tailieunhanh - Statistical Physics of Traffic Flow

The modelling of traffic flow using methods and models from physics has a long history. In recent years especially cellular automata models have allowed for large-scale simulations of large traffic networks faster than real time. On the other hand, these systems are interesting for physicists since they allow to observe genuine nonequilibrium effects. Here the current status of cellular automata models for traffic flow is reviewed with special emphasis on nonequilibrium effects (. phase transitions) induced by on- and off-ramps. | Statistical Physics of Traffic Flow1 arXiv cond-mat 0007418v1 26 Jul 2000 Andreas Schadschneider a 2 aInstitut fur Theoretische Physik Universitat zu Koln D-50923 Koln Germany Physica A285 101 2000 Abstract The modelling of traffic flow using methods and models from physics has a long history. In recent years especially cellular automata models have allowed for large-scale simulations of large traffic networks faster than real time. On the other hand these systems are interesting for physicists since they allow to observe genuine nonequilibrium effects. Here the current status of cellular automata models for traffic flow is reviewed with special emphasis on nonequilibrium effects . phase transitions induced by on- and off-ramps. Key words Cellular automata complex systems nonequilibrium physics 1 Introduction Despite the long history of application of methods from physics to traffic flow problems going back to the fifties it has only recently blossomed into a successfull field of exotic statistical physics 1 . Until a few years ago most approaches were based on classical methods from physics especially from mechanics and hydrodynamics. In general one can distinguish microscopic and macroscopic approaches. In microscopic models individual vehicles are distinguished. A typical example are the so-called car-following theories 2 3 . For each car one writes an 1 Supported by SFB 341 Koln-Aachen-Julich 2 E-mail as@ Preprint submitted to Elsevier Preprint 1 February 2008 equation of motion which is the analogue of Newton s equation. The basic philospophy of the car-following approach can be summarized by the equation Response n Kn Stimulus n for the n th vehicle. Each driver n responds to the surrounding traffic conditions which constitute the stimulus for his reaction. The constant of proportionality Kn is also called sensitivity. Usually also the reaction-time of the drivers is taken into account. A typical example is the .