Dangerous situations within the framework of the Nagel–Schreckenberg model

This paper investigates the occurrence of dangerous situations (DS) within the framework of the Nagel–Schreckenberg model. The conditions of the DS are modified. It is shown that when vmax = 1, there will be no DS in both deterministic and non-deterministic cases. The situation is different for vmax > 1. We show that in the deterministic case, the probability of DS covers a two-dimensional region, which depends on both the density and the initial configuration. As for the non-deterministic case, our results are qualitatively the same as previous ones, but are quantitatively different.

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

[2]  A. Schadschneider,et al.  Metastable states in cellular automata for traffic flow , 1998, cond-mat/9804170.

[3]  Dirk Helbing,et al.  GENERALIZED FORCE MODEL OF TRAFFIC DYNAMICS , 1998 .

[4]  Havlin,et al.  Presence of many stable nonhomogeneous states in an inertial car-following model , 2000, Physical review letters.

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

[6]  D W Huang,et al.  Mean-field theory for car accidents. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Neil F. Johnson,et al.  Cellular automata models of traffic flow along a highway containing a junction , 1996 .

[8]  Nakayama,et al.  Dynamical model of traffic congestion and numerical simulation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  D W Huang,et al.  Car accidents on a single-lane highway. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  H. Lee,et al.  ORIGIN OF SYNCHRONIZED TRAFFIC FLOW ON HIGHWAYS AND ITS DYNAMIC PHASE TRANSITIONS , 1998, cond-mat/9805097.

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

[12]  H. Lee,et al.  Dynamic states of a continuum traffic equation with on-ramp. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  D. Helbing.  Traffic and related self-driven many-particle systems , 2000, cond-mat/0012229.

[14]  Dirk Helbing,et al.  MASTER: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model , 2001 .

[15]  Nino Boccara,et al.  Car accidents and number of stopped cars due to road blockage on a one-lane highway , 1997, adap-org/9704001.

[16]  Michael Schreckenberg,et al.  A cellular automaton model for freeway traffic , 1992 .

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

[18]  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.