Stability of macroscopic traffic flow modeling through wavefront expansion

The state of the art of macroscopic vehicle traffic flow models is discussed and the traffic flow stability of these models is analyzed. A nonlinear traffic flow stability criterion is investigated using the wavefront expansion technique. Qualitative relationships between traffic flow stability and model parameters are derived for an entire class of second-order macroscopic traffic flow models. Numerical results axe obtained using the CLAWPACK package for the well-known Payne-Whitham model, in order to illustrate the stability criterion. The newly derived stability results are consistent with previous reported results obtained using both microscopic models and approximate linearization methods. Moreover, the stability criteria derived in the paper can provide more refined information regarding the propagation of traffic flow perturbations and shock waves in second-order models than previously established methodologies.

[1]  Harold J Payne,et al.  FREFLO: A MACROSCOPIC SIMULATION MODEL OF FREEWAY TRAFFIC , 1979 .

[2]  J. M. D. Castillo.  Propagation of perturbations in dense traffic flow: a model and its implications , 2001 .

[3]  Markos Papageorgiou,et al.  Parameter Identification for a Traffic Flow Model , 1979 .

[4]  G. Whitham,et al.  Linear and Nonlinear Waves , 1976 .

[5]  Anastasios S. Lyrintzis,et al.  Improved High-Order Model for Freeway Traffic Flow , 1998 .

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

[7]  Markos Papageorgiou,et al.  SOME REMARKS ON MACROSCOPIC TRAFFIC FLOW MODELLING , 1998 .

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

[9]  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.

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

[11]  Dirk Helbing,et al.  Numerical simulation of macroscopic traffic equations , 1999, Comput. Sci. Eng..

[12]  Ping Yi,et al.  Continuum modelling of traffic dynamics for congested freeways , 1993 .

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

[14]  J. M. D. Castillo,et al.  The reaction time of drivers and the stability of traffic flow , 1994 .

[15]  E. N. Holland.  A generalised stability criterion for motorway traffic , 1998 .

[16]  Markos Papageorgiou,et al.  Macroscopic modelling of traffic flow on the Boulevard Périphérique in Paris , 1989 .

[17]  H. M. Zhang.  Analyses of the stability and wave properties of a new continuum traffic theory , 1999 .

[18]  A. Movchan.  Stability of processes with respect to two metrics , 1960 .

[19]  Harold J Payne,et al.  MODELS OF FREEWAY TRAFFIC AND CONTROL. , 1971 .

[20]  H. M. Zhang.  A theory of nonequilibrium traffic flow , 1998 .

[21]  C. Daganzo.  Requiem for second-order fluid approximations of traffic flow , 1995 .

[22]  Swaroop Darbha,et al.  Intelligent Cruise Control Systems And Traffic Flow Stability , 1998 .

[23]  D. Helbing,et al.  DERIVATION, PROPERTIES, AND SIMULATION OF A GAS-KINETIC-BASED, NONLOCAL TRAFFIC MODEL , 1999, cond-mat/9901240.

[24]  Kerner,et al.  Cluster effect in initially homogeneous traffic flow. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  R. LeVeque.  Wave Propagation Algorithms for Multidimensional Hyperbolic Systems , 1997 .

[26]  Warren F. Phillips,et al.  A kinetic model for traffic flow with continuum implications , 1979 .

[27]  Francisco G. Benitez,et al.  A FORMULATION FOR THE REACTION TIME OF TRAFFIC FLOW MODELS. , 1993 .

[28]  Anastasios S. Lyrintzis,et al.  Numerical Simulation of Freeway Traffic Flow , 1997 .

[29]  Randall J. LeVeque,et al.  CLAWPACK Version 4.3 User's Guide , 2002 .