A Wave-Based Resolution Scheme for the Hydrodynamic LWR Traffic Flow Model

Resolution of LWR model is considered. The method proposed in this paper differs from (continuous) characteristic based analytical resolutions or from (discretized) finite difference schemes. It is based on an approximation of the flow-density relationship which yields a solution with piecewise constant density. This solution is then exactly calculated by tracking waves and handling their collisions. Extensions for incorporating boundary conditions such as traffic signals or discontinuity of the flow-density diagram are considered and provide an illustration of the potentiality of the method.

[1]  C Buisson,et al.  STRADA, a discretized macroscopic model of vehicular traffic flow in complex networks based on the Godunov scheme , 1996 .

[2]  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.

[3]  C. Dafermos.  Polygonal approximations of solutions of the initial value problem for a conservation law , 1972 .

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

[5]  Carlos F. Daganzo,et al.  Fundamentals of Transportation and Traffic Operations , 1997 .

[6]  S. Chandana Wirasinghe,et al.  DETERMINATION OF TRAFFIC DELAYS FROM SHOCK-WAVE ANALYSIS , 1978 .

[7]  Michael Florian,et al.  A Note on the Entropy Solutions of the Hydrodynamic Model of Traffic Flow , 2002, Transp. Sci..

[8]  J. Lesort,et al.  Analytical Expressions of Incident-Induced Flow Dynamics Perturbations: Using Macroscopic Theory and Extension of Lighthill-Whitham Theory , 2000 .

[9]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[10]  J. Langseth.  On an implementation of a front tracking method for hyperbolic conservation laws , 1996 .

[11]  L. Holden,et al.  A NUMERICAL METHOD FOR FIRST ORDER NONLINEAR SCALAR CONSERVATION LAWS IN ONE-DIMENSION , 1988 .

[12]  S. Wong,et al.  An analytical shock-fitting algorithm for LWR kinematic wave model embedded with linear speed–density relationship , 2002 .

[13]  H. Holden,et al.  Front Tracking for Hyperbolic Conservation Laws , 2002 .

[14]  H. M. Zhang.  A finite difference approximation of a non-equilibrium traffic flow model , 2001 .

[15]  G. F. Newell.  A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks , 1993 .

[16]  Ludovic Leclercq,et al.  A traffic Flow Model for Urban Traffic Analysis: Extensions of the LWR Model for Urban and Environmental Applications , 2002 .

[17]  G. F. Newell.  A simplified theory of kinematic waves in highway traffic, part I: General theory , 1993 .

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

[19]  Jean-Patrick Lebacque,et al.  Two-Phase Bounded-Acceleration Traffic Flow Model: Analytical Solutions and Applications , 2003 .

[20]  R. Ansorge.  What does the entropy condition mean in traffic flow theory , 1990 .

[21]  Gregory Stephanopoulos,et al.  Modeling of Traffic Flow at Signalized Links , 1980 .