The investigation of the reentrance phenomenon in cellular automaton traffic flow model

We investigate analytically and by numerical simulations, the reentrant low density phase for high injection rate in the Nagel–Schreckenberg model. It is found that the reentrance phenomenon is a direct consequence of our injection strategy. Indeed, by adopting our injection rule, an injection rate exists, above which the in-flow begins to decrease by increasing the injection rate. In addition, we have studied the extraction rate interval at which the reentrance of the low density phase appears. It is found that this interval increases with increasing the maximal velocity. For the non deterministic case, the reentrance interval shifts to higher values of extraction rate.

[1]  J Kertész,et al.  Nondeterministic Nagel-Schreckenberg traffic model with open boundary conditions. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Peter Wagner,et al.  Delay times in a cellular traffic flow model for road sections with periodic outflow , 2008 .

[3]  Andreas Schadschneider,et al.  Boundary-induced phase transitions in a space-continuous traffic model with non-unique flow-density relation , 2002, cond-mat/0209384.

[4]  A. Schadschneider,et al.  Empirical evidence for a boundary-induced nonequilibrium phase transition , 2001 .

[5]  D. Fanelli,et al.  Out-of-equilibrium phase re-entrance(s) in long-range interacting systems. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Ning Jia,et al.  Analytical results of the Nagel-Schreckenberg model with stochastic open boundary conditions. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Eytan Domany,et al.  An exact solution of a one-dimensional asymmetric exclusion model with open boundaries , 1992 .

[8]  R. Barlovic,et al.  Localized defects in a cellular automaton model for traffic flow with phase separation , 2001 .

[9]  S. Wolfram.  Statistical mechanics of cellular automata , 1983 .

[10]  J Kertész,et al.  Stochastic boundary conditions in the deterministic Nagel-Schreckenberg traffic model. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  M. Reza Shaebani,et al.  Optimized traffic flow at a single intersection: traffic responsive signalization , 2004 .

[12]  Hamid Ez-Zahraouy,et al.  THE EFFECT OF THE HETEROGENEITY ON THE TRAFFIC FLOW BEHAVIOR , 2010 .

[13]  G. Schütz,et al.  Phase diagram of one-dimensional driven lattice gases with open boundaries , 1998 .

[14]  A. Schadschneider,et al.  Open boundaries in a cellular automaton model for traffic flow with metastable states. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  H. Diep,et al.  Frustrated Spin Systems , 2020 .

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

[17]  Hamid Ez-Zahraouy,et al.  A simulation study of an asymmetric exclusion model with open boundaries and random rates , 1999 .

[18]  Krug,et al.  Boundary-induced phase transitions in driven diffusive systems. , 1991, Physical review letters.

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

[20]  Andreas Schadschneider,et al.  Cellular automata models of highway traffic , 2006 .

[21]  Ning Jia,et al.  Analytical investigation of the open boundary conditions in the Nagel-Schreckenberg model. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Peter Wagner,et al.  Comment on "Analytical investigation of the open boundary conditions in the Nagel-Schreckenberg model". , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Michael Schreckenberg,et al.  Impacts of different types of ramps on the traffic flow , 2005 .

[24]  K. Jetto,et al.  The effect of mixture lengths of vehicles on the traffic flow behaviour in one-dimensional cellular automaton , 2004 .

[25]  Schutz,et al.  Asymmetric exclusion process with next-nearest-neighbor interaction: some comments on traffic flow and a nonequilibrium reentrance transition , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Helmut G Katzgraber,et al.  Simplest model to study reentrance in physical systems. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Michael Schreckenberg,et al.  Effect of the lane reduction in the cellular automata models applied to the two-lane traffic , 2006 .