A new macro model with consideration of the traffic interruption probability

In this paper, we present a new macro model which involves the effects that the probability of traffic interruption has on the car-following behavior through formulating the inner relationship between micro and macro variables. Linear stability analysis shows that consideration of the traffic interruption probability can improve the stability of traffic flow if and only if the drivers’ reactive time required for adjusting their acceleration based on the traffic interruption probability p is not greater than that one based on the non-interruption probability 1−p. Numerical results verify that the new model can be used to analyze the effects of traffic interruption probability and traffic interruption on shock, rarefaction wave, small perturbation and uniform flow. The model has been applied in reproducing some complex traffic phenomena resulted by some traffic interruptions (e.g., signal light, pedestrian and tolling station).

[1]  J. M. D. Castillo,et al.  On the functional form of the speed-density relationship—I: General theory , 1995 .

[2]  Akihiro Nakayama,et al.  Dynamical model of a cooperative driving system for freeway traffic. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  M. Lighthill,et al.  On kinematic waves I. Flood movement in long rivers , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  N N Sze,et al.  Contributory factors to traffic crashes at signalized intersections in Hong Kong. , 2007, Accident; analysis and prevention.

[5]  S C Wong,et al.  A qualitative assessment methodology for road safety policy strategies. , 2004, Accident; analysis and prevention.

[6]  S. Dai,et al.  Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Hai-Jun Huang,et al.  A new overtaking model and numerical tests , 2007 .

[8]  R. Jiang,et al.  Full velocity difference model for a car-following theory. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  N N Sze,et al.  Diagnostic analysis of the logistic model for pedestrian injury severity in traffic crashes. , 2007, Accident; analysis and prevention.

[10]  Ziyou Gao,et al.  A new car-following model: full velocity and acceleration difference model , 2005 .

[11]  Boris S. Kerner,et al.  Local cluster effect in different traffic flow models , 1998 .

[12]  Carlos F. Daganzo,et al.  A continuum theory of traffic dynamics for freeways with special lanes , 1997 .

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

[14]  R. Jiang,et al.  A new continuum model for traffic flow and numerical tests , 2002 .

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

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

[17]  Arvind Kumar Gupta,et al.  A NEW MULTI-CLASS CONTINUUM MODEL FOR TRAFFIC FLOW , 2007 .

[18]  Peng Zhang,et al.  High-resolution numerical approximation of traffic flow problems with variable lanes and free-flow velocities. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[20]  姜锐,et al.  Extended speed gradient model for traffic flow on two-lane freeways , 2007 .

[21]  S. Wong,et al.  Characteristic Parameters of a Wide Cluster in a Higher-Order Traffic Flow Model , 2006 .

[22]  Luciano Telesca,et al.  Analysis of the temporal properties in car accident time series , 2008 .

[23]  Jiang Rui,et al.  Kinematic wave properties of anisotropic dynamics model for traffic flow , 2002 .

[24]  Akihiro Nakayama,et al.  Equivalence of linear response among extended optimal velocity models. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Haijun Huang,et al.  Continuum models for freeways with two lanes and numerical tests , 2004 .

[26]  S. Wong,et al.  Essence of conservation forms in the traveling wave solutions of higher-order traffic flow models. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Michel Rascle,et al.  Resurrection of "Second Order" Models of Traffic Flow , 2000, SIAM J. Appl. Math..

[28]  T. Nagatani.  Stabilization and enhancement of traffic flow by the next-nearest-neighbor interaction. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  Rui Jiang,et al.  A new dynamics model for traffic flow , 2001 .

[30]  A. Schadschneider,et al.  Statistical physics of vehicular traffic and some related systems , 2000, cond-mat/0007053.

[31]  Yu Xue,et al.  Continuum traffic model with the consideration of two delay time scales. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  R. Sollacher,et al.  Multi-anticipative car-following model , 1999 .

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

[34]  Serge P. Hoogendoorn,et al.  Continuum modeling of cooperative traffic flow dynamics , 2009 .