Modeling highway-traffic headway distributions using superstatistics.

We study traffic clearance distributions (i.e., the instantaneous gap between successive vehicles) and time-headway distributions by applying the Beck and Cohen superstatistics. We model the transition from free phase to congested phase with the increase of vehicle density as a transition from the Poisson statistics to that of the random-matrix theory. We derive an analytic expression for the spacing distributions that interpolates from the Poisson distribution and Wigner's surmise and apply it to the distributions of the net distance and time gaps among the succeeding cars at different densities of traffic flow. The obtained distribution fits the experimental results for single-vehicle data of the Dutch freeway A9 and the German freeway A5.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  B. Kerner,et al.  EXPERIMENTAL PROPERTIES OF PHASE TRANSITIONS IN TRAFFIC FLOW , 1997 .

[3]  D. Helbing,et al.  Phase diagram of tra c states in the presence of inhomogeneities , 1998, cond-mat/9809324.

[4]  A. Schadschneider,et al.  Single-vehicle data of highway traffic: a statistical analysis. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[6]  Ihor Lubashevsky,et al.  Order-parameter model for unstable multilane traffic flow , 2000 .

[7]  M. Krbálek,et al.  Headways in traffic flow: remarks from a physical perspective. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[9]  Microscopic versus mesoscopic local density of states in one-dimensional localization , 2001, cond-mat/0107383.

[10]  T. Nagatani.  The physics of traffic jams , 2002 .

[11]  F. Sattin.  Non-Gaussian probability distribution functions from maximum-entropy-principle considerations. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Sven Maerivoet,et al.  Non-concave fundamental diagrams and phase transitions in a stochastic traffic cellular automaton , 2004 .

[13]  Phase Transitions in Traffic Models , 2003, cond-mat/0312459.

[14]  Random matrix theory within superstatistics. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  M. Stephanov,et al.  Random Matrices , 2005, hep-ph/0509286.

[16]  G. J. Rodgers,et al.  Modelling the gap size distribution of parked cars , 2005 .

[17]  Ihor Lubashevsky,et al.  Probabilistic Description of Traffic Flow , 2001 .

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

[19]  A. Y. Abul-Magd.  Modelling gap-size distribution of parked cars using random-matrix theory , 2006 .

[20]  Superstatistics in random matrix theory , 2005, cond-mat/0507034.

[21]  Milan Krbalek,et al.  Equilibrium distributions in a thermodynamical traffic gas , 2006 .

[22]  Hubert Rehborn,et al.  Microscopic features of moving traffic jams. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Distribution of local density of states in superstatistical random matrix theory , 2007, cond-mat/0702395.