Introducing Buses into First-Order Macroscopic Traffic Flow Models

The aim of this paper is to provide a simple model of the interaction between buses and the surrounding traffic flow. Traffic flow is assumed to be described by a first-order macroscopic model of the Lighthill-Whitman-Richards type. As a consequence of their kinematics, which in large measure can be considered to be independent of the flow of other vehicles, buses should be considered as a moving capacity restriction from the point of view of other drivers. This simple interaction model is analyzed, mainly by considering the moving frame associated with the bus in order to derive analytical computation rules for derivation of the effects of the presence of the bus in the traffic flow. After deriving traffic equations in the moving frame associated with a bus, the usual basic concepts of first-order models, including those of relative traffic supply and demand, are generalized to the moving frame. A simple model for the bus-traffic interaction, assuming that the dimension of the bus can be neglected, can be derived from analytical calculations in the moving frame. Finally, some tentative results for the inclusion of buses into first-order traffic flow models, discretized according to Godunov’s scheme, are given.

[1]  S P Harris,et al.  ROGUS - A SIMULATION OF DYNAMIC ROUTE GUIDANCE SYSTEMS , 1992 .

[2]  C. Daganzo.  A finite difference approximation of the kinematic wave model of traffic flow , 1995 .

[3]  J. Lebacque.  THE GODUNOV SCHEME AND WHAT IT MEANS FOR FIRST ORDER TRAFFIC FLOW MODELS , 1996 .

[4]  Panos G. Michalopoulos,et al.  A Freeway Simulation Program for Microcomputers , 1985 .

[5]  K Wood,et al.  BUS TRANSYT - A USER'S GUIDE , 1977 .

[6]  H Mongeot.  MODELLING OF TRAFFIC FLOW DYNAMICS IN INCIDENT CONDITIONS USING THE FIRST-ORDER MACROSCOPIC APPROACH , 1997 .

[7]  Dimitrios E. Beskos,et al.  ANALYSIS OF INTERRUPTED TRAFFIC FLOW BY FINITE DIFFERENCE METHODS , 1984 .

[8]  P. I. Richards.  Shock Waves on the Highway , 1956 .

[9]  Hani S. Mahmassani,et al.  An evaluation tool for advanced traffic information and management systems in urban networks , 1994 .

[10]  Chin Jian Leo,et al.  Numerical simulation of macroscopic continuum traffic models , 1992 .

[11]  Habib Haj-Salem,et al.  METACOR: A MACROSCOPIC MODELLING TOOL FOR URBAN CORRIDOR , 1994 .

[12]  Richard D Worrall,et al.  NETWORK FLOW SIMULATION FOR URBAN TRAFFIC CONTROL SYSTEM , 1971 .

[13]  Paul Nelson,et al.  COMPUTATIONAL REALIZATIONS OF THE ENTROPY CONDITION IN MODELING CONGESTED TRAFFIC FLOW. FINAL REPORT , 1992 .

[14]  C. Daganzo.  THE CELL TRANSMISSION MODEL.. , 1994 .

[15]  Carlos F. Daganzo,et al.  A FINITE DIFFERENCE APPROXIMATION OF THE KINEMATIC WAVE MODEL. , 1993 .

[16]  C Buisson,et al.  THE STRADA MODEL FOR DYNAMIC ASSIGNMENT , 1996 .

[17]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[18]  Carlos F. Daganzo,et al.  THE CELL TRANSMISSION MODEL, PART II: NETWORK TRAFFIC , 1995 .