An urban traffic simulation model

AN URBAN TRAFFIC SIMULATION MODEL by Uno Larsson • This article includes a brief i n t r o d u c t i o n to a s i m u l a t i o n p r o j e c t f ~ ~ carried through at the University of Gothenburg, X D e p a r t m e n t of Business Administration. T h e o u t c o m e of the project has partly been published in a technical report n o w available ( L a r s s o n and Lundin 1971). i Purpose T h e p u r p o s e of the project w a s to increase our k n o w l e d g e of m o d e l building and the application of digital simulation techniques. T h e technical report is only part of a dissertation (for the S w e d i s h licentiate degree) and thus include s : o an outline of a s y s t e m1 a p p r o a c h to u r b a n traffic planning and control, s o an introduction to unique m o d e l building technique that m a y a p p e a r useful in other applications, and o a detailed description of a digital simulation m o d e l feasible to use for key descriptions concerning u r b a n traffic control systems. T h e report does not include any survey or critical review of methodological p r o b l e m s such as validation and experimental design p r o b l e m s w h i c h h o w e v e r w e r e treated to s o m e extent with the project. ~ General Characteristics of the M o d e l T h e s y s t e m considered in the study m a y be described as a multistation, multichannel queueing s y s t e m with d y n a m i c and stochastic properties. T h e simulation m o d e l (the c o m p u t e r model) w a s given a m o d u l a r design in o r d e r to f a c i l i t a t e e a s y a d a p t i o n to v a r i o u s s t r e e t n e t w o r k s a n d m o d e s of t r a f f i c c o n t r o l a s w e l l a s f e a s i b l e r e p r e s e n t a t i o n of a r r i v a l s of v e h i c l e s to the system (deterministic - various stochastic distributions), i U n o L a r s s o n and Roll Lundin: U r b a n Traffic Simulation. Gothenburg Studies in Business Administration, University of Gothenburg, Sweder~, 1971. 2 T h e published report contains a brief history in tabular f o r m traffic studies, starting with Gerlough~s w o r k at U C L A in 1955. 1 76 of u r b an M r . Uno L a r s s o n , e k o n . l i c . , U n i v e r s i t y of G ~ t e b o r g ( S w e d e n ) w i l l be a t t h e G r a d u a t e S c h o o l of B u s i n e s s a n d P u b l i c A d m i n i s t r a t i o n , Cornell Univers i t y in I t h a c a NY d u r i n g t h e 1 9 7 2 - 1 9 7 3 a c a d e m i c y e a r . Simulette r/IV] 1 The model may further be characterised as a critical event model involving time increments. The representation of s t r u c t u r e (streets and intersections), c o n t r o l s y s t e m a n d v e h i c l e s w i l l be c o n s i d e r e d below. The computer program is written in FORTRAN IV a n d t h e m o d e l h a s b e e n used on the I B M 7090/94, 360/50 and 360/65. Variables - A Brief Descriptio n o Arrivals to the system, e.g., negative exponential distributed. o Destination of vehicles, i.e., the 'split up' of the traffic flow within the system.~ o Signal system offset. o Modeof traffic parameters: control within cycle length, split, Exogenous variables : Controllable variables: certain limits. o Modifications in the structure of t h e s y s t e m , e.g., as regards t h e n u m b e r of l a n e s , one-way regulations, etc. Endogenous variables: o For each lane represented system: total waiting time, /number of stops. as well number as for the total of departures, Representatio n of the Structure T h e three-step technique, evolved for the c o m p u t e r representation of the traffic s y s t e m structure (including streets and interesections) m a y be considered as unique. It s e e m s m o s t likely that the s a m e principles can be used successfully to fulfill the need for powerful and simple s y s t e m description in general. [ Figures 1 through 3 are intended to visualize its application. ] In step #i w e start by drawing a simplified m a p oft the structure of interest (Figure I). ,,,r , ,, Figure I : T h e structure -~ i Simuletter/IV/1 II I I Ill I III . . . . . n~ ~ . . . . . . . . . . : ~ " ~ ' ~ 77 ......... ~ An Urban Traffic Simulation Model < continued > Step #Z refers to the transformation of the m a p of the structure (Figure Z). into formalized description ® ia 3010 f 90il i 8011~,.,J-. 6Oil ,-. -~ ,-- 30ZO qp ! - 9022 t lu Figure Z: T h e r e p r e s e n t a t i o n of t h e s t r u c t u r e by s y m b o l s a n d c o d e n u m b e r s T h e m o d u l e s a r e c o u p l e s by l i n k s e a c h o n e o f w h i c h c o r r e s p o n d i n g to a single lane. Each module is described by a n u m b e r of e l e m e n t s . There are eight types of elements. Only seven are used in this illustration in Figure 2. ( A c o m p I e t e l i s t of e l e m e n t s and their symbols is included at the top of the next page - Ed. ) N e xt w e turn to Step #3 w h i c h involves the m a t r i x representation of the structure (see Figure 3 on page 80). A s far as the S M - m a t r i c e s and other matrices in the m o d e l are concerned, there are m o r e efficient designs. W e would r e c o m m e n d a multidimensional a p p r o a c h f r o m a computational point of view. 78 S i m u l e t t e r / I V / 1 Guide to Element Symbols T~ of E l e m e n t S y m b o l and f i r s t d i g i t in the code n u m b e r Direct generation point Indirect generation point (denoting vehicle generation within the system) Intersection © ?) 3 f~ Split point Merger point (not used in the example) ! 6 ! Link Queue element Exit element "Not time consuming connection" between elements [73 R e p r e s e n t a t i o n of the C o n t r o l S y s t e m In the b a s i c v e r s i o n of the m o d e l a s i m p l e p r e t i m e d t r a f f i c s i g n a l s y s t e m is r e p r e s e n t e d . H o w e v e r the m o d e l m a y e a s i l y be a d a p t e d to o t h e r control modes. The c o n t r o l s y s t e m is r e p r e s e n t e d by two m a t r i c e s . One of t h e m c o n t a i n s t h e c o n t r o l p r o g r a m f o r e a c h l a n e (or queue) in the system. T h e o t h e r i n d i c a t e s t h e s t a t u s of the t r a f f i c s i g n a l s at any specific moment. By u p d a t i n g the s e c o n d m a t r i x by p r o p e r t i m e i n c r e m e n t s ( d e p e n d i n g on c r i t i c a l e v e n t s ) a n d by c o m p a r i n g the two of t h e m , it is p o s s i b l e to keep the c o r r e c t s i g n a l i n d i c a t i o n p a t t e r n . Simuletter/IV/1 79 An Urban Traffic Simulation Model ( continued ) SMI 1011 1012 1013 1021 1022 1023 SM4 4011 401 2 4014 4022 4023 4024 R~resentation of the Vehicles SM2 4011 4011 4012 401 2 40~ 2 4013 4013 4014 4014 4014 4021 7010 7'011 7012 7013 7014 60:11 601 2 7017 7018 7019 6021 701 t 7014 7014 7016 7019 7019 7022 7024 7024 7026 7028 7028 7015 7017 7018 7010 7012 7013 7025 7027 7028 7021 7023 7024 E a c h vehicle in the s y s t e m is represented by one single time notation (event) with a few exceptions. The events are arrivals or departures to and f r o m queue elements (or intersections). O n e matrix is used to store the arrival time for vehicles in queues. Another one contains the time for future arrivals regarding vehicles passing links in the system. The scanning for critical events is p e r f o r m e d in a matrix containing the next event for each queue elem e n t (departures) and direct as well as indirect generation points (arrivals). There are several reasons w h y this abstract representation of structure and vehicles is considered m o r e efficient than physical representation (which m e a n s that computer memory units, e.g. bits or words, corresponds directly to the lane segments). SM5 7010 7010 7011 701 2 701 2 8013 4013 801 2 8011 8013 4021 4022 4022 4023 4023 4024 4024 SM3 6022 6021 6012 6011 6022 7023 7024 7025 7026 7027 7028 701.5 '/014 7015 7015 7016 7017 7017 7018 7019 7021 7021 7022 7023 7023 7024 7024 7025 7025 7026 7027 7027 7028 7028 801~ ,40~3 8011 801 2 8013 801 2 4013 801 2 8011 8022 8023 8021 4021 8023 8022 8023 8021 4021 8023 8021 8022 8021 4021 2011 2012 2021 2022 7015 7016 7021 7022 [ References are given on the next page - Ed~. ] Figure 3: The structure matrices. They contain m o r e information which are excluded in order to simplify the description. S M 4 indicates traffic flow in conflict. § Editor's Note: Mr. Rolf Lundin this year is a Ph. D. student at the University of Chicago. Both he and the author, Uno Larsson, were students of Professor Walter Goldberg at the Graduate School of Business Administration, G~teborgs Universitet, Erik Dahlbergsgatan ii B, 411 26 G~3teborg, Sweden. 80 Simuletter/IV/1 References: Larsson and Lundin: _Upon S o m e Methodological Problems Arising in Connection with the Formulation and Application 'of an Urban Traffic Simulation Model. University of Oothenberg, 1968 (mimeographed) ........ :"Some Methodologiual Views on Digital Simulation" f r o m Models and Simulation - Proceedings of a S y m p o s i u m , H. Stockhaus (ed). • ,i Gothenburg, A kademlforlaget, 1970. pp. Z55-ZT0. :"Relevance, Validity, Reliability and the Use of Simulation Models" from Behavioral Approaches to M o d e r n Management, W ~ Goldberg (ed). V o l u m e I' Gothenburg, BAS, 1970. pp. 304-309. -: Urban Traffic Simulation. Gotherburg, BAS, 1971. § Editor's Note: T h e r e a r e two r e c e n t p u b l i c a t i o n s i n t h i s a r e a in w h i c h m e m b e r s i n v o l v e d w i t h t h i s t y p e of a p r o b l e m w o u l d be i n t e r e s t e d . Both a r e p u b l i s h e d - b y the O r g a n i z a t i o n for E c o n o m i c G oope r a t i on and Development [ OECD] a n d m a y be o b t a i n e d f r o m t h e p u b l i c a t i o n s o f f i c e e i t h e r a t : (a) rue A n d r e Pascal, 75 Paris, France or (b) Suite iZ07, 1750 Pennsylvania A v e n u e N W , Washington D C 20006. (D A r e a Traffic Control Systems. 7Z p a g e s . $1.50; DM 4 . 2 0 ; SF 4.75 $Z. 00; (D O p t i m i z a t i o n of B u s O p e r a t i o n DM 6 . 3 0 ; SF 7.00 in U r ban A r e a s . 90 p a g e s . PUBUCATIONS AVAILABLE Three recent publications available from the Order Department, A C M, 1133 A v e n u e of t h e A m e r i c a s , New Y o r k NY 10036 a r e ( p r i c e s l i s t e d a r e for A C M m e m b e r s and books p r e p a i d ; t h e r e is a $Z.00 billing charge for o r d e r s w h i c h a r e not prepaid): P r o c e e d i n g s of t h e N i n t h A n n u a l D e s i g n A u t o m a t i o n W o r k s h o p , 1972, D a l l a s , T e x a s . 375 p a g e s ; $ 1 0 . 0 0 p r e p a i d . o June 26-28, . P r o c e e d i n g s of F o u r t h A n n u a l A C M S y m p o s i u m on T h e o r y of C o m p u t i n g , Denver, Colorado, M a y i-3,1972. 263 pages; $I0.00 prepaid. S I F C S E B u l l e t i n on S e c o n d S Y , ,m p o s i u m . on . E d u c a t. i o .n . i n . C. o m p u t e r S c i e n c e , , . . . . . M a r c h 1972, St. Louis, Missouri. 16i pages; $I0.00 prepaid. Simuletter/IV/1 81