment 2 to 3 83 13. (a) Transition Travel Times Policy 2, Increment 0 to 1 84 (b) Transition Mode Split Policy 2, Increment 0 to 1 84 14. Transition Travel Times and Volumes on Links into Parking Lot 1. Policy 2, Increment 2 to 3 87 (a) Vehicles vs Iterations 87 (b) Time vs Iterations 87 (c) Intersection and Parking Lot #1 87 ix LIST OF FIGURES(continued) Page 15. Transition Travel Times and Volumes on Links into Parking Lot #3 Policy 2, Increment 2 to 3 91 (a) Vehicle Vs. Iterations 91 (b) Travel time Vs. Iteration 91 (c) Intersection and Parking Lot #3 91 16. Total Hours Travelled Vs. Total Travel Cost 94 17. Auto Travel Time Vs Number of Iterations 115 (a) Modifier = .25 115 (b) Modifier = .50 115 (c) Modifier = .75 115 (d) Modifier = 1.0 115 18. 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 (Logit function) 116 19. Mode Split Modified Test System 117 ACKNOWLEDGEMENTS I wish to express my gratitude and thanks to Professors Brown and Navin f or t h e i r guidance and encouragement throughout t h i s t h e s i s . Without t h e i r help and thoughtful suggestions and c r i t i c i s m the project could not have been su c c e s s f u l l y accomplished. CHAPTER 1 1.0 INTRODUCTION The urban planning process which developed during the 1950's and the 1960's was directed primarily towards the analysis of long range capital intensive transportation projects. In the past few years investments in . large scale transportation projects have become expensive. Although this 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 existing f a c i l i t i e s . The early planning tools were designed to produce results for long range investment projects. Few were developed which explicitly analysed short run transportation problems. None were really designed to be sensitive to policy changes. Methods which have been introduced recently in an attempt to optimize the system have included a variety of t r a f f i c management policies. They ranged from the provision of reserved bus lanes to restraints on automobiles in selected areas of the city. The demand side of the problem has also been addressed with flexible work hours, car-pooling and various methods of pricing being attempted. Few of these methods have been analytically evaluated before implementation, partly because there was no appropriate analytical framework available for such evaluations. Most of the work in this area is experimental, hence citi 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 analytical, 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 is needed. Work performed for a paper e n t i t l e d "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." was the genesis for t h i s thesis. A r e l a t i v e l y crude model was developed and the analysis was done using a crude network. The need f o r both the analysis of short run p o l i c y questions and a more precise a n a l y t i c a l framework for the analysis of the questions wer.e recognized i n that paper ^. -The 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 methodology i s focused p r i m a r i l y on the analysis of a l t e r i n g parking charges i n the C.B.D.. With l i t t l e e f f o r t i t could be modified to handle a number of short run transportation problems. This paper provides two major contributions to the f i e l d of modelling these problems. Much work has been addressed i n the past to developing models which describe the movement of automobiles through a road network. Some work (but not a great deal) has been expended i n describing the move-ment of 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 work has been done to l i n k the service l e v e l s a r i s i n g on the two networks i n a dynamic sense to the demand l e v e l s on the networks. The contribution of t h i s 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 t r a n s i t user through h i s t r i p from o r i g i n to destination and the assembly of an auto assignment model, parking a l l o c a t i o n model, t r a n s i t assignment model and an auto-transit demand model into a dynamic framework. This paper i s divided into f i v e sections. Figure 1 g r a p h i c a l l y i l l u s t -rates the flow of the work. The f i r s t section examines the l i t e r a t u r e and discusses general equilibrium concepts. The second section deals with a t h e o r e t i c a l a p p l i c a t i o n of the concepts to short run p o l i c y questions and delves into the approaches av a i l a b l e for producing a technique to provide equilibrium solutions. In the t h i r d section 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 SUITABILITY 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 modelling system are discussed. Its shortcomings with respect to the theory set out i n the second section are also i l l u s t r a t e d . The fourth part sets out the modifications and additions to the current modelling methodology. F i n a l l y , an a p p l i c a t i o n of the revised modelling • z system to a small s t r e e t and bus network i s made and an analysis of the r e s u l t s i s given. FOOTNOTES T. E. Culham, "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 f o r Transportation Studies, University of 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 for short range p o l i c y planning''". Three d i s t i n c t topics must be addressed i n the development of a methodology which solves transportation p o l i c y questions. F i r s t , a general behavioural assumption should be stated which describes the process to be modelled. Secondly, a set of requirements must be established which ensure that the process does i n f a c t model the behaviour. T h i r d l y , a technique ought to be chosen which i s appropriate to the scale of the problem and i s capable of s a t i s f y i n g the stated conditions. Wardrop's f i r s t p r i n c i p l e states that t r a f f i c between o r i g i n s and destinations w i l l tend to s e t t l e into an equilibrium state where no d r i v e r 2 can reduce h i s journey time by choosing a new route . This behavioural assumption was generalized to include a l l t r a v e l choices a v a i l a b l e to the urban t r a v e l l e r . I t i s stated as follows: Travel by car or any other mode between o r i g i n s and destinations w i l l tend to s e t t l e into an equilibrium state where no person t r a v e l l i n g can reduce the generalized costs incurred i n h i s journey by choosing another route or by changing the mode of t r a v e l . The concept of generalized cost r e f e r s to the monetary costs of t r a v e l , 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 comfort, convenience, r e l i a b i l i t y , safety etc. . According to F l o r i a n the simplest and most general d e f i n i t i o n of equilibrium i s that equilibrium i s a steady state that i s reached when the demand f o r transportation gives r i s e to a service 4 l e v e l that maintains that demand . The concept of equilibrium w i l l be discussed i n greater d e t a i l i n part one of Chapter 2. Atherton et a l set out two basic conditions which must be s a t i s f i e d by short range planning models"*. F i r s t , they should be 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 transportation a l t e r n a t i v e s that would r e s u l t from p o l i c i e s being analysed ( i . e . the models must be p o l i c y s e n s i t i v e ) . Secondly, the models must be structured i n such a way that they accurately r e f l e c t the choice process of an i n d i v i d u a l deciding between a l t e r n a t i v e s . Planning may be done at d i f f e r e n t urban scales ranging from regional to l o c a l micro and have several purposes ranging from operational to st r a t e g i c . Table 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 scale and purpose of planning. TABLE 1 URBAN SCALE VERSUS PLANNING PURPOSE X . PLANNING \ . PURPOSE U R B A N X . SCALE \ . OPERATIONAL FUNCTIONAL STRATEGIC REGIONAL X 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 scales of 'urban' and ' l o c a l urban' *\ The former ref e r s to the analysis of major schemes of construction while the l a t t e r r e f e r s to the analysis of short run low c a p i t a l cost schemes. He discusses the a p p l i c a b i l i t y of equilibrium 8. techniques to the various urban scales and comes to the conclusion that without equilibrium techniques i t i s u n l i k e l y that the r e s u l t s of a l o c a l urban analysis would be of any p r a c t i c a l value^. The methodology being developed i n t h i s paper i s directed at solving problems at the l o c a l urban l e v e l . At the beginning of t h i s chapter a generalized behavioural assumption was stated. In i t the concept of equilibrium was introduced and was l a t e r defined. In the discussion above i t was recognized that equilibrium techniques provide the t h e o r e t i c a l basis with which to f a b r i c a t e a method- . ology to solve short run p o l i c y questions. The following discussion enumerates a set of conditions which are necessary to ensure consistency i n equilibrium models. It also discusses the degree with which these models meet the requirements of Atherton. g The conditions as set out by Manhiem are the following : (1) The l e v e l of service factors such as i n v e h i c l e , out of v e h i c l e t r a v e l times, distance, convenience etc. enters at each stage i n the sequence, including generation, unless i t i s e x p l i c i t l y found to be superfluous. (2) The same a t t r i b u t e s of service should enter at each step unless the data indicates otherwise. Service a t t r i b u t e s are bus fares, bus frequencies, parking costs etc. (3) . The same values of the l e v e l of service should influence each sub-model. (4) The l e v e l of service provided by each mode should influence the demand to some degree. These are general conditions which apply to a l l equilibrium models. These conditions are applicable from the general 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 sub-models. Various procedures may be u t i l i z e d i n order to a t t a i n equilibrium of transportation flows. As long as the procedure chosen meets the conditions set out above then the f i r s t requirement of Atherton et a l w i l l be s a t i s f i e d . The second requirement w i l l be s a t i s f i e d i f the model i s structured so that the s i g n i f i c a n t service l e v e l s of the various modes are made av a i l a b l e to a behavioural choice model. The conditions of equilibrium p a r t i a l l y s a t i s f y the second requirement. The s e l e c t i o n of a disaggregate choice model w i l l f u l f i l l the remaining requirements. This s e l e c t i o n w i l l be discussed l a t e r i n the paper. 2.1 Transportation Systems In Equilibrium Before delving into the development of the a n a l y t i c a l framework, a general explanation of the notion of a transportation system i n equilibrium w i l l be given. A transportation system i n equilibrium i s seen to have four components which operate i n t e r a c t i v e l y . They are the following: T, The transportation i n f r a s t r u c t u r e which i s the basic supply. A, The transportation systems associated socio-economic a c t i v i t i e s . These a c t i v i t i e s include locations of work, recreation and home. V, The demand which the a c t i v i t i e s put on the system. This demand takes the form of volume of t r i p s by various modes on the l i n k s of the system. L. The l e v e l of service on the system a r i s i n g out of the volume of t r a f f i c on the system and the system configuration or i n f r a -structure. The l e v e l of service i n t h i s discussion i s comprised of the following components: 10. 1. The service 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 parameters such as bus frequencies, bus fares, parking charges etc.. 2. The remaining portion i s made up of what i s t y p i c a l l y thought of as the l e v e l of service factors ; these are, t r a v e l times and distances by the two modes, convenience etc.. The l e v e l of service as referred to here i s equivalent to the i d e a l i z e d generalized cost concept. Later i n the paper s p e c i f i c references w i l l be made to service 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 service concept. For the graphical presentation and discussion i n parts one and two of Chapter 2 the broader concept of l e v e l of service i s used. A f i n a l v a r i a b l e i s introduced here which i s not normally included i n the l i t e r a t u r e because i t i s a function of the l e v e l of service. However, fo r c l a r i t y i n the following discussion, generalized cost or simply cost of t r a v e l as function of the l e v e l of service w i l l be included. C = the generalized cost of t r a v e l as a function of the l e v e l of service Generally when one thinks of the l e v e l of service improvement one thinks of an improved service where t r a v e l times are shorter and convenience i s better. Figure 2 i s a t y p i c a l representation of a transportation system i n equilibrium. In the l i t e r a t u r e the h o r i z o n t a l axis represents the t o t a l demand and the v e r t i c a l axis the. l e v e l of s e r v i c e . Under these conventions one tends to think that the l e v e l of service increases up the v e r t i c a l axis. However, the diagram makes more sense i f one assumes that the costs of t r a v e l increase up the v e r t i c a l axis and the l e v e l of service deteriorates. Each of the variables above are vectors. The transportation i n f r a -structure i s a vector of l i n k s with associated t r a f f i c c h a r a c t e r i s t i c s . The socio-economic a c t i v i t i e s are the places of residence, recreation and work 11 FIGURE 2 V Q T o t a l T r i p Volumes A GENERAL REPRESENTATION OF A TRANSPORTATION SYSTEM IN EQUILIBRIUM throughout the region.The demand i s the number of 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 population subgroups, by time of day, by mode etc.. F i n a l l y the service l e v e l s are vectors of t r a v e l time, distance, cost, comfort etc. f o r each mode. Generally the demand f o r t r a v e l i s a function of the l e v e l of service L on the system and the socio-economic a c t i v i t i e s A of the region. The volume of t r a f f i c V on the system i s a r e s u l t of that demand and i s given by: V = f(C,A) • 1 where C = f(L) 2 Note that the cost C i s a function of the l e v e l of service L and i t i s determined by the volume of t r a f f i c V on the transportation system T. C = f(L) = f(V,T) 3 12 A graphical representation of the equilibrium state i s achieved by supposing that equations 1 and 2 are continuous f o r the given A and T. A whole family of curves may be defined f o r each of the equations i n the plane defined by the aggregate l e v e l of service and t o t a l demand axis; r e f e r to Figure 3. For each given A and every l e v e l of service, there i s FIGURE 3 AV EV BV DV Total Trip Volumes THE EFFECTS OF SHIFTS IN THE DEMAND AND SUPPLY:-. ON  EQUILIBRIUM IN A TRANSPORTATION SYSTEM a ' curve which describes the demand on the system. S i m i l a r l y , f o r each given T and every demand there i s a separate curve which describes the possible l e v e l of service along i t . Their i n t e r s e c t i o n defines the equilibrium demand and service l e v e l . Figure 3 shows a p a i r df curves i n the family of curves of each r e l a t i o n s h i p . 13 An important notion of generalized equilibrium analysis is that total demand for transit is not fixed. It supposes that an improvement in any :.. facet of the transportation system w i l l lead to an improvement in.the overall system and hence increase the total number of trips made. Figure 4 illustrates this concept. The source of the additional demand lie s in the FIGURE 4 TRANSPORTATION DEMAND AND FACILITY IMPROVEMENTS T o t a l Person T r i p s T r i p s generated due to improvements Auto t r i p s T r a n s i t t r i p s T o t a l t r i p s before-improvement Time latent demand - a topic which i s addressed in greater detail in Chapter 3. With this concept in mind an ill u s t r a t i o n of the intersection of equation 1 and 2 w i l l be given with references to Figure 3. It must be remembered that Figure 3 is a general representation of the complete transportation system including a l l modes. The planner or engineer can directly influence the equilibrium of the system by influencing the service attributes of the modes, altering socio-economic activities and changing the transportation system. An example of changes in each of these areas w i l l be discussed. For example, point A on Figure 3 i s assumed to be the existing 14 equilibrium. Service l e v e l and volumes or demand A^ r e s u l t . In the f i r s t case, the l e v e l of service i s increased by increasing the frequency of bus service. Suppose that through.this change the bus becomes more r e l i a b l e and bus t r a v e l times are reduced. Two things occur. Some people w i l l be attracted to the bus mode from t h e i r cars and new r i d e r s w i l l be att r a c t e d to both modes. The system reaches equilibrium at point B with new service l e v e l s B^ and B^ . The difference between A^ and B^ i s the generated demand. It i s important to note that Figure 3 i s only a p i c t o r i a l representation. The slope of curve 1 could be e n t i r e l y d i f f e r e n t . It may be v e r t i c a l i n the range of the ana l y s i s , i n which case no new demand would be generated. Also, although one f a c t o r of the l e v e l of service 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 net negative r e s u l t . In t h i s case the aggregate l e v e l of service would be reduced. In the second case, a new rapid t r a n s i t system i s i n s t a l l e d . It a f f e c t s s i g n i f i c a n t improvements i n the l e v e l of service. When the f a c i l i t y opens, the new equilibrium conditions are defined by point B. However, over a period of years of operation, the improved l e v e l of service offered by the system influences l o c a t i o n decisions. The socio-economic a c t i v i t i e s of the c i t y increase and the new equilibrium conditions are described by point D. The difference i n demand between A^ and B^ represent newly generated t r i p s from the e x i s t i n g pool of demand. The differn e c e between B^ and represent t r i p s generated by the growth of the c i t y and by l o c a t i o n decisions influenced by the i n s t a l l a t i o n of the f a c i l i t y . In the t h i r d case, the c i t y i s allowed to grow without any improvement i n transportation services. Point E describes the new equilibrium. The l e v e l of service has increased i n cost from A^ to E^ and A^ to E^ represents newly generated t r i p s due to the growth of the c i t y . 15 FOOTNOTES 1. T. J. Atherton, J, H, Suhrbier, and W. A. Jessiman, "Use of Disaggregate Travel Demand Models to Analyse Car Pooling P o l i c y Incentives", Transportation Research Board, 599., 1976, p. 35. 2. J. G. Wardrop, "Some Theorectical Aspects of Road T r a f f i c Research", Proc. Inst. C i v i l Engineers, Part II 1952, p.345. 3. J. H. Shortreed (ed.), "Urban Bus Tran s i t : A Planning Guide", The Transport Group, Department of C i v i l Engineering, 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 et a l , "EMME: A Planning Method f o r Multi-Modal Urban Transportation Systems", Univ e r s i t e de Montreal P u b l i c a t i o n #62, Centre de recherche sur les transports, 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 (ed.), "Equilibrium Models i n Use: P r a c t i c a l Problems and Proposals f o r Transport Planning", T r a f f i c Equilibrium  Methods Proceedings of the International Symposium, at the Univ e r s i t y of Montreal, Springer-Verlag, New York 1976, p. 18. 7. Ibid. 8. 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, p.24. 16 CHAPTER 3 3.0 THEORETICAL DEVELOPMENT OF A SHORT RUN EQUILIBRIUM MODEL The previous discussion has dwelled on the general concepts of equilibrium from a long range point of view. It s purpose was to introduce the concepts and give a general overview of a transportation system i n equilibrium. The following discussion i s more s p e c i f i c . The c r i t e r i a f o r the development of a methodology for the analysis of short run p o l i c i e s are set out. The idea of equilibrium i n terms of the solu t i o n of short run p o l i c y questions are discussed. Proceeding to the theory of the structure of the system, the modelling approach to short run equilibrium solutions i s addressed. F i n a l l y the framework of that approach i s explained. The stated purpose of t h i s paper i s to develop an a n a l y t i c a l framework which provides solutions to short run p o l i c y questions..Implementation' of a p o l i c y implies that the planner wishes to improve the e f f i c i e n c y of the ex i s t i n g system or reduce i t s negative impacts such as p o l l u t i o n , noise etc. on society. In order to determine the e f f e c t s of a p o l i c y the pertinent conditions associated with the e x i s t i n g state of equilibrium and those associated with the state of equilibrium under the new. p o l i c y must be known. Of utmost importance i s the a b i l i t y to accurately p r e d i c t the conditions due to the new short run p o l i c y . The following i s a discussion of the c r i t e r i a which were established for the development of a equilibrium model to s a t i s f y the above goal. A set of assumptions were made based on the c r i t e r i a and the v a l i d i t y of these assumptions i s discussed with respect to the general concepts of equilibrium previously set out. The following c r i t e r i a were established for the development of a new equilibrium 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 in the future. 3. The model could be applied in 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 situation. 5. The framework would u t i l i z e existing 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 trips only. 7. The model would consider both transit and automobile trips in equilibrium. 8. Both the network interaction and the choice between the two modes would be considered. 9. The choice process would consider the significant level of service characteristics of both modes. In order to simplify the solution process the following assumptions were made. 1. The total demand for travel would be fixed. Only trip making trade-offs between the two modes would be considered. 2. The socio-economic activities w i l l not alter significantly during the period of analysis. 3. The transportation system w i l l not be changed during the analysis period. 18 The f i r s t assumption.is c r i t i c a l . From a modelling point of view i t means that t r i p generation can be determined exogenously to the model. I t s i m p l i f i e s the process greatly. B r i e f l y , the model takes current t r i p d i s t r i b u t i o n tables f o r auto and t r a n s i t and computes the equilibrium state given the current l e v e l of service conditions. This allows the analyst to check whether the model accurately predicts observed data. A change i s then made i n a service a t t r i b u t e such as a change i n parking charges. The model then computes the new equilibrium transit-auto s p l i t and outputs the service l e v e l s a r i s i n g from the new s p l i t . It does not a l t e r the t o t a l demand f o r t r a v e l . The following discusses the v a l i d i t y of t h i s assumption. To 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 region may increase due to growth i n population and employment opportunities. Hence, the t o t a l demand for t r a v e l increases. 2. Latent demand may be induced to use the system through increased service l e v e l s ( i . e . lower t r a v e l l i n g costs). The assumption that socio-economic a c t i v i t i e s do not change s i g n i f i c a n t -l y over one or two years i s v a l i d provided the growth rate i n the region i s not excessive and no new major housing or employment developments commence during the period of analysis. An extension of t h i s assumption beyond the two year period would require judgement i n accepting i t s v a l i d i t y . Latent demand i s defined as t r i p s that"*": 1. are desired and can be met by e x i s t i n g transportation systems but are not attempted f o r reasons other than poor l e v e l of service. 2. are desired at a p a r t i c u l a r time but cannot be met by the e x i s t i n g system. 3. are not now desired but may be desired i n the future and can be 19 met by existing systems. 4. are not now desired and cannot be met by the existing system. It would appear that latent demand unsatisfied by existing transportation systems for work trips might have some significance to this model. It would also appear that changes in total demand for work trips are insensitive to changes in level of service. In the case of automobile-restraint measures 2 for work trips, Heggie makes this statement : "Work journeys cannot be easily terminated (except for temporary or part time work) and travellers can usually be forced to use public transit." This suggests that lowering or raising the service levels would not greatly influence latent demand over a short period. It must be noted however that this assumption loses validity 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 , total demand is a function of socio-economic ac t i v i t i e s . To be consistent with the fixed demand function i t is necessary that •-"the'v." socio-economic activities remain unaltered as well. The assumption that the transportation system remains unchanged during the analysis period is valid provided that no infrastructure becomes operational during that period. These assumptions alter the form of Figure 3 from a family of inter-secting curves to a single vertical line. Equation 1 transforms from V = f (L,A) 1 to V = Z 4 where Z is a constant. 20 C = f(L) = f ( V T , V A ) Since V, and T of equation 2 are constants but the aggregate l e v e l of service can f l u c t u a t e , equation 2 transforms from C = f(L) = f(V,T) 2 to 5 where T and A are subscripts denoting the t r a n s i t and auto modes. V i s the volume of t r a f f i c on each mode. It i s hypothesized that by a l t e r i n g the s p l i t between the auto and t r a n s i t modes the aggregate l e v e l of service can be a l t e r e d . The equilibrium state of the system i s a point defined by Equation 4 on the l i n e V = Z ; r e f e r to Figure 5 . FIGURE 5 A GENERAL EQUILIBRIUM MODEL UNDER SHORT RUNASSUMPTIONS Cost of T r a v e l f ( L ) L V f ( v T , v A) T o t a l Volume Maximization of the aggregate l e v e l of service may not be the goal of the c i t y planner or engineer. From the point of view of society, there may be factors outside the l e v e l of service function or factors which are improperly represented i n i t . Such examples are energy consumption, p o l l u t i o n or noise problems. The benefits to society at large however, must be balanced 21 against the aggregate cost to the t r i p makers due to the reduced level- of service. Returning to the main topic , i n the system sense then, the equilibrium s o l u t i o n i s redundant. I t i s simply the sum of a l l l e v e l of service factors p l o t t e d on the stra i g h t l i n e i n Figure 5. The problem l i e s i n determining those l e v e l of service factors for both modes i n equilibrium. The general equation f o r the l e v e l of service i s : L = f (v T,v A) 6 where L = L M + L, 7 T A The l e v e l of service f o r each mode i n equation 7 are functions of the volumes or demands on both the mode networks. L T « 8 L A " f 2 ( V V " 9 The demands on both the networks i n turn are dependent on the l e v e l of service on both the networks. V A " f 3 ( LT» L A > 1 0 V T - f 4 ( L T ' L A ) . 1 1 These equations are s i m i l a r i n form to those presented f o r the general case. Figure 6 i s a p i c t o r i a l representation of the equilibrium state f o r the automobile mode only. A s i m i l a r graph could be developed f o r the t r a n s i t mode i n equilibrium. There i s a family of curves describing the auto demand V f o r every given 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 describing the l e v e l of service of the auto L f o r every given demand of t r a n s i t V . & T 22 FIGURE 6 AN EQmLIBRItM MODEL OF THE AUTO MODE The t r a n s i t and automobile modes are at .equilibrium at point A. The l e v e l of s e r v i c e f o r autos i s reduced by adding a parking charge. The immediate r e s u l t i s an increase i n the costs of d r i v i n g from A^ to D^. However, a f t e r the system users have had a chance to react to the new prices the system s e t t l e s into equilibrium at point B. The new demand for auto t r a v e l i s represented by B^, the difference between B^ and A^ being the s h i f t to t r a n s i t . The process described above i s p r e c i s e l y the problem which i s being addressed i n t h i s paper. Stated b r i e f l y , the problem i s as follows. Given the current equilibrium state of the t r a n s i t and auto modes, what w i l l be the new equilibrium conditions when a change i s made i n the l e v e l of service of either mode? Once the hew equilibrium s o l u t i o n has been found, i t s operational differences and cost benefits over the previous state may be determined. 23 3.1 Approach to Equilibrium Solutions An equilibrium model may be structured in two ways. According to 3 Manhiem the equilibrium state may be obtained through a direct or indirect approach. The direct approach ut i l i z e s a single modelling step while the indirect approach u t i l i z e s several sub-models. An econometric model which estimates the trip generation, trip distribution, mode spl i t and assignment in one step is a direct approach. The Urban Transportation Model System (UTMS) estimates each of the above segments of the problem in four different sub-models and i t is an indirect approach. Although UTMS has been very widely used and accepted, i t has many short-comings. Its problems and limitations 4 with respect to equilibrium c r i t e r i a are discussed by Manhiem . It is generally recognized however, that the indirect approach has many advantages. It allows the analyst to calibrate 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 starting from the beginning again. Although direct models are theoretically the best at satisfying equilibrium conditions, there are problems associated with them. Button"* discusses a number of direct 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 in the parameters obtained ; • a consequence partly resulting from the assumptions employed. 3. no satisfactory method has been devised to ensure that the 24 predictions supplied by e x p l i c i t models f a l l within the bounds of what i s thought i n t u i t i v e l y possible. Given the state of the a r t , i t appears that the sequential i n d i r e c t approach i s the better method to use i f a p r a c t i c a l modelling system i s being developed. Other advantages are offered by the i n d i r e c t approach. Figure 7 ' i l l u s t r a t e s the sequence of steps embodied within the framework developed. This sequence of steps allows changes to be introduced at any point i n the system. For example: i f the parking p r i c e s are changed, then those changes would be introduced to the parking a l l o c a t i o n step. The system then proceeds through the sequence of steps i t e r a t i n g u n t i l equilibrium i s attained. The nature of the i n d i r e c t approach implies that the parking a l l o c a t i o n w i l l i n i t i a l l y be made without knowing the congestion l e v e l s a r i s i n g out of any changes i n congestion. S i m i l a r l y , the mode choice w i l l i n i t i a l l y be made without knowledge of the congestion 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 . It was hypothesized that the commuter makes decisions based on pr i c e s and l e v e l s of congestion experienced, not those anticipated. It i s u n l i k e l y that p r i c e increases would be advertised and also , the commuter would not think of or be capable of estimating the equilibrium congestion l e v e l a f t e r a p r i c e change. The i n i t i a l decision w i l l be based on the new parking charge and the old congestion l e v e l s . Because of the lag i n change of congestion l e v e l s behind p r i c e changes the system may not proceed to equilibrium i n one step but must proceed through several steps. This same concept in v o l v i n g a change i n the transportation system and the user's response over time i s discussed by Hutchinson^. The context of the discussion i n h i s paper i s d i f f e r e n t than the context presented here. FIGURE 7 FLOW CHART OF A SHORT RUN ANALYTICAL FRAMEWORK ASSIGNMENT' PASSENGERS TO TRANSIT EXISTING TRANSIT DEMAND FEEDBACK REVISED TRANSIT DEMAND "NETWORK DATA NETWORK 1 GENERATION FOR TRANSIT, AUTO AND PEDESTRIAN WALK TRAVEL TIME BETWEEN SELECTED ORIGINS AND DESTINATIONS AUTO ASSIGNMENT MODE 6 SPLIT EQUILIBRIUM 7 ALGORITHM CONVERGENCE TEST FINISH PARKING ALLOCATION EXISTING AUTO TRAVEL DEMAND FEEDBACK REVISED AUTO DEMAND 26 It deals with the problem of controlling the response of commuters during : the transition period to the installation of new f a c i l i t i e s . Its significan-ce to this paper i s : 1. i t recognizes that there is a transitory period and; 2. that decisions which lead to travel patterns are based on congest-ion levels during the transitory period. A model which proceeds through several steps to attain a state of equilibrium may in actual fact be approximating the real situation. 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 is simply to show that the indirect approach to equilibrium may be close to the process which the system goes through to attain equilibrium. 3.2 The Modelling Framework An indirect approach was ut i l i z e d for the equilibrium model developed in this paper. The framework includes the following seven steps: 1. Generate pedestrian, automobile and transit networks. 2. Determine walking times between selected origins and destinations. 3. Allocate automobiles to parking spaces so that walking and parking charges are traded off and the availability of space is constrain-ed. A. A multipath probability 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 . *~ J.-. 5. An all-or-nothing assignment of transit users to a bus network which interacts with the automobile t r a f f i c . 6. Determine the demand for each mode through a logit model. 27 7. An application of an equilibrium algorithm for fixed demand and a convergence test. The details and assumptions embodied in these steps w i l l be discussed later. System equilibrium i s achieved through the iteration of steps 2 through 7 and is controlled by step 7. System equilibrium conditions are met by the feedback of the appropriate service and demand levels. 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 spl i t in step 6. Computation of walk travel times was excluded from the iterative process because i t was thought that walk times would not be affected by changes in the level of t r a f f i c . Figure 7 illustrates the flow through the seven steps. This flow chart was not designed to illustrate the computer programs and . their linkages but to show the theoretical form of the system. Table 2 demonstrates more clearly the ut i l i z a t i o n of demand and supply data by the models in the system. The supply side is divided into service attributes and level of service factors. The service attributes are parking charges, bus fares and frequency of bus service. The level of service factors are auto walk times, auto invehicle times, bus walk and wait times, and bus invehicle times. The models in the table are list e d in the order of execution. By referring to Table 2 and Figure 7 i t is easy to trace through the process and determine where the data is computed and utilized. The exogenous demand data provided to the system is in the form of origin-destination trips by car and by transit. The parking allocation model uses parking charges and auto walk times to transform the person 0-D trips by auto into vehicle 0-D trips. The process moves along to the vehicle assignment model u t i l i z i n g the vehicle origin-destination (0-D) trips to compute the auto invehicle travel times and perform the vehicle assignment. TABLE 2 SYSTEM SUB-MODELS VERSUS LEVEL OF SERVICE AND SERVICE ATTRIBUTES 1 SERVICE ATTRIBUTES LEVEL OF SERVICE MODEL DEMANDS PARKING CHARGES BUS FARES FREQUENCY OF SERVICE AUTO WALK TIMES AUTO INVEHICLE TIMES BUS WALK & WAIT TIMES BUS INVEHICLE TIMES parking a l l o c a t i o n person t r i p s by auto X X v e h i c l e assignment v e h i c l e 0-D t r i p s X t r a n s i t assignment person 0-D t r i p s by t r a n s i t X X X X mode s p l i t person t r i p s by auto and t r a n s i t X X X X X X 29 The v e h i c l e 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. The t r a n s i t assignment model u t i l i z e s these maximum speeds, the frequency of bus service and the t r a n s i t origin- destination demand to compute bus walk, wait and i n v e h i c l e times i n order to perform the t r a n s i t assignment. The mode s p l i t model i s the pivot point of the system. It i s through the mode s p l i t that the service l e v e l s computed by the previous i t e r a t i o n are translated into new demands for the next i t e r a t i o n . In t h i s manner also, a l l service l e v e l s are i m p l i c i t l y represented throughout the system by the revised demands. Within the i t e r a t i v e portion of the framework, the commuter i s allowed the following choices: ( i ) t r a n s i t or auto mode; ( i i ) any number of paths i n either mode; ( i i i ) within the auto mode a trade o f f between parking costs and walking times . The i n c l u s i o n of a parking a l l o c a t i o n model o f f e r s more det a i l e d information on the trade o f f between walking and parking charges. This trade o f f has implications on both the assignment of auto t r i p s i n the congested C.B.D. and the choice between t r a n s i t and auto. Increased parking charges generally induce a s h i f t to parking l o t s further from the place of work^. This s h i f t may have the e f f e c t of reducing t r a f f i c flows i n the v i c i n i t y of the zone where the increases were made. The parking a l l o c a t i o n model also has an input to the choice process between auto and t r a n s i t . In t h i s case i t i s included i n the generalized cost of auto t r a v e l ( i n -v e h i c l e time, marginal operating costs, parking costs and walking time) and compared with the generalized cost of t r a n s i t ( i n v e h i c l e time, bus fare, walking, waiting and transfer times). If the generalized cost of auto t r a v e l (including trade-offs) which the driver may choose to make i s too high, then he w i l l choose t r a n s i t . In summary, t h i s framework allows f o r a s h i f t of driver s to d i f f e r e n t parking l o t s or a s h i f t to t r a n s i t . 30 FOOTNOTES 1. L. A, Hoel. et a l ? "Latent Damand For Urban Transportation", Trans^ portation Research, Institute, ..Carnegie-Mellon, University of Pittsgurgh, Pennsylvania, 19.68, p. 215. 2. I. G. Heggie, "Consumer Respeonse to Public Transport Improvements and Car Restraint: Some Practical Finding. Working Paper No. 2 (revised)", Transport Studies Unit/ University of Oxford, 1976, p. 29. 3. M. L. Manhiem, "Practical 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 in 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. Gillen, "Effects of Changes in Parking Prices and Urban • Restrictions on Urban Transport Demands and Congestion Levels", u University of Toronto - York University Joint Program in Transportation, 1975, p. 20. 31 CHAPTER 4 4.0 THE COMPUTER SYSTEM AND COMPONENTS Up to th i s point i n the paper the discussion has dealt with the t h e o r e t i c a l aspects of equilibrium, i t s a p p l i c a t i o n to short-run p o l i c y questions, the approach to modelling a transportation system i n equilibrium and the general structure of that modelling system. The following discussion deals with the actual construction of the modelling system and r e l a t e s the choice of the models and functions imbedded i n the system back to the theory. Two options were open i n the development of the computer system. The whole system could have been developed from scratch or a system which f u l f i l l e d part of, or a l l of the requirements of the study could have been u t i l i z e d . I f a p a r t i a l system was ava i l a b l e i t could be modified and adapted where necessary. A transportation planning model for d e t a i l e d t r a f f i c analysis had been developed by the Un i v e r s i t y of B r i t i s h Columbia and the C i t y of Vancouver"'". The model was designed to study the operational problems of peak hour vehicular commuter t r a f f i c . It i s most appropriately applied to areas of high t r a f f i c a c t i v i t y such as the ce n t r a l business d i s t r i c t of a metro-'. .. po l i t a n area or a r t e r i a l streets of a region-wide network during peak demand. The framework consists of a parking a l l o c a t i o n model and a multipath p r o b a b i l i s t i c assignment model which considers the ph y s i c a l i n t e r a c t i o n r o f auto and t r a n s i t t r a f f i c . This methodology p a r t i a l l y f u l f i l l s the require-ments of t h i s paper. It does not consider the t r a n s i t side of trip-making nor the choice process between the auto and t r a n s i t modes. To meet the requirements of t h i s paper, a t r a n s i t assignment model, mode s p l i t model and equilibrium algorithm would have to be added to the U.B.C. framework. 32 Short range policies and t r a f f i c management programs are directed at, and generally affect only the operational service levels 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 in the C.B.D.. To develop a methodology from scratch would have been a dupli-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 is a description of the U.B.C. framework. Each of i t s :. components is described in detail and the suitability in an equilibrium context is 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 localized t r a f f i c networks. In order to accurately model vehicle delays, the transit and pedestrian t r a f f i c and their interaction with auto t r a f f i c was modelled as well. The framework was designed to be applied-, in an area of high t r a f f i c activity such as the central business d i s t r i c t or the arterial 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 c r i t e r i a : 1. Reproduce observed t r a f f i c patterns. 2. Forecast new t r a f f i c movements after changes in the road network, parking system or office concentration. 3. Be inexpensive and quick to use. 4. The output should be in a form which is 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 is discussed by 2 Navin . The model was put together as a group of programs, each program designed to work independently or interactively with the others. Figure 8 shows a flow chart of the programs. The processing commences with the pedestrian and vehicle network builders which are contained in the program DEBUG. It searches for logical errors in the network and produces a plot of the vehicle network. It also outputs pedestrian travel times. The program TRANSIT performs a similar function in that i t sets and produces a plot of the transit network. These two network programs provide data to both the parking allocaiton 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-:/ trian networks, checks for errors and produces a plot of the vehicle network. It also computes the pedestrian walking times from parking lots 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 transit network and computes the volume of buses on the links which are supplied to the vehicle assignment model STOCH. The purpose and theoretical aspects of the parking allocation model TRANS and the t r a f f i c assignment model STOCH w i l l be discussed in 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 total cost variable. Parking services however, are a distinct 34 F/G UR £• 8 F^OW CHART OF rHE UB.C. COMP(/rFG FfiAMertQRK. &os PATA: ///FA0WAV5 j IgQfjTF*. FTC./ ll /PLOT op 7 VEHICLE A V O PEPEST/VIA/V NFrWOKK JBullDEP I WALK T/ME- 7 —"7 TO \loB IfifiRK/fJc t o r j I JV£MH-l£ 1 ~i HETWOXKJ-L D M . I p/i/cE^ / IOCATIOAIS fl '•S/ZE em / 1 WAVS/71 , 1 / VEH/CIC. />ss ICAJME-A/T FRafsi OP/&>/YS ra I f i o r OF rR>*K,,r Poorrsl It&Uii IJTOPS I & ULL IPA#K//VG /or Aoros I//VAV5I Aiioc/ir/OfiJ OF nu7odi TO PAPK/fi/G iors '/tar or AU7O ' VOLU/4E& ofJ t./tjKS t /wrtKsecr/otss / F/GURE 9 FLOW CHART OF THE MOO/F/ED FRAME WORK. /Peoe^TFjfKtj I FINISH L tUDiCAree PATH OP ITERATION/ PArfit PAoce^-5/A/c NOTE • OAI r u e Fi£t>r irefiaT/otj THE ex/sr/*/c AUTO fiAJO T*A*/6IT DErlArVDS ARE USED. O/V $UBGEQaEAIT ITEPAriOM% THESE /XA<IA/VOS A / ? f REVISED AUTOMATICALLY py r u e MOPE SPLIT-AMD £0<JiLi/3f!'UM fiLGORlTHrt. 35 product or factor input from transportation services and are complementary 3 to auto use . Work that Gillen has done suggests that drivers w i l l capitalize 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 taxi, relying on family members for a chauf-feured 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 is a complex problem with many variables. In the light of these avoidance methods enumerated above, the old assumption that automobile costs rise in equal proportion to the increased parking costs i s false. These reduced real parking costs would have a significant effect on mode sp l i t calculations. Also as mention-ed in 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 in the most congested part of the city, the C.B.D.. From the discussion i t would appear then that to be consistent with equilibrium concepts i t is necessary to include a model which would attempt to describe the processes above. In effect, i t s purpose would be to contri-bute a better description of the service levels for the auto mode and a better description of demand levels on the links in the C.B.D.. 4.2.2. The Parking Allocation 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 for in existing parking models while others cannot. Shifting to taxi mode, being chauffeured and parking i l l e g a l l y cannot be modelled. There is not sufficient empirical data available to formulate descriptions of the mechanisms involved in these types of behaviour. Within a parking allocation framework, guaranteed parking spots, employee reimburse-36 ments and the trade o f f of parking charges and walking times can be passengers can be addressed through the l o g i t model. The parking a l l o c a t i o n model used was designed with a two-fold purpose i n mind. F i r s t l y , i t may be used to determine the r e d i s t r i b u t i o n of parking a f t e r a l t e r a t i o n s i n the organization, p r i c i n g and structure of the downtown parking system. Secondly, i t provides o r i g i n and destination data f o r the t r a f f i c assignment program. Given that the f i n a l destination of the commuter i s known the model uses a l i n e a r programming approach and optimally assigns v e h i c l e s to parking l o t s on an uncongested network. Optimal l o c a t i o n as defined by the model theory i s the set of locations which minimizes the t o t a l cost f or the system of commuters given the contraint of parking l o t c a p a c i t i e s ^ . The costs to be minimized are the cost of parking and that of walking. The value placed on walking i s determined by the socio-economic status of the worker. A provision i s included i n the model which takes into account workers with high incomes or workers who have t h e i r parking fees subsidized or guaranteed. They are lumped into an i n e l a s t i c component of the demand. The function to be minimized i s : i>g>k,l where 0 ( i , g , k , l ) = the number of 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 destination i n zone k and parking i n zone 1. W(g,k,l) = cost of walking time f o r group g from zone 1 to k. C(l) = parking charges i n zone 1. addressed. Within the larger framework of the paper the problem of carrying (.0(i,g,k,l) x (W(g,k,l) + C(l) ) 12 37 The constraints imposed on the system are; \ ~ ~ 0(i,g,k,l) = T(g,k) — 13 1,1 i,g,k,l) S(l) 14 where T(g,k) is the number of trips in group g whose final, destination :*. is zone k, and S(l) i s the parking capacity in zone 1. The output from TRANS consists of vehicle origin/ destination informat-ion which is used in the t r a f f i c assignment program,:-and parking and walking costs which are used in the logit model. There are several drawbacks with this 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 allocation based on an uncongested network. The allocation of "parkers" to f a c i l i t i e s is based on the overall 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 their individual benefits would be more reasonable. The data requirements and a more complex calibration of the parameters is required in the behavioural models. The model used in this framework was selected because i t was readily available and i t i s an adequate and accepted tool for determining parking allocation. 4.2.3 An Equilibrium Model for Vehicle Traffic A t r a f f i c assignment model is a method of determining the equilibrium flows of vehicles on a road network. There is a hierarchy to the application 38 of equilibrium models. At the beginning of this paper such a model was described which considered the interaction of variable socio-economic activities over a multimodal transportation network with associated variable demand levels and resulting levels of service. For the overall short run thesis of this paper this general model was constrained to one of fixed demands, fixed socio-economic activities and a fixed multimodal transportat^ ion network. The level of service is variable and the equilibrium model consists of the interaction of the demand levels and service levels of the auto and transit modes. In order to determine the demand levels and service levels of the two modes an equilibrium model is needed which describes the interaction of the demand and service levels on the paths in the network -for each mode. There are numerous approaches available for solving single-mode equilibrium problems. Traffic 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 far predominated the other classes in actual application and in number of variants. The following deficiences have been noted in these approaches in solving network equilibrium problems^: 1. Link travel times have often been kept constant, thereby ignoring the existence of link supply functions. 2. Origin-destination trips have often been kept constant thereby ignoring the existence of travel demand functions. 3. The number of paths travelled between each origin and destination have often been limited to one, making i t impossible, normally, to satisfy Wardrop's f i r s t principle. 4. The accuracy of the approaches as approximations of equilibrium 39 has not been determined. (This includes both t h e i r convergence properties ( i f they involve i t e r a t i o n s ) , and t h e i r expected - : : errors upon completion.) The D i a l Stochastic Assignment used i n the framework presented i n t h i s paper avoids a l l except the l a s t of 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 function of the demand on the l i n k s . The o r i g i n -destination 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 switch to the t r a n s i t mode) and more than one path i s considered. C r i t i c i s m s have been leveled at the D i a l model from other sources however, when assembling a modelling framework more than t h e o r e t i c a l 8 9 considerations must be taken into account ' . Probably no matter what modelling methodology was selected i t would be subject 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 les s than r e a l i t y . The model se l e c t i o n must be made within a set of time and resource constraints and must perform adequately the necessary functions i n order to solve the problem. The D i a l model i s s i g n i f i c a n t l y better than a l l - o r - n o t h i n g assignment techniques^. Conversely, i t i s not the best technique a v a i l a b l e . It performs the functions which are needed to solve the problem being addressed. It has been used by the T r a f f i c Engineering Department of the Cit y of Vancouver for operational t r a f f i c analysis, whether i t produces r e s u l t s s u f f i c i e n t l y accurate f o r the requirements of t h i s paper i s some-thing which w i l l 'have to be determined. 4.2.4 The Stochastic Vehicular Assignment Model The v e h i c l e network i s loaded with t r a f f i c using the p r o b a b i l i s t i c multipath approach developed by Dial"'""'". Trips are assigned to e f f i c i e n t paths between o r i g i n and destination pairs . u t i l i z i n g an algorithm which 40 precludes the necessity of enumerating the paths. The Dial method has the following five basic specifications: 1. A l l reasonable paths between a given origin and destination have a non-zero probability of use. 2. A l l reasonable paths of equal length should have equal probability of use. 3. 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 expl i c i t l y enumerate a l l paths. An efficient path is defined as one which proceeds in the direction of the destination and does not "back-track". The distribution of trips along routes with different travel times is assumed to be determined according to the decreasing exponential function: (• exp ( e t P . ) 15 where t _ t r a v . e ^ time along an efficient path ^ is a model parameter which determines the dispersion of trips along paths of different lengths. 4.2.5 Vehicle Delay There are two components to vehicle 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 is considered to be minor compared to the delay at intersections. In general the intersection 41 12 constitutes the region of minimum capacity of the l i n k . It was assumed that only volume delays due to the i n t e r a c t i o n of t r a f f i c at i n t e r s e c t i o n s are considered i n the model. The i n t e r a c t i o n of t r a n s i t and pedestrian t r a f f i c with v e h i c l a r t r a f f i c i s considered as w e l l . The>problem of capacity r e s t r a i n t i s addressed by u t i l i z i n g an incremental approach to assignment. The program allows the analyst to break the assignment period into a number of smaller assignment periods. It also allows him to assign any combination of proportion of the vehicular load to the set of smaller assignment periods. For the f i r s t assignment period, i t assumes t r a v e l times due to free flow conditions and for each subsequent assingnment i t uses t r a v e l times computed by the previous i t e r a t i o n . 42 FOOTNOTES 1. C. Fisk, "A Transportation Planning Model for Detailed Traffic Analysis", Transportation Research Series Report No, 11, The University of British Columbia, Department of C i v i l Engineering, 1977. 2. F. P. D.Navin, C. Fisk, '. "A Downtown Traff i c Management System", Prepared for the Canadian Transportation Research Form Annual Meeting, St. Andrews, New Brunswick, 1977, p.13. 3. D. W. Gillen, "The Effects 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. Gillen, "Effects of Changes in Parking Prices and Urban Restriction on Urban Transport Demands and Congestion Levels", University of Toronto- York University, Joint Program in Transportation, 1975, pp. 20 - 25. 5. C. Fisk, op. c i t . , pp. 11 - 13. 6. E. R. Ruiter, "Implementation of Operational Network Equilibrium Pro-cedures", Transportation Research Board, 491., 1974, p. 43. 7. Ibid. 8. J. D. Murchland, M. A. Florian (ed.), "The Structure of Model Research", Traff i c Equilibrium Methods, Proceedings of the International Symposium at the University of Montreal, Springer-Verlag, New York 1976, p. 8. 9. J. E. Burrell, M. A. Florian (ed.), "Multiple Route Assignment: A Comparison of Two Methods", Traff i c Equilibrium Methods, Proceedings of the International Symposium at the University of Montreal, Springer-Verlag, -New York, 1976. 10. R. B. Dial, "A Probabilistic Multipath Tra f f i c Assingment Model Which Obviates Path Enumeration", Transportation Research Vol. 5, 1970, pp. 84 - 85. 11. Ibid., 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 choice was made to u t i l i z e the computer modelling system developed at U.B.C. It p a r t i a l l y s a t i s f i e d the t h e o r e t i c a l requirements outlined i n Chapters 2 and 3. The addition of a t r a n s i t assignment model, mode s p l i t model and an equilibrium algorithm complete those requirements. This chapter deals with the functions, d e t a i l s and assumptions imbedded i n the a d d i t i o n a l work. The three new models are a l l contained i n the program c a l l e d BUS. It i s executed a f t e r the ve h i c l e assignment program; r e f e r to Figure 10. There follows a b r i e f d e s c r i p t i o n of the functions of the program. The t h e o r e t i c a l basis of these functions are described i n greater d e t a i l l a t e r i n t h i s chapter. The t r a n s i t assignment model assigns t r a n s i t t r i p makers to bus routes. Walking, waiting and transfer times are considered. The i n -ve h i c l e bus times are a function of the number of stops the bus makes, the number of persons loading and of f - l o a d i n g and the average speed of the stream of t r a f f i c . The t r a f f i c speeds are computed by the v e h i c l e assign-ment model and are supplied to the t r a n s i t program. The mode s p l i t model takes the service l e v e l s computed by the parking 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 estimated mode s p l i t . The equilibrium algorithm computes a t r i a l mode s p l i t based on the mode s p l i t form the previous i t e r a t i o n and the one j u s t calculated. A new set of o r i g i n s and destinations f or both modes are computed using 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 input back into the park-ing a l l o c a t i o n model and the t r a n s i t 0/D back into the t r a n s i t assignment model. Before the i t e r a t i v e process i s begun again with the parking a l l o c a t i o n model, a tes t i s made to determine the change i n t r a v e l times Figure 10 FLOV fa) PlAiN fxocgsiAl PEAO IN DATA •DO I- 1, P OF oPl&l/VS CALL. P1/NP77/ C A / / A S S / / <ZQNT/AIUP r-^-DO L-J, itoAOAti&lrJS PEAL? PRESENT Avro JouE.riE^/ TIPIE t LENGT/, ftEAO PREVIOUS AUTO \JOUPlAfEy TP AVEL. p//vjPS FPtOAO -SEQUE/J-TIAL. PILE:. v/;;i7£ PSIESEA/T ~jQun//ey TIME ro s eo UF/ATIA, L FIL E. W/R/rC TFIA.</EL TIMES COAS&/T/0MS FOfX PPF&ENT ANO PAEVtOVb IFEAATIONS CAJTSPUT '•—I CONTINUE AIPITE WOPE SPLITS AC"? PAIS SFA/T \/TEAIP. TIO/-'  WRITE, our STATISTICS Aon i3o& LWE?, (6) SUBROUTINE M/NPTH. INITIALIZE VECTOIS TATi TABIC Tir?ies*9999? S T E P ! PINO WAIK UNKii TO S " S STOPS W/THrrf « Pee ser WALK'NC 7i#ie PerefiMi»e WALK / vva/r T>ME POA BUS \ WNTEH Tines i PATHS \iNrri rue LIST  Ser E-AeYtLWS LWK OEST/ASATIONS ra NEV/ Fii/D LINKS d Mooes \NITH BUS i W f f Of/ CALL T/AJ DETERMINES /NVEMCLE. TRMEL TIME £ F/flA/SAF^ rime. P//TEP LINKS/CUAIotflllVt TAP VEL TIM£ TO DESTINATION NopE /Uro tisr I 5 T E P 3 I 4A6EL WAlK Llf/KS TO E/NAL QBiT/AJATIDH Mo MINIMUM PATH 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 \PAMOVE FFONI ChTr. [P//IEA. slew THA/EC TIMB TN TAPE TA&LE. fiOS STOPS TO firJAL DESTIEIATION Mr///'/ PAECET WAir rime OETCMINEL INAIK rime. Fo* LiNKS •  ADO To Bot, sroP w * f S ANO ANTTA Cu/ficiT\ri'it TAAVf-L. T'rtFS t LINKS ifjTo rue L/sr.  CHART OF PROGRAM BUS ICALLPO FPcMP,INPTU oo/^Puie. TIME TO ScfAD BUS $ Tfi.fiYEL TIME. ON UNK 1 •• 1 STdtAE. 60S LINE*, cW Srr?P • RBTOASfJ | \CoikPaia /NVEHiciF. 1 r x k VBL TIKI e ON i3id\ Oo J- J #DFS7iNfiriat&-\A0& [coA*fPA#£ 6US LINES, 'w/|r/y THOSE. STo/eei? ATirpe PPiVIOUQ imp j y e s \AQ/Q TPAN3 FE At 7H1E\ SmRE &OSLsNE5 O A / A.NfKS PASS'NG THE. cunyieNr B P S =s TQP_ CcwPor£ THE Afvf~<(!(g. OF PSrSzCtJCrtA?. rAAYE£l.liVc, /SAlWfLAl OO J-r 1 ) 4 OA A,NFS ASSI&K/ PAS-~eA/ce#z> ACCQAP'NC TO FFequEA/cy o= sfewc^ / Aio. OP 0ck' A s/YF 5 PASS INS THE STOP \ASSICH PASSENOFte TO SUS H / A / r f S lAJ TFB SAAtE AlAMfieiZ. IF^ FPGrf>-/Jo ^JXANSFEG FAvrt L//JE TO A/JOTh'E£. yes ViPO TAirtS^eAS TO ^TOP& CPNTIHUC AlETuAA/ CoMAut'F /-lone •sa/T BSl<EO O/J O^TA (Zas-iPurFG FY T.'/E COAPerir ITp/ZATWrJ O/JL y . \COMPOTE NEYV ECHO \AfJO TpAfJilT epplErlQ^ WfiiTp, coMPufFC A^ooe \SPLITS TO P • tSE&CENflEL P/L/E RETUAN. A?FAO OLD /AOOE SPLIT CO/JPUTFO BY PAE/IOL& ITEAATIQ/S F~fi?or* SFGUENTfAL PILE spur SA,seo aN/OAiA IOMAVTEO JBY T//E. COP Ae A/T /IfSGATlCll/ Cap,PJlE A TPIAL AiOOL SPLIT BA^eoo/F THE DLL~> ANO A/ElAA AAOPE-SPLITS '(.OMPOTE. AUTO ANO TP^NSTE OFpffiNOS CIS/N& TRIAL Aiooe. SPLIT.  rVP/re TP/AL AIOA>E • \SPLITi TO TA£ s E <Z PENT i At PILE SuG/KrOr/N£ p u p r A~WD TAP. AU7 O L/NCS WfilCN 7AH BiTi* A'-K/li SAL6C7FA) r o s e PXiA/rp/} L/SPS . OcrefiMI/'E 7/>A:JPL-7/A-/F 0Y TP>P:*/SrT ON me 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~~ Z l 45 between i t e r a t i o n s . If the change i s below a predetermined l e v e l then the process i s stopped. 5.1 An Equilibrium Model For Transit Before proceeding to the discussion of the theory behind the t r a n s i t assignment i t may be us e f u l to discuss the term i t s e l f . When one speaks of ve h i c l e assignment one thinks of the assignment of automobiles to 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 to the assignment of t r a n s i t passengers not only to the t r a n s i t network but to walking l i n k s to and from the network. Transit passengers are assigned to paths on an al l - o r - n o t h i n g basis without a capacity r e s t r a i n t function. Travel times arecidetermined on the loaded network for use i n the l o g i t model. These congested t r a v e l times are not used to a f f e c t the assignment of people to routes i n the t r a n s i t network. The use of an al l - o r - n o t h i n g assignment technique may be questioned from an equilibrium point of view. S i m i l a r l y , the lack of a capacity r e s t r a i n t function may also be questioned. Herein appears a discussion on why t h i s may be acceptable from a t h e o r e t i c a l point of view. Its v a l i d i t y can only f u l l y be accepted when these ideas are tested. A t h e o r e t i c a l equilibrium assignment can be described as a convex type of function. The s o l u t i o n i s located at the minimum point of the function. No user can reduce h i s generalized t r a v e l l i n g costs by a l t e r i n g h i s route. This s o l u t i o n has the c h a r a c t e r i s t i c that each path which i s used between any p a i r of points has a cost which i s no greater than any other path between those points. When dealing with automobile assignment the nature of the road network allows for a choice between multiple paths which have s i m i l a r costs between a given 0-D p a i r . All-or-nothing assignment of auto t r i p s assigns a l l the 46 t r i p s to paths which may be only a few seconds shorter than p a r a l l e l paths. In c e r t a i n applications t h i s leads to u n r e a l i s t i c assignments. The t r a n s i t network d i f f e r s from the automobile network. The service i s provided on a coarser g r i d and hence there are fewer p a r a l l e l paths with s i m i l a r costs. The p o s s i b i l i t y of multiple path use between any given 0-D p a i r i s reduced due to the l i k e l i h o o d of greater differences i n costs between p a r a l l e l paths. S i m i l a r l y , because there are greater differences i n costs between p a r a l l e l paths the consideration of capacity r e s t r a i n t i s not l i k e l y to have a s i g n i f i c a n t e f f e c t on route choice i n t r a n s i t . Congest-ion i s l i k e l y to increase t r a v e l times but i s not 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 the advantages of one route over another. Where the congestion e f f e c t s may have more impact i s i n the mode choice. I t i s f o r t h i s reason that t r a v e l times on the f u l l y loaded t r a n s i t network are computed. More important i n t h i s paper i s the desc r i p t i o n of t r a n s i t t r a v e l times. The generalized costs of t r a n s i t t r a v e l are more complex than auto t r a v e l . Whereas the auto d r i v e r attempts to 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 of walk times, waiting, t r a n s f e r r i n g and i n v e h i c l e times. I t i s widely accepted that the commuter values a l l of these components d i f f e r e n t l y . Also, the c a l c u l a t i o n of t r a v e l times r e l i e s on d i f f e r e n t delay functions. The problem i n t r a n s i t equilibrium solutions i s one of accurately describing the generalized costs of t r a n s i t t r a v e l . An attempt has been made i n t h i s paper to address that problem. 5.2 The All-Or-Nothing Assignment Model This section deals with a de s c r i p t i o n of the computer model developed for t h i s paper'.' Figure 10 i s a d e s c r i p t i v e flow chart of the functions • performed by the program. There i s a main program and f i v e subprograms. 47 The general functions of the subprograms are: MINPTH: Determines the minimum path ASSN: Assigns passengers to the minimum paths SPLIT: Performs the mode s p l i t and some of the equilibrium functions 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: Preparation of vectors f or print-out of selected bus l i n e s . The purpose of t h i s i s to i l l u s t r a t e the organization of the program. However, within t h i s organization f i v e important functions are performed. They are: (1) minimum path search; (2) t r a n s i t t r a v e l time computations; (3) assignment of passengers to the minimum path; (4) mode s p l i t computation and (5) equilibrium computations. Each of these functions w i l l be addressed with references to the flow chart. The main program reads data, controls the subroutines and writes out the f i n a l r e s u l t s ; r e f e r to Figure 10(a). The following equilibrium s t a t i s t i c s are also written out: - The average of the current and previous t r a v e l times from each o r i g i n to a l l destinations by car 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 destinations by each mode and the s p l i t . - The average change i n mode s p l i t between i t e r a t i o n s . - The s t a t i s t i c s of bus usage such as numbers of passengers on the bus, numbers at the stop and the average speed of the bus. 5.3 Minimum Path Algorithm This algorithm finds a minimum path from the t r a v e l l e r ' s o r i g i n to h i s destination. This includes walking to, and waiting f o r the bus, r i d i n g the bus, any t r a n s f e r r i n g necessary, and the f i n a l walk to the destination. The algorithm has two basic functions: a path generator which generates 48 paths and stores them i n a l i s t , and a minimum path f i n d e r which removes the minimum paths from the l i s t and stores them i n a tree table. Figure 10 '.(b) i l l u s t r a t e s the flow of the processing i n the subroutine MINPTH. The path generation process i s broken into three segments: 1. the walk to, and wait at the bus stop; 2. the t r i p on the bus, including transfers and 3. the walk to the destination. The f i r s t segment u t i l i z e s the walk l i n k s and t r a v e l times computed by the program DEBUG and the o r i g i n s and destinations associated with those l i n k s . A set of pedestrian o r i g i n s and destinations and a maximum walk time are designated by the analyst. The program DEBUG finds destination nodes which are within the maximum walking time from the o r i g i n s . The path generator s e l e c t s destination nodes which are bus stops and c a l l s the sub-routine TIM to compute the wait time f o r the bus. The t o t a l time to the bus" stops and the nodes at the bus stop are stored i n a l i s t . The minimum path f i n d e r selects the path to the bus stop with the minimum t r a v e l time, stores i t i n a minimum path tree table and removes i t from the l i s t . The paths to other bus stops remain i n the l i s t to be used l a t e r on. A f u l l e r explanation of the minimum path f i n d e r w i l l be given l a t e r . The second segment of the path generator uses the bus stop node found by the minimum path search as an o r i g i n f o r l i n k s proceeding away from i t . The l i n k considered must have bus l i n e s on them. In t h i s path generating process, the program takes t r a n s i t network data from the program TRANSIT and superimposes i t upon the v e h i c l e network data from program STOCH. In adding l i n k s to the l i s t i t i s not important which bus l i n e i s a v a i l a b l e , i t i s only important that there i s a bus l i n e along that 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 along the l i n k s are computed i n subroutine TIM. The passenger i s allowed to make as many transfers as necessary to reach h i s destination. 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 destination. He cannot get o f f , walk and reboard the bus. I f the destination of the new l i n k i n segment 2 i s a bus stop then the program con t r o l moves into the t h i r d segment. The function of the t h i r d segment of the path generator i s much the same as the f i r s t . In t h i s case destination nodes and the cumulative t r a v e l times including walking are added to the l i s t . Again only those destinations which are within a maximum walking time from the bus stop are considered. At t h i s point, control of the program moves to the minimum path f i n d e r . Control can move to the minimum path finder a f t e r the second segment i f none of the destinations of the new l i n k s are bus stops. Control always moves to the path fi n d e r a f t e r the f i r s t and t h i r d segments. The function of the path generator i s to add new l i n k s to the paths and store the destination nodes of those l i n k s along with the cumulative t r a v e l time to the nodes i n the l i s t . In general, there are three steps to the minimum path finder function. The f i r s t step i s to f i n d the node with 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 step i s to compare that t r a v e l time with what i s already stored f or that node i n the tree table. ( The tree table i n i t i a l l y i s set to a very large number. ) If the time from the l i s t i s less than that already stored then the old t r a v e l time i s replaced by the new value. The f i n a l step i s to return c o n t r o l of the program to the second segment of the path generator. Here the destination node of the tree table becomes the o r i g i n node f o r the generation 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 already stored i n the tree table then c o n t r o l gees back to step one of 50 the minimum path f i n d e r . The process i s complete when no more l i n k s can be added to the paths and when the l i s t i s emptied. In order to prevent walk l i n k s from becoming intermediate l i n k s , a l l nodes which are part of the bus network must be removed from the l i s t f i r s t . 5.4 Transit Travel Time Computation A l l components of t r a n s i t t r a v e l time are computed i n subroutine TIM except the walk times to and from the bus l i n e s . The t o t a l t r a n s i t t r a v e l time i s described mathematically i n t h i s manner: TT = f(WT) + f(W) + f(IV) + f (TF) + f(WF) 16 where TT = t o t a l t r a n s i t t r a v e l time WT = walk time to the bus W = wait time and time to load IV = i n v e h i c l e time TF = trans f e r 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 to any number of bus stops which are within a maximum walk time set by the analyst. These walk times (as already mentioned) are inputs from the program DEBUG. Another portion of the walk l i n k i s the wait time and t h i s i s comprised of waiting for the bus to a r r i v e and waiting for the bus to load and get under way. The amount of time spent waiting for the bus i s given by the following equation. W = 0.13/( +2.8 17 where W = wait 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 Everall . 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 lines with head-ways less than 7 minutes were assumed to be half the headway. Where there", is more than one bus line available going in the desired direction the headway is assumed to be the average of the lines available. The loading time is given by the number of persons times a per person boarding time set by the analyst. Off-loading is 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 travel 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 is the same. Bus t r a f f i c flows over road links designated for use by the transit network program TRANSIT. The bus lines which travel on the links are used for headway calculations for transfers and so that u t i l i z a t i o n of particular lines may be tabulated. Invehicle travel time on any link is 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 velocity Stopped time is 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 t r a f f i c 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 bus N = number of bus stops along the l i n k The average v e l o c i t y i s an input from the automobile 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 are set by the a n a l y s t . The running time at average v e l o c i t y i s the time taken to cover the distance of the l i n k not covered 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 . The STOCH program considers i n t e r s e c t i o n delay, cornering v e l o c i t i e s , a c c e l e r -a t i o n and d e c e l e r a t i o n of the v e h i c l e s from stops. The time to t r a v e r s e a l i n k i s given by the above mentioned components. Rather than breaking them down i n t o t h e i r separate components f o r the t r a n s i t computations, the average v e l o c i t y i s simply taken to 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 time on that l i n k . The t r a n s f e r time i s h a l f the average of the headways of the bus l i n e s going i n the d e s i r e d d i r e c t i o n up to a maximum of 5 minutes. This assumption was made on the b a s i s that during rush-hour, buses w i t h headways greater than 10 minutes w i l l meet at t r a n s f e r p o i n t s so that the maximum wait time i s 10 minutes and the average wait time i s 5 minutes. There d i d not appear to be much work done i n the f i e l d of s t u d i e s of t r a n s f e r time. However, these assumptions seem to be reasonable f o r rush-hour c o n d i t i o n s . As there are u s u a l l y a number of bus l i n e s t r a v e l l i n g along the same route i t i s not p o s s i b l e to determine e x a c t l y which bus l i n e the passenger i s on. The only way that the program knows : that a passenger has t r a n s f e r r e d i s when none of the bus l i n e s on the present l i n k are the same as on the previous l i n k . When t h i s occurs the t r a n s f e r 53 t r a v e l time function i s activated. The minimum t r a n s i t paths are computed twice. This i s done so that the loading of the system with passengers can be taken into account. The program computes the minimum paths from o r i g i n s to a l l destinations and assigns passengers to the paths sequentially. It i s not a simultaneous process whereby a l l minimum paths are computed and the passengers are loaded on to the system at once. Because passengers from more than one o r i g i n share parts of the same path,- the paths computed f i r s t and assigned f i r s t are under-', loaded and hence have low t r a v e l times. To overcome t h i s problem the minimum paths are computed once again with the system f u l l y loaded. In order to r e f l e c t the delays to passengers due to overloaded buses the wait times are considered to 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 are comprised of walk times, wait times, trans 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 times are s e n s i t i v e to the number of automobiles sharing the same l i n k s and the number of people using the bus system. 5.5 Assignment of Passengers to the Network ~ The subroutine ASSN assigns the passengers to the minimum paths computed by MINPTH. Two assignments are c a r r i e d out. Transit users are assigned to the bus stops as well as to the buses. Therefore, i t i s possible to determine the number of people waiting at the stops and the number of persons on the bus. This data i s used i n the second execution of MINPTH (see Figure 10(a)) to account f o r the delay due to people boarding and e x i t i n g the bus. The instantaneous demand on a minimum path i s given by the equation: ID = D x H / ( P x N B ) . 20 54 where ID = instantaneous demand along the ent i r e route H = headway of the bus D = t o t a l demand over the assignment period P = the length of the period NB = number of bus l i n e s on l i n k Instantaneous demand i s the average number of people at a bus stop waiting f o r one bus l i n e or one bus at any instant throughout the assignment period. This i s computed f or each of the minimum paths. Where these-paths share the same bus l i n e s , stops and transfer points, the instantaneous demands for the i n d i v i d u a l paths are added together to produce the t o t a l instantaneous demand on the system. One of the d i f f i c u l t i e s encountered i n the assignment process i s that where there i s more than one bus l i n e serving a bus stop or a route i t i s not possible to determine which one the passenger w i l l use. To overcome t h i s , where a number of bus l i n e s are a v a i l a b l e the passengers are loaded equally among them. S i m i l a r l y , the average of the headways of the buses are used to compute wait times. 5.6 The Mode Choice Model The subprogram SPLIT containing the l o g i t model i s set up so that with 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 generalized cost components made av a i l a b l e to the mode s p l i t model are the: in v e h i c l e t r a v e l times f o r both modes, the walking time f o r the auto mode, the parking costs, the distance t r a v e l l e d by car, and the out of ve h i c l e t r a v e l time f o r bus users. The out-of-bus t r a v e l times include walking, waiting and transfer times. A l o g i t model already 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 for demonstration purposes'*. If a study was being done i t would be necessary to collect data and calibrate a logit model to the particular city being studied. In the model given below G(x) is a : function of the choice variable and P £ is 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 21 P = e G ( x ) / ( l + e G ( x ) ) 22 c where TT/TC =. ratio of door to door travel times for transit and car respectively FT/FC = ratio 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 = social status variable, SS = 1 i f the individual is a middle manager or higher, otherwise SS = 0 Y = gross income of the individual in thousands of dollars EPC = the inclusive parking price associated with choosing the auto mode for a given trip 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 logit 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 social factors could be included in the analysis. The following simplifying assumptions were made about the input data to the logit model. The modal cost of transit 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 capability of handling three different 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. Similarly, f i f t y i 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 dollars). Given these assumptions Gillen'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 in 1964. The parameters of the model are most appropriate to that year and place. It is thought however, that for the purposes of demonstration the above equation w i l l yield results which are responsive to changes in travel times and parking costs. 5.7 A System Equilibrium Algorithm The transportation model presented in 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 is determined through assignment methods. The validity and assumptions of these methods have been discussed. The global equilibrium of the system (both modes combined) is solved using an equilibrium algorithm. A general equilibrium algorithm for the single mode was suggested by Ruiter^. The equilibrium model, here follows the procedural framework outlined in his paper and is 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 the best d i r e c t i o n i n which t o proceed to ob t a i n a new t r i a l s o l u t i o n . 3. Develop a t r i a l s o l u t i o n . 4. Obtain 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 not r e t u r n to step 2. The i n i t i a l i z a t i o n c o n s i s t s of executing a l l of the steps shown i n Figure 9. This serves a four f o l d purpose: (1) I t performs the 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 allows the ana l y s t to determine whether the model i s accurate i n p r e d i c t i n g the current s i t u a t i o n . (3) Rather than s t a r t i n g o f f the process w i t h f r e e flow s e r v i c e l e v e l s corresponding to zero flow c o n d i t i o n s , the network i s already loaded. This reduces the number of i t e r a t i o n s needed to approach e q u i l i b r i u m at the new parking c o s t s . (4) I t tab u l a t e s and st o r e s the cost b e n e f i t f a c t o r s such as t r a v e l times, t o t a l d i s t ance t r a v e l l e d e t c . f o r comparison w i t h the co n d i t i o n s of the t r a n s p o r t a t i o n system under the 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 the d i r e c t i o n f o r the 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 the e x i s t i n g s i t u a t i o n and stor 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 to Figure 10;Cei)v-. The new parking charges are introduced at the park i n g a l l o c a t i o n step. The v e h i c l e and t r a n s i t assignment steps are executed and then the mode s p l i t step i s executed. The s i g n of the d i f f e r e n c e between the o l d mode s p l i t and the 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 of the 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 determined as a function/of the o l d s o l u t i o n , the d i r e c t i o n of the new mode s p l i t , and the d i f f e r e n c e between the new and ol d mode s p l i t s . I t i s not p o s s i b l e to use the new mode s p l i t as the t r i a l 58 so l u t i o n f o r the next i t e r a t i o n because i n congested systems i t tends to overestimate the s o l u t i o n ( i . e . on subsequent i t e r a t i o n s , the d i r e c t i o n of the s o l u t i o n reverses d i r e c t i o n ) , The t r i a l s o l u t i o n i s obtained i n t h i s manner: When M Q ^ .5 - <; *E = M 0 + M 0 ( MN " V 2 4 When M Q < : .5 M T = M Q + ( 1 - M Q) (MJJ - M Q ) 25 where M = the auto mode s p l i t .computed by equation 22 and the subscripts N = new 0 = old T = t r i a l The t r i a l mode s p l i t i s used to determine the t r a n s i t and auto demands in the n e x t • i t e r a t i o n . The l e v e l of service r e s u l t i n g from these demands i s used to determine a new mode s p l i t (step 4) and the t r i a l mode s p l i t on the previous i t e r a t i o n becomes the old mode s p l i t . The old mode, s p l i t was chosen as the moderator because i t was found that i t worked well. Appendix A documents the work done to determine t h i s f i n d i n g . The process continues u n t i l the system converges. The convergence test (step 5) simply indicates the percent change i n t r a v e l times from one i t e r a t i o n to the next. Since the i t e r a t i v e process i s i n the cont r o l of the analyst i t can be halted according to the judgement of the analyst. In summary, the e f f e c t s of a p o l i c y change i n the transportation system are determined by executing the computer models i n the following manner. The programs are run f i r s t with current data and p o l i c i e s . The reason for t h i s i s outlined above. The analyst 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 appropriate program and commences the i t e r a t i v e process. 59 If changes i n parking charges were being examined, then the analyst would a l t e r the parking costs i n the parking a l l o c a t i o n model and run that program. Next, the vehi c l e assignment program, and the ensueing programs i n the i t e r a t i v e process 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 Arrivals at a Bus Stop", Transportation Science No. 3 Vol. 9, 1975, p. 280. D. A. Lynam and P. F. Everail, "Public Transport Journey Times in 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. Gillen, "Effects of Changes in Parking Prices and Urban Restrict-ion on Urban Transport Demands and Congestion Levels", University of  Toronto - York University, Joint Program in 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 theoretical aspects of an e q u i l i -brium model and the approach to constructing the model. The following sections delve into five topics. The f i r s t discusses the network used for the demonstration. The second enumerates the capabi-"' i l i t i e s of the transit program. The third traces an example through the modelling process to obtain equilibrium. The fourth section i s concerned with the problems and anomalies encountered in the example problem. The f i f t h and f i n a l topic deals with an example of how the system could be used for analyzing a short run policy question. Throughout this analysis the reasonableness of the results w i l l be discussed. "Reasonable" in this case implies: (1) any changes in service levels or parking costs w i l l result in shifts of demand in the appropriate direction and (2) that the changes in demand w i l l be in proportion to the change in level of service and vice versa. 6.1 A Demonstration Using A Small Network In the development of a computer modelling framework, i t is important to determine whether i t produces reasonable results before an application of the model is made to a real 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 practical, reliable and economical"'". These c r i t e r i a are important in satisfying the users' needs and must be defined by the potential user. The purpose of this demonstration is to determine whether the model produces reasonable results. The task of determining r e l i a b i l i t y and costs w i l l be leftcto -.others..' i ~ ~ o: . -goo.' F/GURLZ 11 A DEMONSTRATION NETWORK LEGENDi Bos STOPS 005 LINES PARKING LOTS ZOM£ Cy\//s/oA/—. —-TRAFFIC DIRECTION"-63 A small network was developed for the purposes of demonstration in which (see Figure 11) there are 4 parking lots, 4 bus lines, and 8 different streets laid out on a grid. The east-west streets are 800 feet apart and the north-south streets 1000 feet apart. The network is divided into 4 zones with a parking lot and entrance to the network in each zone. The network is intended to represent a C.B.D. with a restricted number of access points. Due to the fact that i t is such -a small network some modifications were made to the mode sp l i t model to make the input parameters more con-sistent with the choice situation faced by the downtown commuter. It was assumed that car drivers had already driven an average of 5.6 miles to arrive at the C.B.D. and had spent 20 minutes in their cars. Similarly 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 in 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 results, the assumptions liste d above and the size of the network should be kept in mind. Some unrealistically large delays were obtained at the entry points and the parking lots. 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 later. 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 transit -was generated by t r i a l and error so that the network would be congested. Several steps were involved in the t r i a l and error process: (1) Headways for the bus routes were selected. (2) The capacity of the parking lots and the prices charged were selected. 64 (3) The demand levels for auto and transit were selected. (4) The framework was run unti l the system had reached equilibrium. (5) The average speed for the automobiles on the network was used as an indicator of a congested network. (6) Steps one to five were repeated un t i l a reasonable level of congestion was attained (average automobile speeds less than 10 mph). The demonstration was divided into three parts: (1) an il l u s t r a t i o n of the capabilities of the transit program, (2) an ill u s t r a t i o n of the equilibrium process and (3) an analysis of a short run policy question. In the f i r s t two, the differences induced in the system by specific price changes were examined. For example when demonstrating the capabilities of the transit 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 lots. Similarly the equilibrium process was examined by increasing the prices on three lots by 2bi and the fi n a l lot by 50^. This differential increase served to highlight important points in the iterative process of obtaining equilibrium. Finally the analysis of a short run policy question entailed determining the aggregate effects on the transportation system due to incremental price increases on one parking lot only and incremental price increases on a l l parking lots. A l l of these price changes mentioned above are referred to as policies. They are considered to f a l l into two categories: (1) specific 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 policy A, B, C, etc. and the latter with numeric notation such as policy 1, 2, etc. 65 6.2 C a p a b i l i t i e s of The Transit Program The features and c a p a b i l i t i e s of the parking a l l o c a t i o n model and the. 3 ' , V ^ % ^ v e h i c l e stochastic assignment model are well documented by F i s k . The " assignment model i s backed up with an extensive graphical presentation system and may be used with the modified framework for a n a l y s i s . The expanded portion of t h i s framework which now includes the t r a n s i t side of t r a v e l can be operated i n two modes. It i s possible to a n a l y t i c a l l y examine the operation of the e x i s t i n g t r a n s i t system i n a l i m i t e d i n t e r a c t i o n with the automobile network. On the other hand, i t i s possible to examine short-run planning questions where the analysis involves a f u l l i n t e r a c t i o n of both the automobile network and the t r a n s i t network. Limited i n t e r a c t i o n implies u t i l i z i n g average v e h i c l e speeds on the roads to determine the maximum speed of the buses. An operational examination might e n t a i l deter-mining the loading of the buses, f i n d i n g out where people get on and o f f the bus, determining the paths passengers follow through the t r a n s i t system etc.. No i t e r a t i o n of the modelling system would be necessary to perform th i s type of study. F u l l i n t e r a c t i o n implies the i n c l u s i o n of both the e f f e c t s of the physical i n t e r a c t i o n of the two modes and the i n t e r a c t i o n of the demand for the two modes. A short-run planning examination might include determining the e f f e c t of increased bus frequencies or parking charges on t r a n s i t r i d e r s h i p and general congestion. I t would be necessary to put the frame-work through several i t e r a t i o n s for t h i s type of a n a l y s i s . I t i s possible to obtain the following information from the t r a n s i t model: 66 (1) The minimum transit path from any transit origin 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 lines taken and transfer points. (2) Equilibrium data which includes the auto invehicle travel time for the previous and current iteration, the invehicle travel time for the bus for the current iteration, and the mode s p l i t from each origin to a l l destinations. (3) The bus line st 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 total time to run the route (one way) and the average speed over the route. Two parking policies were tested i n order to show the capabilities of the transit program. They are policies A and B and are shown in Table 2(a). The price difference between these policies i s $1.00 on a l l parking lots. TABLE 2(a) PARKING POLICIES USED TO ILLUSTRATE THE PROGRAM CAPABILITIES AND THE EQUILIBRIUM PROCESS PARKING ZONE 1 2 3 4 POLICY 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 Tables 3, 4, and 5 show the data output for the test. The minimum path print-out allows the analyst to trace the path of a transit user through any part of the system. The effects of any changes in the system on a particular origin-destination pair can be easily detected. Table 3(a) shows a minimum path print-out from the 3rd Street entrance to 4th Avenue. This particular minimum path is associated with parking pricing policy A. The total travel time is 671 seconds or 11.1 minutes with % minute taken to transfer. Since in this case the destination point is at a bus stop and the bus line is a through line (the people are already on the bus before i t enters the study area), the out-of-vehicle travel time is 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 line 3 to bus line 1. Also at that bus stop passengers transferred from bus line 1 to bus line 3 to set the total departing : on bus line 3 at 41 passengers. The total on bus line 1 departing • from the same bus stop is 20. Table 3(b) shows the same minimum path print-out under policy B which is $1.00 greater on a l l lots than under policy A. This has a profound effect on the transit travel time on this particular path. It 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 travel times from the given inter-sections to a l l destinations for both the automobile and bus mode. Note this i s different from Tables 3(a) and 3(b) which give the travel time for an individual using the bus between a specific origin and destination. A comparison of Table 4(a) and 4(b) show that in 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 level of congestion. MINIMUM TRANSIT PATH DATA TABLE 3 (a) PARKING PRICE POLICY A total travel time (sees) 671. transfer, wait and walk time (sees) 30. INTERSECTION PERSONS ON THE BUS BUS LINES AT THE NODE 4th AVENUE 4th AVENUE 4th AVENUE 3rd AVENUE 2nd AVENUE 1st AVENUE 4th STREET 3rd STREET 3rd STREET 3rd STREET 3rd STREET 3rd STREET 0. 11. 7. 7. 20. 41. 17. 1 1 1 1 1 3 3 TABLE 3(b) PARKING PRICE POLICY B total travel time (sees) 388. transfer, wait and walk time (sees) 30. INTERSECTION PERSONS ON BUS LINES THE BUS AT THE NODE 4th AVENUE 4th AVENUE 4th AVENUE 3rd AVENUE 2nd AVENUE 1st AVENUE 4th STREET 3rd STREET 3rd STREET 3rd STREET 3rd STREET 3rd STREET 0. 13. 8. 8. 24. 49. 20. 1 1 1 1 1 3 3 NOTE: Policy B i s a $1.00 increase i n parking prices on a l l parking lo 69 Page 69 omitted in numbering 70 TRAVEL TIMES FROM THE GIVEN INTERSECTION TO ALL DESTINATIONS  TABLE 4(a) PARKING PRICING POLICY A AUTO BUS INTERSECTION CURRENT PREVIOUS IN VEHICLE EXCESS TRAVEL TIME TRAVEL TIME TRAVEL TIME 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 AUTO BUS INTERSECTION CURRENT TRAVEL TIME PREVIOUS TRAVEL TIME IN VEHICLE EXCESS TRAVEL TIME TRAVEL TIME 3rd STREET 4th AVENUE 1st AVENUE 3rd AVENUE 2.1 3.3 2.6 2.3 2.3 3.7 2.6 2.1 4.5 4.2 5.8 3.1 0.7 3.9 0.7 2.6 NOTE: P o l i c y B i s a $1.00 increase i n parking prices on a l l parking l o t s 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* 3rd STREET 4th AVENUE 1st AVENUE 3rd AVENUE 947. 1038. 986. 918. 1126. 1084. 1285. 1102. .457 .489 .434 .454 TABLE 5(b) PARKING POLICY B INTERSECTION PERSONS BY PERSONS BY AUTO SPLIT CAR BUS 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 is the proportion of tripmakers travelling by car NOTE: Policy B is a $1.00 increase in 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 results, however, cannot be construed as general indications of what might occur in a city 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 in the travel time between the current iteration and the previous iteration. This is used as quick check to determine whether the equilibrium process has converged or not. Since the number of iterations is controlled manually, judgement is used to decide whether to terminate the process. In this case the d i f f -erences were considered insufficient to warrant any further iterations. The bus line statistics shown in Table 6(a) and 6(b) allow the analyst to determine the effects of any changes on any particular bus line. It i s possible to determine where the maximum load point i s , the load profile, the links of greatest delay and the average speed of the bus. The $1.00 increase in 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 reiterate, the program provides information about the passenger's trip through the system, equilibrium stat 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 Illustration of the Equilibrium Process The following is an example il l u s t r a t i n g the process whereby equilibrium of the system is obtained after a change in parking prices. The purposes of this test is to show that a change in parking allocation has an effect on the outcome of the equilibrium state, and also, to trace the process through 73 to equilibrium. The change i n p r i c i n g i s as shown i n Table 2(a) under p o l i c i e s C and D. In p o l i c y D, a l l prices are raised 25<: except zone 3 which i s raised 50c. The d i f f e r e n t i a l increase i n parking prices was chosen f o r demonstration because when the prices are uniformly increased there are 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 to parking l o t s . The only changes that occur are i n the mode s p l i t and the vehicular assign-ment. D i f f e r e n t i a l p r i c e increases r e s u l t i n su b s t a n t i a l changes i n parking a l l o c a t i o n i n the case chosen. Before going s t r a i g h t into the example, the theory behind the e q u i l -ibrium algorithm given i n Chapter 5 section 5.7 w i l l be restated and the example w i l l be explained with references to the theory. The t h e o r e t i c a l framework for equilibrium 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 the best d i r e c t i o n i n which to proceed to obtain a new t r i a l s o l u t i o n . 3. Develop a t r i a l s o l u t i o n . 4. Obtain a new solut 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 . If i t i s not, return to step 2. Recall that there are several i t e r a t i o n s required to obtain equilibrium a f t e r a parking p r i c e change i s made. Re c a l l also that several programs make up one i t e r a t i o n . After 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 consist of the execution of the parking a l l o c a t i o n model (TRANS), vehicular 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 algorithm model (BUS). BUS STATISTICS FOR BUSLINE! NUMBER 3 TABLE 6(a) PARKING PRICING POLICY NUMBER A headway = 1. minute busline number = 3 busline name = Georgia the average speed of the bus i s 5.6 mph. BUS STOP INTERSECTION PEOPLE ON THE BUS PEOPLE LINK, TIME BUS LINES AT THE STOP & TOTAL TIME AT THE STOP 3rd STREET 17. 17. 6.2 0 3 1st AVENUE 3rd STREET 41. 18. 2.3 3 2nd AVENUE 2nd STREET 11. 0. 1.6 3 3rd AVENUE 1st STREET 13. 0. 0.7 3 3rd AVENUE 0. 0. 10.7 2 3 NOTE: TIMES ARE IN MINUTES TABLE 6(b) PARKING PRICING POLICY NUMBER headway = 1. minute busline number = 3 busline name = Georgia the average speed of the bus i s 10.2 mph. BUS STOP INTERSECTION PEOPLE PEOPLE LINK, TIME BUS LINES ON THE BUS AT THE STOP & TOTAL TIME AT THE STOP 3rd STREET 20. 1st AVENUE 3rd STREET 49. 2nd AVENUE 2nd STREET 12. 3rd AVENUE 1st STREET 15. 3rd AVENUE 0. 20. 1.3 0 3 22. 2.4 3 0. 1.5 3 0. 0.7 3 0. 5.9 2 3 NOTE: P o l i c y B i s a $1.00 increase on a l l parking l o t s 75 TABLE 7 (a) AVERAGE TRAVEL TIMES FROM GIVEN INTERSECTIONS TO ALL DESTINATIONS FOR EACH ITERATION BETWEEN POLICY C AND D NOTE: The price increase i s 50c on parking lot 3, 25c on a l l others \ ITERATION NO. INTER- \. SECTION 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 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 INTER -X . SECTION 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 * 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 increase i s 50c on parking l o t s , 25c on a l l others. (a) f i r s t i t e r a t i o n \ . parking \ z o n e 1 2 3 4 work >v zone ^ \ 1 « 1315 2 1250 207 3 1243 4 191 1250 (b) second i t e r a t i o n work parking \ zone v 1 2 3 4 zone 1 1312 2 1250 206 3 1252 4 188 1250 * Persons a r r i v i n g at the parking l o t 77 TABLE 8 (cont'd) TRANSITION PARKING ALLOCATIONS FOR EACH ITERATION BETWEEN POLICY C AND D (c) third iteration parking \ z o n e work zone 1 2 3 4 1 1213 2 1250 166 3 . 1192 4 175 1250 (d) fourth iteration parking N. zone work zone 1 2 3 4 I 1211 2 1250 137 3 i / 1172 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 2 3 4 1 1192 2 1250 127 3 1171 4 145 1250 79 The program BUS is the last program of the iteration to be executed. The output of BUS is examined to determine whether another iteration should be undertaken or not. If the changes in the auto travel times, or changes in the auto mode sp l i t between iterations are small, then an equilibrium solution has been obtained and the iterative process is stopped. Table 7(a) and 7(b) show the travel times and auto mode splits for the iterations between policies C and D. The f i r s t iteration travel times and mode splits shown in Tables 7(a) and 7(b) are the conditions associated with the equilibrium state of policy C. (see Table 2(a)). Table 8(a) shows the parking allocation associated with the same policy. The f i r s t iteration is the i n i t i a l network solution S. The second iteration commences when the parking price changes are made and the parking allocation model produces the parking configuration shown in Table 8(b). The vehicle assignment model is run and then the transit assignment mode s p l i t model is run. The second iteration results of these two models are shown in Tables 7(a) and 7(b). The running of the three models in this order correspond with the process of determining the best direction in which to proceed to obtain a new t r i a l solution, the second step in the framework set out above. The third step is imbedded in the transit mode s p l i t program, BUS. It takes the i n i t i a l network solution S (the mode splits 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 sp l i t is used to compute auto and transit demands for the next iteration. The average travel time and mode spl i t displayed in Tables 7(a) and 7(b) is used to determine whether the solution is satisfactory or not. If i t is not (and generally i t is 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 process returns to step 2. The newly computed auto and t r a n s i t demands are used i n the next i t e r a t i o n of the models. The same steps are followed through without changing the parking p r i c e s . This allows the mode s p l i t , t r a v e l times and parking con-fi g u r a t i o n s to converge. The f i n a l and intermediate i t e r a t i o n s to e q u i l -ibrium are shown i n Tables 7(a) and 7(b) and 8(b) to 8(e). The previous discussion traced the modelling process with references to the theory. The following discussion touches on some of the changes i n demands and t r a v e l times which took place during the process. The p r i c e s for a l l zones were increased by 25c except f o r zone 3 which was increased by 50c. The 50c increase i n zone 3 r e s u l t s i n a s h i f t of 188 auto users (150 cars) from the parking l o t i n zone 3 to the l o t i n zone 1. Tables 8(a) and 8(b) show t h i s . This change r e s u l t s i n a reduction of auto t r a v e l time as shown i n Table 7(a) between the f i r s t and second i t e r a t i o n s . The auto mode s p l i t for i t e r a t i o n #2 i s shown i n Table 7(b) second i t e r a t -ion. Although 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 increase i n parking costs and walking costs o f f s e t t h i s gain and the auto s p l i t i s smaller. The mode s p l i t of 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 matrices of the t h i r d i t e r a t i o n . 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 of auto users i n the t h i r d i t e r a t i o n (Table 7(b)). The reduction i n auto d r i v e r s r e s u l t s i n further reductions i n auto t r a v e l times (Table 7(a) t h i r d i t e r a t i o n ) . The mode s p l i t for 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 are i n the same d i r e c t i o n except the one for 3rd Street. The reason f o r i t s reve r s a l i n d i r e c t i o n w i l l be discussed l a t e r . The others behave i n a manner as predicted by the equilibrium theory, see Chapter 5 section 5.7 and Appendix A. There are 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 also be addressed l a t e r . The t r a v e l times and mode s p l i t s for 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 drastic 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 for this drastic change i s that the parking a l l o c a t i o n algorithm optimizes the trade-off between parking costs and walking time for the whole system ( i . e . a l l users), not the i n d i v i d u a l . Another possible problem was noted with this model. Invehicle travel time was not considered to be important i n the choice of parking l o t . The choice was thought to be dictated by the parking cost and walking time. In this small demonstration network some l i n k s are heavily congested; so much so that walking i s faster than driving. This condition may occur occasionally i n the re a l world and the driver may choose to park further away from his destination and walk because walking i s faster. In a heavily congested network a few extra vehicles 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 travel times and become important i n determining the equilibrium state. 82 It appears that a parking a l l o c a t i o n model which optimizes the i n d i v i d u a l ' s trade-off between parking costs and walking would be better. Some work should be done to determine whether i n v e h i c l e t r a v e l time should be considered i n the trade-off. When a parking p r i c e increase resulted 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 the system did not converge to equilibrium i n the fashion expected.,. I t converged by o s c i l l a t i n g about a value. When the p r i c e increase resulted i n a s h i f t of the mode s p l i t only, the system converged asymptotically as expected. Figures 12(a) .and 12(b) ahow the convergence patterns for t r a v e l time and mode s p l i t f o r the former case and Figure 13(a) and 13(b) show the patterns f o r the l a t t e r case. These figures i l l u s t r a t e i n graphical form the values of t r a v e l times and the mode s p l i t s produced by the i t e r a t i o n s between the equilibrium states of each p o l i c y . Figure 12 i s the r e s u l t of a p r i c e increase of 50c on parking l o t 3 and 25c on a l l other l o t s . The i n i t i a l p o l i c y i s C and the f i n a l i s D; r e f e r to f i g u r e 2(a). Figure 13 i s the r e s u l t of a p r i c e increase of 25c on a l l parking l o t s where the i n i t i a l p o l i c y i s E and the f i n a l i s F. According to the theory the system should have approached the e q u i l -ibrium state asymptotically; r e f e r to Chapter 5, section 5.7 and appendix A. Figure 12 i l l u s t r a t e s that t h i s was not the case. Several reasons were postulated for the problem. The s i z e , c o n f i g -uration and t r a v e l demands on the network produced some l i n k s with low volumes and low t r a v e l times and produced others with high volumes and u n r e a l i s t i c a l l y high delays (over 20 minutes per automobile i n one case). The number of models and the manner i n which they 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 with the small s i z e of the network also caused d i f f i c u l t i e s . .83 FIGURE 12(a)  TRANSITION TRAVEL TIMES POLICY C TO D NOTE: The price Increase i s 50<j; on parking lot 33 25cfc on a l l others Time i n minutes 8 h 7 6 4 \-I 1 2 3 4 I t e r a t i o n s FIGURE 12(b) TRANSITION MODE SPLIT POLICY C TO D 3rd S t r e e t 4th Ave. 1st Ave. 3rd Ave. Auto mode s p l i t .550 530 .490 2 3 I t e r a t i o n s 4th Ave. 3rd S t r e e t 3rd Ave. 1st Ave. FIGURE 13(a) TRANSITION TRAVEL TIMES POLICY E TO F 84 Time 12.0 in minutes 1 2 3 FIGURE 13 (b) TRANSITION MODE SPLIT POLICY E TO F 3rd Street 4th Ave. & 1st Ave. 3rd Ave. i t e r a t i o n s Mode s p l i t . 570 4th Ave. 3rd Ave. 1st Ave. 3rd Street i t e r a t i o n s NOTE: The price Increase Is 25<fc f o r a l l parking l o t s 85 Figure 12 shows the configuration of the network. There are four entrances and four parking l o t s . Delay and congestion i s concentrated on the l i n k s around these points. The volumes on the l i n k s not d i r e c t l y connected to them are such that t r a v e l times are generally at s l i g h t l y greater than free flow conditions. One would expect delays at entrances to the C.B.D., such as the bridges to Vancouver and at parking l o t s where vehicles converge. However, one would also expect the delays throughout the network to be of the same magnitude as those at the more heavily congested points. 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 while those at the congested areas range between 300 and 1000 seconds. This c l e a r l y i s not r e a l i s t i c . Some work was done i n order to a l l e v i a t e t h i s problem by adjusting the network and the l o c a t i o n of the parking 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 costly i n computing costs. A f t e r several adjustments and some improvement i t was decided to go ahead with the example runs. The d i f f i c u l t y encountered on the example run's then, was large changes i n t r a v e l times with small changes i n volumes on heavily congested l i n k s . This phenomenon of having 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 being l i g h t l y congested had repercussions on the r e s u l t s throughout the a n a l y s i s . Perhaps one of the advantages of the problem mentioned above i s that i t highlighted the weaknesses i n the l o g i c of the system and made i t much easier to locate f a u l t s and make recommendations. The second d i f f i c u l t y was found to have i t s source i n the nature of the modelling system. Within the o v e r a l l system there are three sub-systems which can a l t e r demands on the vehicular and t r a n s i t network. They are: the parking a l l o c a t i o n , the v e h i c l e assignment and mode s p l i t models. In the example chosen for demonstration a l l three 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 for this is that none of the parking lots gain an advantage over the others in terms of walking and parking costs. The approach to equilibrium i s faster in this case. When prices are increased differentially a l l three sub-systems interact: and the approach takes longer. The problem was seen to be two-fold. It appears that f i r s t l y , the number of systems interacting has a significant 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 in time and the models interact by passing aggregated demand data between one another. This is a sequential process and the d i f f i c u l t y with i t l i e s in the fact that each sub-system — except the mode sp l i t model — perform their functions without any consideration of what has happened in the other sub-systems or in the previous iteration. To il l u s t r a t e this, the intersection of 3rd Street and 1st Avenue w i l l be examined more closely. Figure 14(c) shows the intersection in detail with the location of parking lot #1. Only the links which are important to this analysis are shown. Figures 13(a) and 13(b) show the travel times and the volumes on congested links at this intersection for each of the iterations. This intersection is a good il l u s t r a t i o n of the interaction of the three models through the iterative process. The impact of the parking allocation model is noticed in the second iteration. The parking price increase reallocates cars from parking lot #3 to parking lot #1 and an increase in volumes on links 99, 31 and 77 are seen. These links enter the parking lot. Correspondingly there is a decrease of t r a f f i c on link 98 which feeds a l l the other parking lots. 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 Sees« 1 2 3 4 5 1 2 3 4 5 (c) Intersection showing Parking Lot #1 31 STREET 88 The effect of the assignment model i s seen in the computation of the travel time. The travel times on links 31 and 77 increase while on links 99 and 98 they decrease. One would expect there to be less travel time on link 98 because there are fewer vehicles turning l e f t . However, on link 99 the" travel time i s also less although there are more vehicles on that link. This is due to the reduced interference with cars turning l e f t on link 98. On the third iteration the impact of the mode s p l i t model is seen in the change of volume of vehicles on the links. It must be remembered that the mode sp l i t is based on the whole journey time and is 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 result of the parking allocation, and the assignment of vehicles, and computes the aggregate demands for the next iteration. In this case i t is the third iteration. This is 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 in volumes and there is an increase in volumes in link 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 sp l i t to reduce the number of cars travelling to parking lot 1 via link 77 and 31. Link 98 carries t r a f f i c to a l l other parking lots from the entrance at 3rd Street and probably lost vehicles because of increased parking charges in other lots. Link 100 is not important because i t carries only 14 to 20 cars. Link 99, on the other hand, gained auto t r a f f i c . Most of the t r a f f i c on this link goes directly to parking lot 1, so the reduction in travel time on this link between interation 1 and 2 was sufficient to offset the parking charge increase and induce more transit riders to take the car for this trip. 89 The process continues i n t h i s manner through the t h i r d , fourth and f i f t h i t e r a t i o n s . I t can be seen from the discussion above that the process i s quite complex. When a l l three models are making changes simultaneously, the amplitude of the o s c i l l a t i o n s i n t r a v e l time and vehicular volumes i s quite large. In the t h i r d , fourth and f i f t h i t e r a t i o n s where only two models i n t e r a c t , the system s e t t l e s down. I t appears that t h i s may be one of the drawbacks of using an i n d i r e c t approach to equilibrium. However, the approach does converge and does produce reasonable r e s u l t s (as defined at the beginning of Chapter 5); r e f e r to Chapter 3, section 3.1 for a discussion on d i r e c t and i n d i r e c t approaches. The more independent the models are i n the sequential process, and the greater the number of models or systems i n t e r a c t i n g , the greater the number of i t e r a t i o n s required to reach equilibrium. Since i t i s not possible to reduce the number of models and be consistent with the theory set out previously, perhaps work should be done to reduce the independent of the models. This could be achieved by modifying the equilibrium algorithm (refer to Chapter 5, section 5.7).so that i t would allow smaller incremental changes i n the mode s p l i t when large changes i n t r a v e l time between i t e r a t i o n s were detected. There may also be other methods which could be examined. It must be emphasized that before any of these changes can be consider-ed; the system should be tested on a more r e a l i s t i c network. The problems noted here may simply be a r e s u l t of the network used. 90 The f i n a l problem noted was the computation of the automobile t r a v e l time which i s used to compute the mode s p l i t . The s t o c h a s t i c assignment model d i d not compute the cumulative t r a v e l time from o r i g i n to d e s t i n a t i o n . I t was necessary to add a f u n c t i o n to the assignment model which would e x t r a c t t h i s i n f o r m a t i o n . I t was thought that a minimum path search 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 associated w i t h that assignment had been computed would be adequate. I t was expected that there would not 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 set of p o s s i b l e routes connecting 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 that 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 route of sh o r t e r time and hence, t h i s method of computing automobile t r a v e l would be a good approximation of the journey time. I t must be pointed out again that 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 high t r a v e l times are h e a v i l y loaded, they are d i r e c t l y connected to the entrances of the network or the parking l o t s , 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 parking 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 Figure 15(b) and 15(c). The l i n k s connecting these l i n k s have t r a v e l times under 100 seconds, w i t h the exception of one case which i s 830 seconds and that i s due to the t r a f f i c e n t ering the network at 3rd Avenue. The minimum path search can avoid the l i n k w i t h the t r a v e l time of 1300 seconds by tak i n g a c i r c u i t o u s route through the network and compute journey times which are considerably l e s s than the 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 real world conditions, and delays on a l l links were of the same magnitude, this problem would not be signi-ficant. It is recommended, however, that the sensitivity 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. As already noted, there are some unrealist-i c a l l y congested links in the network. Two short run policy questions were posed. The f i r s t was: what would be the effect of raising the cost of parking in parking lot #3 by increments of 25c three times with a f i n a l increase of $1.00. The second entailed determining the effect of increasing parking prices on a l l parking lots in the same manner as above. There was one exception in this case where the prices of parking lot #3 were increased 50c on the second increment. This is the scenario which was analysed in detail previously. Table 9 shows the price increase for the two policies in each parking lot. The reason that the two different policies were selected for analysis was because municipalities generally control only a fraction of the parking spaces in the C.B.D. The f i r s t policy approximates the case where the municipality decides to increase the rates in i t s own parking lots. The second policy approximates the case where the government is able to levy a tax on a l l parking lots. With the data output from the programs, i t is possible to examine the policies at several levels. Total hours of travel time versus total travel costs can be examined. The shift in the mode s p l i t for each of the different policies can be looked at.. Usage and statistics on particular bus lines can 93 TABLE 9 PARKING PRICE POLICIES PARKING ZONES 1 2 3 4 ORIGINAL POLICY 1.25 1.25 1.50 .75 POLICY #1 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 POLICY #2 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 A l l Prices are in Dollars NOTE: Policy #1 is an Incremental Increase of the Parking Price in Parking Lot 3 only. Policy #2 is an Incremental Increase of the Parking Price on a l l Parking Lots 94 be examined. The e f f e c t of the changes on the i n d i v i d u a l ' s t r a n s i t t r i p can be traced. Generally, the purpose of increasing parking p r i c e s i n the C.B.D. i s to induce more e f f i c i e n t use of the auto and better u t i l i z a t i o n of p u b l i c t r a n s i t f o r the purpose of reducing road congestion.The ef f e c t i v e n e s s of these p o l i c i e s i s generally measured i n the number of hours of t r a v e l time saved. Figure 16 i s a p l o t of the t o t a l hours t r a v e l l e d versus the t r a v e l costs f o r each p o l i c y . The t o t a l hours t r a v e l l e d include walking time and FIGURE 16 TOTAL HOURS VERSUS TOTAL TRAVEL COSTS 2200 r T o t a l Hours 9000 10000 11000 12000 13000 $ T o t a l Costs i n v e h i c l e time f o r both modes. The t r a v e l costs include; parking charges, bus far e s , and the marginal cost of d r i v i n g the car. The marginal cost of d r i v i n g was approximated by assuming that the average t r i p was 6 miles and the gasoline costs were 10c per mile (1964 d o l l a r s ) . The f i r s t p r i c e increase i n p o l i c y 1 r e s u l t s 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 t r a v e l l e d and a s l i g h t reduction i n the t o t a l cost 95 of travel. This result can partly be attributed to the unrealistically congested links and may not be valid. One would expect an increase in total travel time with a reallocation of parked cars due to a price increase. A price increase on one lot should result in either a shift to another lot which is further from the f i n a l destination and therefore a longer walk, or a shift to transit which is usually slower than the automobile. This is a case of the parking allocation model not taking into account the fact that there may be a trade-off between walking and driving when driving is the more time consuming. The remaining results appear more r e a l i s t i c . Policy 2 is much more effective in reducing congestion. However, the costs to society are much greater. If one were to raise the parking prices to the highest level shown for policy 2, the cost to society would be $2,669 and the total time savings are 906 hours. The value of time would have to be no less than $2.90 per hour to justify this course of action. On the other hand, i f one were to raise the prices to the highest level shown in policy 2, the cost to society would be $473 and the time savings 437 hours. The value of time in order to justify 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 is 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, pollution, 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 STATISTIC ORIGINAL POLICY POLICY #1 INCREMENT #4 POLICY #2 INCREMENT #4 Average transit 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 *Average Speed of the Car with High Link Delays Adjusted 7.5 MPH 9.15 MPH *N0TE: The average speed of the car is lower than the bus in the f i r s t two policies because the bus does not travel over some of the heavily travelled links. There were 6 links with travel times greater than 300 seconds (5 min or less than 2.3 mph.). In order to demonstrate the distortion created by these large delays, the average speeds were recalculated by reducing the travel times on these parti-cular links to 200 seconds. Table 10 shows the aggregate transit statistics for the different parking policies. Policy 1 results in very l i t t l e change in the average speed of the buses and l i t t l e change in the numbers of people using the bus. Policy 2, on the other hand, shows considerable improvement in both the transit ridership and the average speed of the buses. The benefits of policy 1 are due to a slight reduction in congestion only. The benefits of policy 2 are a result of a considerable reduction in congestion, increased ridership of transit, increased speed fo the buses and reduced pollution and noise due to the fewer number of cars on the road. Although generalized conclusions should not be drawn from this 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 increases. That i s , that where the municipality attempts to increase the prices of parking l o t s under i t s cont r o l , l i t t l e i s gained i n the way of reduced congestion or increased t r a n s i t r i d e r s h i p . I t suggests 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 reducing congestion and increasing t r a n s i t r i d e r s h i p , i t i s necessary to control a l l parking - which includes i l l e g a l parking, o f f - s t r e e t parking, street parking and parking provided free by employers. The modelling system developed f o r t h i s paper i s capable of analysing changes i n the bus system and auto network as well as the parking system. Bus l i n e s may be dropped or added; the frequencies may be changed or bus stops may be relocated and the e f f e c t of exclusive bus lanes may be tested. The street 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 of flow on the stre e t s may be changed and t r a f f i c l i g h t s and in t e r s e c t i o n design may be changed. Before any new analysis should be done, the modelling system should be tested on a more r e a l i s t i c network. FOOTNOTES F.P.D. Navin, C. Fisk, "A Downtown Traffic Management System", Prepared for 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 Traffic Analysis", Transportation Research Series Report No. 11, The University of British 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 short range p o l i c y questions. This type of framework i s needed because u n t i l recently most models dealt with long range c a p i t a l investment decisions while many urban transportation problems may be solved through short range p o l i c i e s . F i r s t , the t h e o r e t i c a l considerations of the short range planning framework were examined. The l i t e r a t u r e indicated that i n order f o r the framework to be responsive to p o l i c y changes i t must be s e n s i t i v e to changes i n a t t r i b u t e s of transportation a l t e r n a t i v e s that would r e s u l t from p o l i c i e s being analysed"'". Also i t must be structured i n such a way that i t r e f l e c t s the choice process of an i n d i v i d u a l deciding between the alternate trans-portation modes. Changes i n parking p r i c e s i n the demonstration network resulted i n changes i n t r a v e l times and mode s p l i t s . The modelling system developed has been shown to be responsive to changes i n service l e v e l s of the d i f f e r e n t modes and r e f l e c t the choice process. The accuracy of the model's predictions cannot be obtained u n t i l a f u l l scale network i s tested. Several conditions enumerated by Manhiem were deemed as being necessary to ensure consistency i n t h i s type of a model. The equilibrium conditions are as follows: (1) The l e v e l of service must enter at each stage i n the sequence unless i t i s e x p l i c i t l y found to be superfluous. (2) The same a t t r i b u t e s of service should enter at each step unless the data indicates otherwise. (3) The same values of the l e v e l of service should influence each sub-model. 100 (4) The level 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 in the same order as they are l i s t e d above. (1) The system developed in this paper computes four level of service factors. They are the auto and transit in-vehicle and out of vehicle travel times. Table 2 shows each of the models in the system and indicates whether the listed levels of service are considered in the models. The models in the table are listed in the order in which they are executed. It is easy to trace through the process and determine where each of the levels of service are utilized. It begins with the parking allocation model which, using the parking charges and auto walk times, transforms the person 0-D trips by auto into vehicle 0-D trips. The person 0-D trips are in the form of ultimate origin and destination while the vehicle 0-D trips are in the form of ultimate origin and parking lot destination. It was suggested in Chapter 6 section 6.4 that the inclusion of the auto in-vehicle travel times might improve the allocation. The remaining two transit levels of service are unnecessary in the parking allocation 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 trips and the auto in-vehicle travel times to compute the vehicle assignment. Chapter 4 section 4.2.5 discusses how travel times are incorporated in the assignment model. The vehicle travel times are translated into average speeds on the links which set the maximum speed for the buses in the transit assignment. The computation of bus i n -vehicle travel times and walk-wait times is described in Chapter 5 section TABLE 2 SYSTEM SUB-MODELS VERSUS LEVEL OF SERVICE AND SERVICE ATTRIBUTES MODEL DEMANDS SERVICE ATTRIBUTES LEVEL OF SERVICE PARKING CHARGES BUS FARES FREQUENCY OF SERVICE AUTO WALK TIMES AUTO INVEHICLE TIMES •BUS WALK & WAIT TIMES BUS INVEHICLE TIMES parking a l l o c a t i o n person t r i p s by auto X X ve h i c l e assignment v e h i c l e 0-D t r i p s X t r a n s i t assignment person 0-D t r i p s by t r a n s i t X X X X mode s p l i t person tri p s by auto and t r a n s i t X X X X X X 102 5.4. The mode s p l i t model i s the pivot point of the system. A l l service l e v e l s are represented. It i s through the mode s p l i t that the service l e v e l s computed by the previous i t e r a t i o n are translated into new demands for the next i t e r a t i o n . In t h i s manner also, a l l service l e v e l s are i m p l i c i t l y represented through out the system by the revised demands. (2) The a t t r i b u t e s of service are the parking charges, bus fares and frequency of bus service. These enter the sub-models where they have a d i r e c t impact. As i s the case with the l e v e l of service f a c t o r s , they are i n d i r e c t l y represented i n a l l systems through the mode s p l i t . (3) Where the l e v e l of service factors are repeated i n the d i f f e r e n t sub-systems they are the same value throughout any given i t e r a t i o n . It i s a f t e r the mode s p l i t and when a new i t e r a t i o n begins that the l e V e l of service factors are changes. (4) The l e v e l of service provided by each mode influences the demand for 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 point of view a l l of the equilibrium conditions set out by Manhiem have been met, however, an examination of the impact of including the auto t r a v e l times i n the parking a l l o c a t i o n model has been recommended. The modelling system was tested using a small network. Several recommendations and conclusions arose out of t h i s test procedure. The purpose of t e s t i n g was to show that the system produced reasonable r e s u l t s . It was defined that to be "reasonable" the r e s u l t s should meet the following c r i t e r i a : (1) any changes.in service l e v e l s or parking charges would r e s u l t i n s h i f t s of demand i n the appropriate d i r e c t i o n ; 103 (2) that the changes i n demand w i l l be proportionate to the change . i n l e v e l of service and v i c e versa. The s i z e and configuration of the demonstration network produced delays on some l i n k s which were not representative of delays on a r e a l network. I t was concluded that although these r e s u l t s served 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 should be developed with the test network the system of models produced r e s u l t s which were reasonable. The f i r s t c r i t e r i a was s a t i s f i e d i n that when t r a v e l times of a mode were reduced the use of that mode increased and when the parking costs increased the use of the automobile dropped. I t appeared also, that a l l changes i n l e v e l s of service were proportionate to changes i n demand and vice versa except i n the case of the parking a l l o c a t i o n model. In t h i s case a large change i n the parking a l l o c a t i o n occurred due to a small change i n p r i c e . I t was thought that t h i s occurred because the parking model optimized the trade-off between parking costs and walking time for the whole system, not the i n d i v i d u a l user. Some problems were noted i n the equilibrium algorithm. The system did not converge asymptotically as expected. I t converged by o s i l l a t i n g with decreasing amplitude about a value. The problem was seen to be two-fold. I t appeared that the number of systems i n t e r a c t i n g and the independence of the sub-systems from one another caused the problem. It was thought that the independence of the sub-models could be reduced by modifying the e q u i l i -brium algorithm so that i t would allow smaller incremental changes i n the mode s p l i t when large changes i n t r a v e l time between i t e r a t i o n s were detected. It was noted that the computation of the automobile journey times for the mode s p l i t using a minimum path algorithm produced low t r a v e l times f o r 104 the auto mode., This was l a r g e l y a t t r i b u t e d to the f a c t that the delays on the l i n k s on t h i s p a r t i c u l a r network varied from tens of seconds to thousands of seconds. I t was thought that 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 algorithm would compute t r a v e l times repre-sentative of r e a l times. Despite the problems with the network, the analysis of the two parking p o l i c i e s tested generally confirmed the experience with parking p r i c e increases. The r e s u l t s suggests that f or parking p o l i c i e s to be e f f e c t i v e i n reducing congestion and increasing t r a n s i t r i d e r s h i p , i t i s necessary to control a l l parking. At the beginning of t h i s demonstration i t was noted that a model must be shown to be p r a c t i c a l , r e l i a b l e and economical. The objective of the demonstration was to show that the model was p r a c t i c a l and produced reasonable results..• The remaining c r i t e r i a mentioned above could be addressed by others. The demonstration was successful i n showing the .reasonableness and p r a c t i c a l i t y of the r e s u l t s . I t i s not possible at t h i s point to state that the model i s accurate. I t i s possible to say that i n general i t produces r e s u l t s as expected, given the t e s t i n g network. The demonstration did succeed i n p i n -pointing several weaknesses and providing i n s i g h t s into how the system behaves. FOOTNOTES T. J. Atherton, J, H, Suhrbier, and Wr A,. Jessiman, "Use of Disaggregate Travel Demand Models to Analyse Car Pooling Policy Incentives", Tran- sportation Research Board, 599., 1976, p.35. 106^ CHAPTER 8 8.0 RECOMMENDATIONS A set of recommendations arose out of the analysis of the test network. Before any of the following suggestions are c a r r i e d out i t i s recom-mended that an unmodified version of the modelling system developed i n t h i s paper be tested on a more r e a l i s t i c network. This may r e s u l t i n the c l a r i -f i c a t i o n of the doubts which gave r i s e to some of the following recommendations. Two d e f i c i e n c i e s were noted i n the parking a l l o c a t i o n model. The model considers a trade-off between parking costs and walking time i n representing the decision made by the commuter. I t was thought that the model would be improved i f the in v e h i c l e t r a v e l times on a congested network were also considered i n the model. This suggestion was made because the choice of a parking l o t not only a f f e c t s walking time and parking costs but on a heavily congested road system i n the C.B.D. the choice could 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. It was thought that there may be a problem i n the way the parking a l l o c a t i o n modelled the trade-off between the two varia b l e s . The model minimizes the sum of the parking costs and walking costs for a l l users. This resulted i n large s h i f t s i n parking demand due to small changes i n parking pr i c e s . I t was thought that t h i s behaviour was not r e a l i s t i c . However, a conclusive statement cannot be made due to the lack of empirical data concerning parking behaviour.. A model which optimizes the trade-offs •: f o r the i n d i v i d u a l rather than a l l of the drivers would represent the choice process better. I t i s recommended that research be undertaken i n order to more f u l l y understand the behaviour of commuter parking i n the C.B.D.. With t h i s knowledge the model may be modified so that i t accurately r e f l e c t s that behaviour. 107 Appendix A illustrates the reasoning behind the choice of a modifier for the mode sp l i t in 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 efficient in bringing the system to convergence. Under a test model and network in Appendix A the system reached convergence through an asymptotic approach in three or four iterations. The results produced by the larger framework were different. Equilibrium was obtained by osillating with decreasing amplitude about a value and four to five iterations were required for convergence. Two factors were seen to contribute to the difference. First there are four sub-models in the larger system whereas there were only three in the test system of Appendix A. Secondly, the sub-systems operate relatively independently from one another. One recommendation has already been made to include invehicle travel time in the parking allocation. This would serve to reduce the independence between the parking allocation and vehicle assignment models. It i s also recommended that the influence of the modifier in the equilibrium algorithm be examined more thoroughly. The testing should be done on the f u l l size modelling system. Research in this area may provide a better understanding of the mechanisms involved in the convergence to equilibrium and lead to improvements in the modifier. The automobile journey time for the mode spl i t model i s computed by a minimum path algorithm after the network has been loaded. Due to the large variations of travel 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 links with low volumes and small delays). It is recommended that the sensitivity 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 sp l i t model used was developed and calibrated in 1964 for a 108 study i n Toronto"'". It was s a t i s f a c t o r y f o r the purposes of 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 should be c a l i b r a t e d to the conditions of the area being studied. The development of a modelling system proceeds i n several stages. The theory and a modelling system have been developed. The system has been t e s t -ed on a small 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 for further t e s t i n g . Subject to the outcome of those tests a set of refinements and s e n s i t i v i t y tests were recommended. Once these have been completed the f i n a l task i s to show that the system i s p r a c t i c a l , r e l i a b l e and economical. Upon s a t i s f a c t o r y completion of the recommendations above the system would be ready for a p r a c t i c a l a p p l i c a t i o n . 109 FOOTNOTES D. W. Gillen, "Effects of Changes in Parking Prices and Urban Restrict-- . ion on. Urban Transport Demands and Congestion Levels", University of  Toronto-York University, Joint Program in 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 in a C.B.D.," Highway  Research Record 444, 1973. Burrell, J.E., M.A. Florian (ed) "Multiple Route Assignment: A Comparison of Two Methods," Traffic Equilibrium Methods, Proceedings of the International Symposium Held at the Universite de Montreal, Apringer-Verlag. New York, 1976. Button, K.J., "The Use of Economics in 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," Traffic Engineerings and Control, June 1977. Chriqui, C., and P. Robillard, "Common Bus Lines," Transportation Science, Vol. 9, No.2, 1976. Culham, T.E., "An Examination of the Costs and Benefits of Various Parking Pricing Policies in the C.B.D.," Student Paper Number 21, Centre for Transportation Studies, University of British Columbia, 1977. Dial, R.B. and R.E. Bunyan, "Public Transit Planning System," Socio- Economic Planning Science, Vol. 1, 1968. Dial, 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. Dial, R.B., "A Probablistic Multipath Traffic Assignment Model. Which obviates Path Enumeration," Transportation Research, Vol. 5, 1971. Fisk, C., "A Transportation Planning Model for Detailed Traffic Analyses," Transportation Research Series, Report No. 11, Department of C i v i l Engineering, University of British Columbia, 1977. Florian, M., "A Traffic Equilibrium Model of Travel by Car and Public Transit Modes," Transportation Science, Vol. 11, No. 2, May 1977. Florian, M. and S. Nguyen^ . "A Method for Computing Network Equilibrium with Elastic Demands," Transportation Science, Vol. 8, No. 3, 1974. Florian, M., S. Nguyen, and J. Ferland, "On the Combined Distribution Assignment of Tra f f i c " Transportation Science, Vol. 9, No. 1, 1975. Florian, 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. I l l 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. Gillen, D.W., "Effects of Changes in Parking Prices and Parking Restrictions on Urban Transport Demands and Congestion Levels," Research Report No. 25. University of Toronto, York University Joint Program in Transportation, 1975. Gillen, D.W., "The Effects 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 Practical 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 Institute, Carnegie-Millon University Pittsburgh, Pennsylvania, 1968. Hutchinson, B.G., "Principles 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 in Multi-Travel Mode Assignment Programs," Highway Research Board Bulletin, 347. J o l l i f f e , J.K., and T.P. Hutchinson, "A Behavioural Explanation of the Association Between Bus and Passenger Arrivals at a Bus Stop," Transportation Science, No. 3, Vol. 9, 1975. King, D.J., "Control of Congestion in the City of Vancouver: An Investigation of Parking Charges," A Study prepared for the City of Vancouver, 1974. Kulash, D., "Parking Taxes for Congestion Relief: A Survey of Related Experience," The Urban Institute, Washington, D.C, 1974. Kulash, D., "A Transportation Equilibrium Model," The Urban Institute, Washington, D.C, 1971 Leblanc, L.J., "An Accurate and Efficient Approach to Equilibrium Traffic Assignment on Congested Networks," Transportation Research Board 491, 1974. Manhiem, M.L., "Practical 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 Traffic Management System," A paper prepared for the Canadian Transportation Research Form Annual Meeting, 1977. Ruiter, E.R., "Implementation of Operational Network Equilibrium Proceedures," Transportation Research Board, 491, 1974. Ruiter, E.R., M.A. Florian (ed) "Network Equilibrium Capabilities for the UMTA Transportation Planning System," Traffic 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 Traffic Research," Proceedings, Institute of C i v i l Engineering, Part II, 1952. Whitlock, E.M., "Use of Linear Programming to Evaluate Alternate Parking Sites," Highway Research Board, 444, 1973. Wigan, M.R., (M.A. Florian (ed)), "Equilibrium Models in Use: Practical Problems and Proposals for Transport Planning," Traffic 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 following i s a discussion on the development of a modifier of the mode s p l i t . The computation of the t r i a l mode s p l i t i s the p i v o t a l point of the methodology set out i n the main text. The t r i a l mode s p l i t computes the new transit-auto demands f or the next i t e r a t i o n . T h e o r e t i c a l l y the t r i a l mode s p l i t can range from the old mode s p l i t to the new mode s p l i t . The old mode s p l i t i n fac t i s the t r i a l s p l i t of the previous i t e r a t i o n . T:he new mode s p l i t i s computed based on the l e v e l of service and service a t t r i b u t e s of the present i t e r a t i o n . It was found that the value of the t r i a l mode s p l i t within t h i s range had a s i g n i f i c a n t influence on the convergence of the s o l u t i o n . Figures 17 a to b i l l u s t r a t e the e f f e c t of d i f f e r e n t modifiers on the convergence of the so l u t i o n . The purpose of t h i s appendix was to develop a modifier of the new mode s p l i t such that the t r i a l mode s p l i t would produce a swift convergence to the s o l u t i o n . It was not possible to develop such a modifier mathematically and accurately predict i t s e f f e c t s . This was due to the i n d i r e c t nature of obtaining the equilibrium s o l u t i o n ; see Chapter 3 section 3.1. I t was necessary to determine the function of the modifier e m p i r i c a l l y . Two approaches could have been taken i n order to solve t h i s problem. The f u l l set of computer programs could have been written and run using d i f f e r e n t functions to compute the modifier. T'he second approach would have been to i s o l a t e the e s s e n t i a l functions i n the larger framework and b u i l d them into a small, system which r e p l i c a t e s the larger system. It was decided to take the second approach because i t was thought to be more f l e x i b l e and amenable to experimentation. I t was also less c o s t l y and time consuming than the f i r s t approach. The draw-back of the second approach would be the loss of an understanding of the exact behaviour of the larger system. FIGURE 17 PARKING PRICE INCREASE FROM $1.50 TO $2.50 (a) modifier = .25 (b) modifier = .50 timei min. 50 h 40 30 X X X X X 1 2 3 4 5 6 7 8 9 10 it e r a t i o n s t imei m in . 50 h 40 30 X X X X 2 3 4 5 6 7 8 9 10 it e r a t i o n s (c) modifier = .75 (d) modifier = 1.00 timei min. 50 h 40 h 30 h X X X X 1 2 3 4 5 6 7 8 9 10 it e r a t i o n s 1 2 3 4 5 6:i7 8 9 10 i t e r a t i o n s 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. 50 40 30 time min. 50 ] _ f | Z ( l o g i t f u n c t i o n ) dx 40 J L J L 30 JL • I I L 1 2 3 4 5 6 7 8 9 10 i t e r a t i o n s 1 2 3 4 5 6 7 8 9 10 i t e r a t i o n s 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. 50 time min. 50 1 _ f ^ ( l o g i t f u n c t i o n ) dx v 40 30 40 30 -L 1 2 3 4 5 6 7 8 9 10 i t e r a t i o n s 1 2 3 4 5 6 7 8 9 10 i t e r a t i o n s ORIGINAL PARKING CHARGE = $0.00 INCREASE PARKING CHARGE TO $1.00 117 The composition of the test framework was dictated by the inputs required by the l o g i t model and the c r i t e r i a that i t should resemble the larger framework as much as possible. The e s s e n t i a l elements of the larger system are the parking 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 equilibrium algorithm; r e f e r to Figure 7, Chapter 3 section 3.2.. The inputs to the l o g i t model are, the t r a n s i t t r a v e l time, auto t r a v e l time, number of miles t r a v e l l e d by auto and the parking costs; r e f e r to Chapter 5 section 5.6 equation 23. The parking a l l o c a t i o n model was not included i n the test framework f o r the following reasons: (1) I t did not have d i r e c t input to the l o g i t model; r e f e r to Figure 7. (2) The network to be run on the test framework was such that i t would not be affected by the parking a l l o c a t i o n model. The test system i s shown i n Figure 19 below; r e f e r to Figure 7 for a comparison with the f u l l s c a l e system. FIGURE 19 MODE SPLIT MODIFIER TEST SYSTEM t r a n s i t person t r i p demand t r a n s i t 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 auto person t r i p demand revised equilibrium algorithm auto-transit demand revised t r a n s i t demands auto demands 118 The important aspect to be considered in the choice or development of the functions to compute transit and auto travel times was not that they be exact or extremely accurate; they must be responsive to changes in demand and representative of the subsystems being modelled. The test network was simply a 6 mile long road with a free flow velocity of 25 mph. It was assumed to carry buses as well as cars. One end of the link was assumed to originate in the suburbs and the other in the C.B.D.. It was assumed that there was a parking lot in the C.B.D. which would accomodate any size demand. The demand for both bus and auto travel was assumed to be distributed uniformly over the length of the link. The functions for each of the stops in 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 — 28 where: V = velocity VF = free flow velocity K = density of cars on the road KJ = the jam density M = the number of miles PD = person trip demand by auto AO = auto occupancy Equation 27 was developed by May - Keller ^ and computes the average velocity on a link as a function of the free flow velocity, jam density (200 cars per mile) and actual density. The actual density is a function of the demand for travel by car. In order to compute the average velocity the auto person trip demand was translated into vehicle demand by assuming 119 there were 1.2 persons per car. This demand was then assigned to the route as a uniform d e n s i t y over the length of the l i n k . This d e n s i t y i s then used i n equation 27 to determine the average v e l o c i t y and equation 28 computes the a c t u a l auto t r a v e l time over the l i n k . 2. Bus T r a v e l Time BT = AT x 1.15 + BP x LT 29 where: BT = the bus t r a v e l time over the route AT = the t o t a l auto t r a v e l time over the route BP = the number of bus passengers LT = the l o a d i n g time per 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 time and the number of passengers using the bus. The 1.15 f a c t o r accounts f o r the slower average speed of the bus due /to slowing down f o r bus stops. The number of passengers and l o a d i n g time per passenger account f o r the stopped time of the bus. 3. The L o g i t Model The l o g i t model i s the same as defined i n equation 24 and 25 i n the main report and are repeated here f o r c l a r i t y sake. P c = e GC*) / ( 1 + e G ( x ) ) 2 4 £.:..= -.83 + 1.27TJT; / TC + .095 (.35 / MILES x .08) - .615 EPC 25 where: P^ = the p r o b a b i l i t y of using the car 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 of v e h i c l e time TC = auto t r a v e l time i n c l u d i n g out of v e h i c l e time MILES = length of t r i p i n miles EPC = the cost of p a r k i n g the car 120 The Development of the Modifier Function As noted earlier the value of the modifier function must l i e between the values zero and one. Also as noted earlier the t r i a l mode sp l i t is 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. MT = MQ + ''xC MN - MQ ) 30 where: x = the modifier M = the mode sp l i t and the subscripts N = new 0 = old T = t r i a l A two step approach was taken in defining the modifier. Fi r s t an optimal range of the function was defined. Theoretically i t was known that the value lied between zero and one but i t was. hoped to narrow the range by testing the system with different values in that interval. The second step after an optimal interval 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 split values between ,4 and .6 were used for this experiment. These conditions were selected because (1) the travel times on a heavily congested network are sensitive to small changes in demand and (2) the slope of the logit function is at i t s greatest within the values defined above and hence is also most sensitive to changes in input paramet-^ ers. The convergence of the system can be determined by examining any of the following values: the auto travel time, the transit travel time and the ...... 121 auto-transit t r a v e l demands. When the difference between any one of these values from one i t e r a t i o n to the next i s equal to zero or i s small then the system i s said to have converged to a solution. The auto t r a v e l time was selected as the parameter to be used to test for convergence. Figures 18 (a) (b) (c) (d) show the auto t r a v e l time versus the number of iterations for each modifier. Table 10 shows the values for a l l of the . parameters through the i t e r a t i v e process for each of the modifiers. It can be seen that the system converges to a solution fastest when the modifier . i s equal to 0.50. I t appears then, that the optimal range for the modifiers when the mode s p l i t i s between ,4 and .6 i s the in 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 possible to improve upon the results produced by the .5 modifier. Table l^'tb^sRows that a solution was reached i n 3 to 4 it e r a t i o n s . I f this was reduced to 2 to 3 iter a t i o n s then that would be close to achieving a direct solution. 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 price. The ultimate then would be to achieve convergence i n the t h i r d , possibly the fourth i t e r a t i o n . The l o g i t function ranged between .54 and ,46 for 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. Theoretically t h i s was thought to 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 function i s less sensitive to changes. The t r i a l mode s p l i t then i s computed as follows: when M ^ .5 122 Mm = M„ + M„ (MT - M j T 0 O N 0 when MQ ^ .5 M_ = M. + ( 1 - M_ ) ( M.T - M. ) T 0 O N 0 The variables and subscripts are as defined earlier. 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 logit function was taken and is shown below: S = e:X- / (1 + 2 e X' + e 2' X ) 31 where S = the slope of the logit function -X-' = generalized cost difference between modes S = .25 @ 'x' = 0 MAX L s M T M = 0 @ V - = ± MIN 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 positive or negative i n f i n i t y and is equal to zero. The purpose of the modifier is to reduce shifts in the t r i a l mode s p l i t . It i s not possible to use the slope directly for this purpose but the residual function, ( 1 - S. ) suffices. The value of this function when the generalized cost difference i s zero is equal to .75. The t r i a l mode s p l i t using the slope residual i s computed as follows: MT = MQ + ( 1 - S ) ( - MQ ) 32 A l l variables are defined previously. Four scenarios were tested in order to determine the performance of the modifier functions. These scenarios were divided into two,groupings. The f i r s t entailed parking pricing changesron a heavily loaded network when, the mode s p l i t was in the range of .4 to .6. The second was performed on a heavily loaded network when the mode sp l i t was in the range of .7 to .8. 1 2 3 One parking p r i c e increase of $1.00 was considered;' The base parking p r i c e f o r the mode s p l i t range of .4 to .6 was $1.50 and for the .6 to .75 range was $0.00. At these base p r i c e s the average auto speed on the route was approximately 7 miles per hour. A f t e r the p r i c e increases i t was approximately 9 miles per hour. The demand at the $1.50 base p r i c e was 1081 persons by car and 918 by t r a n s i t and at the $0.00 base p r i c e was 1083 by car and 446 by t r a n s i t . The auto demand was maintained approximately equal i n both cases so that the tests would be performed on the routes with the same l e v e l of congestion. The test showed that the l o g i t function modifier was superior to the de r i v a t i v e of the l o g i t function. In fac t i n each test case the equilibrium s o l u t i o n i s attained a f t e r 4 i t e r a t i o n s and i s very close at the t h i r d i t e r a t i o n when the l o g i t function modifier i s used. Figure 18 shows the graphs of the auto t r a v e l times versus the number of i t e r a t i o n s . Table 12 i l l u s t r a t e s a l l of the parameters i n d e t a i l . Several more tests were con-ducted with the l o g i t modifier under d i f f e r e n t conditions. In a l l s i t u a t i o n s a s o l u t i o n was attained a f t e r 3 to 4 i t e r a t i o n s . Table 13 shows the r e s u l t s of these t e s t s . I t was decided at t h i s point that the l o g i t modifier would be used. 124 TABLE I I THE ITERATIVE PROCESS USING FOUR CONSTANT MODIFIERS  PARKING PRICE INCREASE FROM..$1.50 TO $2.50 (a) modifier = .25 ITERATION .. AUTO ..... BUS NEW TRIAL AUTO BUS NO. TIME TIME MODE SPLIT MODE SPLIT DEMAND DEMAND 1 54 79 .54 .54 ...1081 918 2 54 79 .39 .50 1005 994 3 45 70 .42 .48 962 1037 4 41 66 .43 .47 938 1061 5 39 64 .44 .46 926 1073 6 38 63 .45 .46 920 1079 7 38 63 .45 .46 917 1082 8 38 63 .46 .46 915 1084 (b) modifiei - = .50 1 54 79 .54 .54 1081 918 2 54 79 .39 .46 916 1082 3 38 63 .46 .46 913 1086 4 37 63 .46 .46 913 1086 5 37 63 .46 .46 913 1086 (c) modifiei : = .75 1 54 79 .54 .54 1081 918 2 54 79 .39 .43 853 1145 3 33 58 .49 .47 945 1053 4 40 65 .44 .45 899 1100 5 36 62 .46 .46 920 1078 6 38 63 .45 .46 909 1089 7 37 62 .46 .46 915 1083 8 37 63 .46 .46 913 1086 (d) modifiei c = 1.0 1 54 79 .54 .54 1081 918 2 54 79 .39 .39 778 1221 3 28 55 .53 .53 1066 933 4 53 77 .39 .39 787 1211 5 29 55 .53 .53 1054 944 6 51 76 .40 .40 796 1203 7 30 56 .52 .52 1044 956 8 50 75 .40 .40 802 1196 . ALL TIMES ARE IN MINUTES DEMANDS ARE IN PERSONS 125 TABLE 12- THE ITERATIVE PROCESS USING TWO MODIFIER FUNCTIONS (a) PARKING INCREASE $1.50 to $2.50 m o d i f i e r = f ( l o g i t f u nction) ITERATION AUTO BUS NEW TRIAL AUTO BUS NO. TIME TIME MODE SPLIT i MODE SPLIT DEMAND DEMAND 1 54 79 .54 .54 1081 918 2 54 79 .39 .46 916 1082 3 38 63 .46 .46 914 1085 4 37 63 .46 .46 913 1085 5 37 63 .46 .46 913 1085 (b) PARKING INCREASE $1.50 to $2.50 m o d i f i e r = 1 - f --f- ( l o g i t f u nction) 1 2 3 4 5 6 7 8 54 54 33 40 36 38 37 38 79 79 59 65 61 63 62 63 .54 .39 .49 .44 .46 .45 .46 .45 .54 .42 .47 .45 .46 .45 .46 .46 1081 849 947 897 921 909 919 910 918 1150 1052 1102 1078 1090 1080 1088 (c) PARKING INCREASE $0 .00 to $1. 00 m o d i f i e r = f ( l o g i t f u n ction) 1 2 3 4 5 55 55 39 39 39 71 71 55 55 55 .71 .57 .61 .61 .61 .71 .61 .61 .61 .61 1083 930 929 929 929 446 598 599 599 599 Cd) PARKING INCREASE $0 .00 to $1. 00 m o d i f i e r = 1- ( l o g i t f unction) 1 2 3 4 5 55 55 38 39 39 71 71 55 55 55 .71 .57 .61 .61 .61 .71 .60 .61 .61 .61 1083 920 931 930 930 446 608 598 599 599 TIMES ARE IN MINUTES DEMANDS ARE IN PERSONS 126 TABLE 13' VARIOUS PARKING INCREASES AND CONGESTION LEVELS USING  THE LOGIT FUNCTION MODIFIER (a) PARKING PRICE INCREASE $2.50 to $2.75 MODERATELY CONGESTED ITERATION AUTO BUS NEW TRIAL . AUTO BUS NO. TIME TIME MODE SPLIT MODE SPLIT ': DEMAND DEMAND 1 37 63 .46 .46 914 1086 2 37 63 .42 .44 879 1120 3 35 60 .44 .44 876 1123 4 34 60 .44 .44 876 1123 (b) PARKING PRICE INCREASE $2.50 to $2.75 LIGHTLY CONGESTED 1 17 29 .47 .47 471 528 2 17 29 .43 .45 453 546 3 16 28 .45 .45 449 551 4 16 28 .45 .45 449 551 (c) PARKING PRICE INCREASE $2.50 to $3.50 MODERATELY CONGESTED 1 37 63 .46 .46 914 1086 2 37 63 .31 .39 782 1218 3 29 55 .38 .39 773 1227 4 28 55 .39 .39 772 1228 Cd) PARKING PRICE INCREASE $2.50 to $3.50 LIGHTLY CONGESTED 1 17 29 .47 .47 471 528 2 17 29 .33 .40 402 597 3 15 28 .37 .39 389 609 4 14 28 .38 .39 386 612 5 14 28 . 38 .38 386 612 TIMES ARE IN MINUTES DEMANDS ARE IN PERSONS 127 FOOTNOTES 1. A.D. May, H.E. Keller., "Non-Integer Car Following Models," Highway Research Record, 199, 1967, pp. 19-32. APPENDIX B THE COMPUTER PROGRAM BUS (SHIN '1=1' ( i ) naHiN) (s's) 3V33 ( 8 d O N ' L = l ' (I) d X S 3 N ) ( S ' S ) a V l d ****************** sit ********* ********** 3 SNOiiVHixsaa NV S N I9 I H O I I S H V B I QNV a i n v NT av3a 3 3 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 3 0 = I Z T 3 ? n Z N * 3 = XXI o * o = a o w i 0 '0=1113 *************** ** ************************** **********°jr*<i<*:****#*3 3 XXT3 3HX H31N3 S3 NIT' S03 353 HM S3GON 3HX =uHHIN 3 vaav x a n x s 3 3HX a a x o sawn sna SHSHK SSGON 3 0 OR 3 H i =HHXN 3 xno a a i K i a a s w i a a 3 S I HDIBM SX3VXS 3NI*I SO0 V H3II1M XV SOON. 3HX =dIS3N D XQO aaXNIHd 33 OX S3 N i l Su3 30 *0N 33X =dS3N 3 SHXVd EOWTNIH 3HX 30 S300N N0I IVNIXS3G 3HI =CiIdON 3 NISiaO 3 H X I d 01 * 3 HUM <33XNiad 33 OX SHXV3 WnWIWIW 30 "OH 3HI =GdON 3 QSLNIHd 33 OX HXVd UOWIKIW 3HX 30 NI9IH0 3HX =X30I 3 s N o i x v a a x i XNanOasans 3 GNV anz=i N o i x v a a x x XSL=O xaaur MOIXVS3XI aex =aoi 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'is3GN+ 'NSIHON'XSIN ' 3 3SXR ' 3 3 V 3 33 '(IHV03 'dOXSR '3NITT (S3 '9 ) 31iaM aaoN ' e aoN '+ i a O l ' a 9 l ' a H I N ' d O X S N ' 2 S I N'33SXN '3HV03 ' 3 3 V 3 3 G U ' S ) 3V33 XS*3GN'N9iaON'3(IONH'MITN'XSVI ' G 0 I H 3 d ' (3L)GV3a 3Mill (EL) 3V33 "• ' . HX'SV7.3Nl'lX3N 'anOHSN'SROZrc (8L)aV33 D * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 3 D S33I3EVHYd KVH90S3 NT dVIH 3 3 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 3 (XSI ' l ' 0 0 8 ' 0 t?3) «/ 3113 3NI33Q • (OOL) 3' (OOty)MMISaK' (SL )3N ' ( 0 S L ' 0 S L ) d t t ' + (OOL'OOL'E) GOX' (OSL ) 3 ' (OE) 3N0ZW' (OSL 'OSL) « ' (0S3> A V X V + (0S3) SNISAN ' ( 053) SIGV (0S3> AVI' (0S3) AVX3 ' (OE) 3K0ZT '+ (SL) 3 W (SL) Sf' (OOL 'OOL ' £ ) O' (OOL'OOL) RIO /JIHVaYNOHWOD (OOSD 3 V X I ' (OOSL ) RN' (OOSE) 03 3 d l /SStfV SOW MOD 0333T13 ' (OOSL ) 3 0 S 3 3 d ' + s H r i V i a ? o a ' + DOV030' (S 'OOSL) NNN' (005 L )N0SH3d ' (000L)GV3H/3WX/N0WW0D (OOSL) S333' (OOL3) ON' (OOL Z) XSIQ * (OE' OOL3) Sf!3N + ' (0 0L3)X3N' (00L3)aN'3aONN 'XSV3'MMI3N' (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 'OOL 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) wna ' (0S3) a x v w ' (0S3) oxvw N D i s M i w i a 6 Z l (053) OXXW' (0S3)QXXW' (03 '00OL) 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 ( cH)av33 xi=-(i) IHH (XT 'L = M' (M 'I) SOON) 'XI (El)a?3S MKI1N'L=I 031 OQ D sq^buax 5 saffiiq. T S A E I ; MUTT 'seavu ; e e i ^ s pp^H D / O (EE '9 )3113* SflNIIMOD 531 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; s e u x x snq p^eg D D 3 DM U N 03 091 t = (ww) im WW 1 V I 3 <JOISN*l=I DEL Oa sdo^s snq ppsa D D aOMIIMOD S l l 0 = (I) U N ' 0=(T)ttN o=( i )xas o "0= (i ) i o s a g d 0'C = (DN DS 333 0 = ( I > 1 S N 0= (I) d3IWriM XSVT 'L=I 511 oa (c"E'9> 31IHM 0t?l * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 3 0 smm. N O S3NH sne O N ? SMNii ' s a a o N a-o N T atfis D D * ** ** * * * * * * * * * * * * * * * * * * * * * *************************************D anNiLNoa ooi (VI'L=N' (N'M^)OiLi) (6666=aa3 JLD a\f ia M I = (MM) i » r ( M T ' L - N ' ( N ' H M ) I L N ) 'MM'HI (0i7l=ati5 ' Ll) 3 V 3 3 OOOE'I=I ooi oa * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * o 0 SdOIS SOB W08J QMV 01 S3KIX ST 3tf33 3 0 * * * * * * * * * * * * * * * ************************************************D (L t *9> 3IIHM ( I S 3 C I N ' l =1' (I) MTSAN ' (I) Q.LVW) (9'Sl)aV33 (NOItfON. ' l = l ' (I) oivw) ( s ' s i J a v a a (0E'9> 3II3M (MS1N ' 1=1' (I) MNISdK ' (I) ailW) (9'S)aV33 (3 DSIN * L =1 * (I) 01IW) (Z'9) Jtflff • (adON' i = i ' ( i ) aidON) ( s ' s ) a v i a OCT (adON'l=I* (I) 0X3ON) ( 5 ' S ) a V 3 B JJ=NUMDEP (Mitf) 1 3 1 LINKDP (MN,JJ)=-I 120 CGNHNDE WFITE(6,34) C C Read i n e l a s t i c auto demand C 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) 150 CON 1IN U E C C Read e l a s t i c autc demand C 155 DO 160 M=1,NGROUP DC 160 I=1,NOBIGN BEAD (19,7) (0(M,.I,K) ,K=1 ,KZON£) 160 CONTINUE WKITE{6,35) If(NEXT.EQ.0) GO TO 16U DO 161 I=1,NORIGN 161 RI AI (19,4) F C C Read t r a n s i t demand C 164 DC 16 5 fl=1,NGBOUP DO 165 I=1,NOBIGN BEAL (19,7) (TOD(H,I,K) ,K= 1,NZONE) 165 CONTINUE WRITE (6,36) C C Read parking data . c DC 170 K=1,NZONE REAC(18) J5 (K) , MR (K) ,LZCNE(K),HZCNE(K) ,C (K) 170 CCMUMUE WRITE (6, 37) C C Read walk tr a v e l times C 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 DC 180 1=1, NZCNE MC(I)=0 180. CONTINUE DC 190 M=1,N1SK LL= NPSINK (t'i) L=M ZO N E(LL) NC (I)=NC (L) +1 190 CONTINUE C C F i r s t execution cf minpth witout passenger loadinq C Assignment of passengers tc bus lines and stops C DC 300 I=1,NTSCiiN HO ME = M TTO (I) CALI MINPTH (MHOf-lE, MTTD, NTSK,0,NS , EW , NTHR, NTHRU, NOPTD , NOPD) CALL ASSN (FJTTD, N HOME, NTSK , NZONE, NG ROUP ,I,TOD ,NC , NPSINK 132 +,MZCNE,PERIOD) 300 CONTINUE r C I n i t i a l i z e s c a l a r s f o r manaqeinent of s e q u e n t i a l f i l e C II=NEXT+1 IXT=2*NZONE+3 IXXT=NZCNE+1 IZT = 0 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 C KBITE (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) C C Second e x e c u t i o n c f minpth w i t h passenqer l o a d i n g C CALL MINPTH(NHOME,MTTD,NTSK,IOPT,NS,EW,NTHB,NTHRU,NOPTD,NOPD) C " C 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 C s u b r o u t i n e SPLIT C DG 470 L=1,NZONE TAV(L)=0.0 ETAV(L)=0.0 A D I S ( L ) = C 0 ATAV{l)-0.0. 'CNT1 (L) =0.0 I F (NC (L) . EG. 0) TAV (L) =999999. I F ( J S ( L ) .EQ.0) ADIS(L) = 9 9 S 9 9 9 . 470 'CONTINUE C C Aggregate data from node l e v e l t o zone l e v e l f o r SPLIT C DO 480 M=IL,NDEST LL=NVSINK (M) L=MZCNE ( I I ) I F (JS (L) . EQ. 0) GO TO 480 ADIS (L) = ADIS (L) +EIS {MJ/ILOAT (JS (L) ) A l A V (L) = ATAV (L) + ATRAV (H) /FLOAT (JS (L) ) 480 CONTINUE C C Bead w r i t e auto t r a v e l t i m e s t o s e g u e n t i a l f i l e C IF (IGE. EQ. 0) GO TO 320 GO TO 340 / 320 I2T=IZT+1 IS1=IZT C C F i r s t i t e r a t i o n w r i t e t o s e q u e n t i a l f i l e C • WRITE (4'1ST) (ATAV (J) ,J= 1 ,NZONE) IXXT=IXXT+1 IST=IXXT . WRITE.(U11ST) (ATAV(J) ,J=1,NZCNE) 3 40 ' IF(IGD.GE.I) GO TO 350 1 3 3 GO 10 360 350 IXXT=IXXT+1 IST-IXXT C C 2nd 3rd 4th ... i t e r a t i o n read of pr e v i o u s t r a v e l time C READ (4'1ST) (BTAV(J) , J= 1, NZONE) IST=IXXT C C 2nd 3rd 4th ... i t e r a t i o n w r i t e of c u r r e n t t r a v e l time C WRITE (4'IST) (ATAV (J) ,J-= 1,NZCNE) C C P r e p a r a t i o n of data f o r w r i t e of e q u i l i b r i u m s t a t i s t i c s C 360 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 . 4 90 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) 370 CONTINUE TOTA LA=TOTALA/(NZONE*60) TOT AlB=T CT ALB/(NZGNE*60) C C Write e q u i l i b r i u m 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 a l l SPLIT compute mode s p l i t and new a u t o - t r a n s i t C demands C CALL SPLIT (I,NHOME,N GRUU P,NZONE, IG E,IXT,DIFr,IMOD,TMA X) 400 CONTINUE C C Write e g u i l i o r i u m s t a t i s t i c s produced b y SPLIT c 134 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) 455 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) 450 CONTINUE DO 460 M=1,NGROUP DO 460 I=1,NOFIGN KRITE(19,7) (IOD(M,I,K) , K= 1 ,NZONE) 460 CONTINUE C c c I F (IGD. GT. 0) GO TO 510 GO TO 550 510 ER R C R= DI FF/TMGD WHITE (6, 11) ERROR C C \ P r i n t o p t i o n f o r s t a t i s t i c s on bus l i n e s C 550 I F (NOPB.EQ.0) GO TO 999 8 DC 600 JJ=1,NOPB LIN=NOPTB(JJ) KM=NBSTP(JJ) C C C a l l BNET p r e p a r e bus l i n e d ata f o r p r i n t o u t C 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) ,LIN, (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 IXT-KTT (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 3 3 34 35 36 FORMAT (I4,8X,I4) FORMAT (F20.0) FORMAT (2014) FORMAT (214) FORMAT(8F10.0) FORMAT (8F10. 0) FORMAT (/10X,'THE 135 PERCENT CHANGE IN TRAVEL TIME FROM ONE C I TER AT ICN TO THE NEXT IS',F10.5) FORM AT (1 OX,2 (3A4) ,5X,f6.0,5X,F6.0,10X,F4.3) FOEMATf1',10X,» BUSLINE BUSLINE*) FCBMAT (10X, • HEADWAY NUMEER NAME') FORMAT(/10X,F3.0,' MIN•,3X,12,6X , 20A4) FORMAT(/18X,»EUS STOP',14X,* PEOPLE',11X,'PEOPLE' ,11X + ,'LINK,TIME',11X,'BUS LINES') FORM AT(16X,'INTERSECTION' ,10X,•CN THE BUS',7X,'AT THE STOP' + ,7X,'S T CT AL TiaE',8X,'AT TEE STOP*) FORMAT(10X,2(3A4) ,8X ,F3.0,14X,F3.0,12X,F5. 1, 10X,1014/89X,1014 +/89X,10I4) FORMAT(////50X, 'EQUILIBRIUM STATISTICS ») FORMAT (1 OX ,2 (3 A4) ,7X , F6. 1, 5X, F6. 1 , 1 OX , F6 . 1 , 8X, F6 . 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 SPLITS FOR THE GIVEN ' +,'INTERSECTION TO ALL DESTINATIONS') (/ 10X , ' NUMBER OF BUS LINES=',I4, NUMBER OF BUS ST0PS=',I4, BOARDING TIME FOR THE BUS (SEC PER P ER SON ) =' , F4. 1 , FORMAT +/1GX, +/10X, +/10X, +/10X, + /1 0 X , +/10X, +/10X, +/10X, +/10X, +/10X, +/10X, +/10X, +/ 10 X , +/1CX, +/10X, +/10X, +/10X, +/10X, BUS ACCELERATION BUS DECELERATION NUMEER CF TRANSIT OF OF OF OF OF OF CF TRANSIT VEHICLE VEHICLE LINKS=' ( F T / S E C / S E C ) - ' , F 4 . 1 , ( F T / S E C / S E C ) = ' , F 4 . 1 , 0B1GINS=',14, DESTINATIO NS=',14, ORIGINS=»,14, DESTINATIONS^',14, ,14, EXTERNAL VEHICLE ORIGINS^' 20NES=»,I4, SOCIOECONOMIC GROUPS=',I4, 1 4 , NUMBER NU M E ER NUM E ER NUMBER NUMBER NUMBER NUMBER MAXIMUM WALKING TIME='>F 10.0, PERIOD OF ASSIGNMENT^' ,F5.0 , ITERATION INDEX=',I4, ORIGIN NODE FOR MINIMUM PATH PRINT OUT IS=',.I4, NUMBER CF PATHS PRINTED IS=»,I4, NUMBER OF 1US LINES TO BE PRINTED OUT IS=»,I4) FORMAT(/16 X, ' INTERSECTION' ,11X,'PERSONS',5X, 'PERSONS' ,5X, +'AUTG SPLIT') FORM AT (4OX,'BY CAR',6X,'BY FCRKAT(///10X,'THE AVERAGE FORMAT (/4 7X,'AUTO',2 4X, * BUS') FORMAT(//10X,'DATA FROM UNIT 5 READ IN') FORMAT(//10X, 'VEHICLE ORIGINS & DESTINATIONS +'UNIT 15 READ IN') FORMAT(//10X,'PEDESTRIAN WALK TIMES FOR TRANSIT +'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') BUS') SPEED OF THE BUS IS ',F4.1,« MPH. *) FROM * READ FORMAT (//10 X, 'AUTO TRIPS READ IN FCRfAT(//10X,'TRANSIT TRIPS READ FROM UNIT 19») IN FRCM UNIT 19 ' ) 37 FOB M AT{//10 X , 1 P AE KlNG C AT A READ IN FROM UNIT 18') 38 FORMAT (//10X,'ZONE TO ZONE WALKING TIMES FOR AUTO DRIVERS * +,'BEAD IS 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 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 (1500,50),NBL (1500) ,NUMDEP (1500) , + LINK DP (1500, 10) , TLI NK (2100) ,TRAV(150 0) ,NT (1500,50) -+ ,IKT(1500) ,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) , IPED(3500) ,NCUM ( 1500) , TCUM ( 1500) +, ETT D (1500) ,KEEP (5) , TCM (5} , E SE (5) ,NS (2100,4) , EW (2100, 4) + ,NTHBU(30) ,NOPTD (50) ,ECUM (1500) COMMON /ASS/ I P E E O ( 3 5 0 0 ) ,NN< 1500) ,ITAC(1500) C C I n i t i a l i z e v e c t o r s C DC 100 1=1,LAST TRAV (I) =999999. ITAC(I)=0 NN(I)=0 100 ECES(I) = 0 DO 105 1=1,LAST DC 105 J=1,5 105 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 Determine whether niicme i s on a t h r u bus l i n e o r not C -DC 110 1=1,NTHR IF ( NHCME.EQ.NTHRU (I) ) GO TO 129 110 CONTINUE Q*************************************************************** c C. DETERMINE WALK TIMES TC BUS STOP & WAIT TIME FOR BUS C :SECTION #1 i J / C C**************** *********************************************** C C F i n d walk l i n k s & t i m e s t o bus s t o p s C IK= IKT (N fl) DC 120 J=1,IK K=N3(NM,J) IF (NBL (K). EQ.O) GO TO 120 SUM = 0 N=0 ECE=0.0 IN= NUMDEP(K) IF(IN.EQ.O) GO TO 120 C C F i n d bus l i n e s p a s s i n q bus s t o p C DO 125 L=1,IN 1 = 11 N KDP (K , L) I f (NBUS(I,1) .EQ.O) GO TO 125 IT-NET (I) C C Compute w a i t t i m e f o r bus C DC 126 IA=1,IT IS=NB0S(I,IA) N=N + 1 SUH=S0M + HEAD (IS) *60.0 126 CONTINUE 125 CONTINUE IF (N. EQ. 0) GO TO 127 -EC£=SUM/ (N*2) I F (ECE.GT.210) ECE=. 13*SUM+ 2.3 • IF (PERSON (K) .GT.60) ECE=ECE+SUM C C E n t e r t i m e s S l i n k s i n t o 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 IFF DC ( I I ) = NM 120 CONTINUE 1FLAG=0 GC TO 180 r j * * * ************************************* ******** ************ ** * C C DETERMINE TRAVEL TIME EPCM NODE TO NODE BY BUS C -.SECTION #2 C r j * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 129 NTH fE-2 NM=NHCME TRAV (NM) =0.0 11=11+1 NN (MS) =11 , > C 138 C f i n d v e h i c l e l i n k s d e p a r t i n g the bus sto p C 130 IN= NUMDEP (Nil) NTB=0 I F (IN. 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 re buses r u n n i n g on t h e l i n k c IF (NBUS (I,1) .EQ.C) GO TO 150 I f (TRAV (K)-999999.) 145,140,145 145 IF ( NN (K) .LE. NLINK) GO TO 150 140 NCK=NCM+1 KZZ=K2Z+1 C C For l i n k s w i t h bus l i n e s c a l l TIM f i n d t r a v e l t i m e C on l i n k c CALI TIM (KM,K,I,TIME, NTREE, EC£,LINK) C C E n t e r l i n k & t i m e s i n t o l i s t C TCUM |NCH)=TRAV ( N M) +TIME ECUM (NCM)= ECES(NM) + ECE NCUK (NCM) =1 NBU(NCM)=0 ITAC (K) = 1 NZZ = K iI F (NBL (K) . EQ. 1) GO TO 147 -GO TO 150 C C Determine i f d e s t i n a t i o n node i s a bus s t o p C 147 RTB=NTB+1 KEEP (NTB) = K TCM (NIB) =TCUM (NCM) ESE (NTB) = ECUM (NCM) 150 CONTINUE IF L A G= 1 ICOUNT=0 NM=NZZ IF ( NTB.Gl.0) GO TO 155 C C I f d e s t i n a t i o n node i s a bus s t o p qo t o s e c t i o n 3 C GO TO 180 r * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C ' C DETERMINE TRAVEL TIME FBOM LAST BUS STOP TO FINAL C DESTINATION :SECTION #3 C C rj * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 155 DO 167 JJJ=1,NTB NQ=KEEP (JJJ) 'IFLAG=1 ICGUNT=ICCUNT+1 IK=IKT(NQ) -L C C F i n d walk, l i n k s from bus s t o p s C DO 160 J=1,IK K= N T (NO,J) IZ= 1 IF (TRAV ( K ) - 9 9 9 9 9 9 . ) 170, 165, 170 170 ABC=TRAV (K) AE-TRAV (NG) +TTO (NQ, J) IF(AE.G1.ABC) GO TO 160 165 KCM=NCM+1 C C I f t o t a l time t o d e s t i n a t i o n i s l e s s than minimum C a l r e a d y s t o r e d add t o l i s t . C TCOM (NCM) = TCM (JJ J ) + TTO (NQ,J) •ECUK JNCH) = ESE ( J J J ) +TTO(NQ,J) 11=11+1 NCUM (NCM) = 1 1 'NBU(HCM)=1 ITAC(K) = 1 IPE C ( I I ) = 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 from the l i s t . Then c o n s i d e r walk l i n k s . C IF (NBU (K) .SQ.1.AND.KZZ.GI.0) ' GO TO 200 IF (T HIN-ICU M ( K) ) 200,200, 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 than t h a t a l r e a d y C s t o r e d then chanqe s t o r e d v a l u e t o new v a l u e . c 1 4 0 210 1-1 C C I f t r a v e l time i s q r e a t e r than t h a t a l r e a d y s t o r e d C don't chanqe s t c r e d v a l u e . C GO 10 230 220 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 & t i m e s frcm l i s t C 230 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) 240,250,240 240 CONTINUE C 250 NCM=NCM-1 IF(L.LT.MLINK) KZZ=KZZ-1 C C I f s t o r e d v a l u e was not chanqed qo t c 180 C I F ( I ) 180,260, 180 260 '[II (NN (K) . GT. NLINK. AND. I f AG. NE. 2) GO TO 130 C C I f l a s t l i n k was a walk l i n k qo to 130 S use o r i q i n C node (bus st o p ) of l i n k as the new o r i q i n node f o r C t h e next bus l i n k . C NM=K GO 10 130 C C P r i n t o p t i o n of minimum t r a n s i t p ath. . 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 IF(TRAV (KK) .GT. 999990.) GO TO 312 WRITE (6,4) , TRAV (KK) , ECES (KK) WRITE (6,7) WEI1E (6, 8) 1.1= NN (KK) DO 5C5 JJ=1,NLINK 1X1= NET (LL) WRITE(6,6) (N5(KK,M) ,M=1,3) , (EW(KK,M) ,M= 1 , 3) , NN (KK) + , P E F S C N { K K) , ( N B U S {LL , 11) ,11=1, IX T) GC TO 290 290 IF(LL.GT.NLIMK) K K=.I P EDC (LL) I F ( I L . LE. NLINK) KK-NO(LL) IM = L L LL=» N (KK) IF (LL.GT,NLINK) GO TO 3 11 IF (KK. EQ. NliCME) GO TO 3 1 1 305 CONTINUE 3 1 1 WHITE (6, 6) (NS(KK,M) , H= 1 , 3) , (E U { K K , M) , M= 1 , 3) ,NN (KK) +,F£FSCF(KK) , (NBUS (LM,II) ,11= 1, IXT) GC TO 310 3 1 2 WRITE (6,5) KK 3 1 0 CONTINUE 3 2 0 RETURN 4 FORMAT (///1 OX,'TOTAL TRAVEL TIME (SECS) ',F10.0, + /1GX,«TRANSFER, 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) ,110,F10.0,5 X,1414 / 5 9X,1414) 7 FORM AT(/13X,'INTERSECTION',15X,'LINK',3X,'PERSONS ON' + ,3X,'BUS LINES') 8 FORM AT(48X,'THE EUS',5X,'AT THE NODE'). 9 FORMAT(////10X,'MINIMUM PATH TREE FROM INTERSECTION',2(3A4)) 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 (1500,1 0 ) , TL1N K (2100) ,TL(AV (150 0) , NT (15 0 0 , 5 0 ) + ,IKT( 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),DEC,ACC,LLINE +,BOARD +,PERSOF(1500),FREFLO DIMENSION NN (1500) C********************************************** ***************** c C TRAVEL TIME FOR PASSENGERS JUST EOARDING THE BUS C £************ ********************************** ***************** ECE=0.0 IF (NTREE.EQ.2) GO TO 1 0 0 GC TO 120 1 0 0 I T= N ET (I) SUM = 0 C C S t o r e the bus l i n e s which use l i n k ' I * . C DC 110 M 1=1, IT 11= NEliS (I,MT) NNN (I,MT) = NBUS (I,MT) 1 1 0 CONTINUE C N N (I) =IT IF (TLINK (I.) . EQ. 0) GO TO 115 VEL-DIST (I) /TLINK (I) GC TO 117 C C Compute st o p p e d time and l i n k t r a v e l t i m e . C 115 VE1=FEEF10 117 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 IF(SS.LT.O) TT=0 TIME=STOP+AT + .ET+TT GO TO 200 Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c C TRAVEL TIME FOR PASSENGERS ON TfcE BUS WITH PROVISIONS C FCR STOPS TO PICK UP PASSENGERS C Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 120 N=0 IFLAG-O IT=NN (LINK) 1D=NBT (I) C C Determine i f passenger t r a n s f e r s . C DC 130 J=1,IT DC 130 MT=1,ID IF{NNN(LINK,J).EQ.NBUS(I,MT)) GO TO 140 GC TO 130 • 140 N=N+1 NNN ( I , N) =NBUS ( I , MT) C WRITE(6,1) NN N ( I , MT) , N M , K , NT EE E ,1, TR AV (N M) , ECES (NM) , LINK IFLAG=1 130 CONTINUE NN(I)=N SUM = 0 c C Compute st o p p e d t i i c e t o p i c k up passengers & l i n k t i m e C IF(TLINK (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 IF(SS.LT.O) TT-0 TIME=STOF+AT+DT+TT C WRITE(6,2) TIME,STOP,AT,TT,SS,S,VEL,DIST (I) rTLINK (I) IF(1FLAG.EQ.C) GO TO 160 GO TO 200 158 TIME=1L INK(I) IF (IFIAG. EQ. 0) GC TO 160 GO TO 2 0 0 C*************************************************************** C C TRAVEL TIME FOR PASSENGERS MAKING TRANSFERS C Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 160 DO 150 MT=1,ID 11= NEUS ( I , MT) SUM = SUM+fiEAD(II) * 6 0 . 0 NNN (I,MT) = NEUS(I,MT) C WRITE ( 6 , 1 ) NNN (I,MT) , Ntl, K , NTREE,!, TRAV (NM) ,ECES(NM) ,LINK 15 0 CONTINUE NN(I)=ID ECE=SUM/ (ID*2) IF(ECE.GT.300) ECE=300 C C Compute t r a n s f e r t i m e C TIME=TItfE+ECE 200 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 SI 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 , 10) ,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 (2 100) , 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 00) , PERSON ( 150 0) , NNN ( 1 5 0 0, 5) , DEC , ACC ,LLINE +,EOARC +,PEBSGF(1500),FREFLO CCMMON /ASS/ 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 90 K=1,NZGNE TTT(K)=0.0 DC 90 M=1,NG5CUP T1T(K) = TTT(K) + TOD(M,I,K) 90 CONTINUE C C Compute number o f per s o n s t r a v e l l i n q between C o r i q i n - d e s t i n a t i o n p a i r s C DO 100 J=1,NTSK NSTART=MTTD (J) KK=NPSIN.K ( J ) K=MZCNE (KK) TOTAL=TIT (K)/NC (K) I f { I T A C ( N START).EQ.0) GO TO 100 I=NN (NSTART) IF(L.GT,NLINK) GO TO 120 C C IT= SET (L) DC 110 MT-1 /IT 110 NQQ (MT) = NBUS (L, MT) NX=IT KH=H0(L) GC TO 140 C C 120 N M= I EE DC (L) L=NN (NM) IT= N BT (L) I F ( I T . E Q . O ) GO TO 100 DC 130 MT=1,IT 130 NQQ(MI)=NBUS(L #M1) NM=NG(L) NX=IT C c 140 DO 150 I I I I = 1 , N L I N K L = NN(NM) IF (L. GT. NLINK) GO TO 135 T.T= NOT (L) I F (IT.EQ.0) GC TO 10 0 N = 0 ,SUM=0.0 C C DC 160 M1= 1 ,IT DC 160 £10=1, NX C C Compute number o f p e o p l e b o a r d i n q bus. C I F (NCQ(MO) .NE.NBUS(L,MT)) GO TO 160 II=NBUS (L, MT) SUM = SUM+BEAD (II) N = N + 1 UQQ (N)=NBUS <L,HT) 160 CONTINUE NX = N IF(N.EQ.O) GO TO 180 SUK=SUM/NX C C A s s i q n p e o p l e t o b u s e s . C ' FEB SCN ( NM) =PERSON (NM) +TCTAL*SUfl/ (PERIOD*NX) GO TO 150 180.. DC 190 MT=1,IT NQQ {MT) = NBUS (L,MT) 1 1 = NBUS(I,MT) 190 SUM=SUM + HEAD (II) NX=IT SUM=SUM/NX C C A s s i g n people t o bus s t o p s 145 C 185 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) IF(L.GT.NLINK) GO TO 100 IF (NO (L) . EQ. NFiOME) GO TO 100 150 NK=NC(L) 100 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(3,100,100) f 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) Q******************* ***************************** *************** C C 1ST ITERATION COMPUTATIONS C c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * IF(IGD.GT.O) GO TO 200 BC 100 K=1,NGROUF IXT=IXT+1 C WRITE (6,121) IXT C C I n i t i a l i z e v e c t o r s and s c a l a r s C 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 P r e p a r e d a t a f o r rocde s p l i t c o m p u t a t i o n s c DO 120 L = 1 , NZONE IF (WP (K,L) . IT. .05) GO TO 120 Vii- W (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)*WP(K,L) DIS = DIS + A DIS (1) * W P (K , L) CT=CT + C (L) *wP (K, I) CNT=CNT+WP(K,L) 120 CONTINUE WK=WK/CNT ATTT= ATTT/CNT + 1200 B.1S= (D.IS/CNT + 30000)/5280 . CT=CT/CNT ± 4 0 C C Compute mode s p l i t C GX=-.83*1.27*(TTTT/ATTT)+.095*(.3 5/(DIS L*.08))-.615*CT IF (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 0 (M,I,K)=TOTAL*PA TOD (8,1, K)-TOTAL-0 (M , I , K) P(K)=PA 110 CONTINUE IST=IXT C C W r i t e mode s p l i t to s e q u e n t i a l f i l e C WRITE (4MST) (P (K) ,K=1, NZONE) 100 CONTINUE 60 TO 1000 C*************************************************************** c C MODE SPLIT COMPUTATIONS FOB SUBSEQUENT ITERATIONS C C************************************ *************************** 2 00 DC 3CO M=1, NGEOUP iIXT=IXT+1 IS1=IXT C C Bead from 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 I n i t i a l i z e v e c t o r s and. s c a l a r s C TTTT-TAV (K) +ETAV (K) +1560 WK=0. 0 CNT=0.0 ATTT=0.0 DIS=0.0 C1=0.0 C C P r e p a r e d a t a f c r mcde s p l i t C ' DO 315 L-1,NZONE IF(WP (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 CONTINUE 147 WK=WK/CNT A T T T= A T T1 /C N T + 1 2 0 0 EIS= (DIS/CNT + 30000)/5280 C7 = CT/CNT-C C Compute mode s p l i t C GX=-.8 3+1.2 7*(TTTT/ATTT)+.095*(.3 5/(DIS L * . 0 8 ) ) 6 1 5 * C T 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 based on p r e v i o u s mode s p l i t C 330 DDD = P(K)-PA PP=P(K) IF(FP.LT.0.5) PP=1-PP FA= E (K) -PF*CID TMOD = TMOD + P (K) DIFF=AES (F (K)-PA) P(K)=PA C C Compute a u t o - t r a n s i t demands C TOTAL=TOD(M,I,K) +0 (M,I,K) 0 (M,I,K) =TOTAL*PA TOD(M,I,K)=IOTAL-0(M,I,K) 310 CONTINUE 1 ST-1 XT -C C W r i t e new mode s p l i t t o s e q u e n t i a l t i l e C WRITE (4* 1ST) {P (K) , K= 1 , NZCNE) 300 CONTINUE 1000 RETURN END 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 (1500, 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 I n i t i a l i z e v e c t o r s c E T T = 0.0 SPED=0.0 148 DST=0.0 IET=1 11=0 NCB (IBT)= N M DC 120 1=1,100 120 BTM(I)=0.0 C C F i n d auto l i n k s w i t h bus l i n e on i t C 400 IN= N UMDEP (NM ) IF(IN.EQ.O) GO TO 100 IAT = 0 DO 200 L=1,IN I=LINKDP (NM,L) K=ND(I) IB=0 IXT=NET(I) C C Aqqreqate auto l i n k s between bus s t o p s i n t o bus l i n k s C DO 300 KK=1,IXT N = NE US {I r KK) KS= NTT(K) IF(KS.EQ.O) GO TO 340 DC 320 J J = i , K S IF(N.EQ.NTR (K,JJ) ) GO TO 350 320 CONTINUE 340 NTT (K) = N 1 T (K)+1 KS= NTT (K) NTE(K,KS)=N '•IF (IET. GT. 1) GO TO 350 NTT (NM) =NTT (NM) + 1 KS=NTT(NM) • NT.R (NM,KS) =N 350 IF (L I S , NE. N) GO TO 300 I K= 1 3 00 CONTINUE IF(IH.EQ.O) GO TO 200 I F ( I E T . E Q . I ) NT REE-2 IF(IBT.GT.I) NTREE=100 C C Determine t r a v e l t i m e s on l i n k s by bus c CALI TIM(NM,K,I,TIME,NTBEE,ECE rLINK) LINK=I NM = K IT=IT+1 C Compute a q q r e q a t e bus l i n k t r a v e l time c BT M (I ET) = ETM (I BT) +TIME C C Compute t o t a l bus t r a v e l t i m e 5 t r i p l e n q t h C E T T = E1T + TIM E £ S T - £ S T + D13 T (I) IF (NBI (K) . NE. 1) GO TO 400 IET=IBT+1 NOB (IET) =K 2 0 0 1 0 0 GC TO 400 CONTINUE IF(IBT.EQ.O) GO TO 4 50 ETM (I ET) = ETT 149 C C c Compute average speed of bus SEED= (DS1/BTT) *. 6318 18 18 18 GC TO 4 7 C 4 5 0 WRITE (6,1) NH FOE AT(1 OX,'THE INPUT SPECIFIED A START NODE FOR A BUS LINE' + ,» WHICH HAS NO EXIT',14) 470 RETURN END 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0062868/manifest

Comment

Related Items