Order parameter model for unstable multilane traffic flow

We discuss a phenomenological approach to the description of unstable vehicle motion on multilane highways that explains in a simple way the observed sequence of the phase transitions "free flow -> synchronized motion -> jam" as well as the hysteresis in the transition "free flow synchronized motion". We introduce a new variable called order parameter that accounts for possible correlations in the vehicle motion at different lanes. So, it is principally due to the "many-body" effects in the car interaction, which enables us to regard it as an additional independent state variable of traffic flow. Basing on the latest experimental data (cond-mat/9905216) we assume that these correlations are due to a small group of "fast" drivers. Taking into account the general properties of the driver behavior we write the governing equation for the order parameter. In this context we analyze the instability of homogeneous traffic flow manifesting itself in both of the mentioned above phase transitions where, in addition, the transition "synchronized motion -> jam" also exhibits a similar hysteresis. Besides, the jam is characterized by the vehicle flows at different lanes being independent of one another. We specify a certain simplified model in order to study the general features of the car cluster self-formation under the phase transition "free flow synchronized motion". In particular, we show that the main local parameters of the developed cluster are determined by the state characteristics of vehicle motion only.Comment: REVTeX 3.1, 10 pages with 10 PostScript figure

Derivation, Properties, and Simulation of a Gas-Kinetic-Based, Non-Local Traffic Model

We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average velocity contain a non-local interaction term which is very favorable for a fast and robust numerical integration, so that several thousand freeway kilometers can be simulated in real-time. The model parameters can be easily calibrated by means of empirical data. They are directly related to the quantities characterizing individual driver-vehicle behavior, and their optimal values have the expected order of magnitude. Therefore, they allow to investigate the influences of varying street and weather conditions or freeway control measures. Simulation results for realistic model parameters are in good agreement with the diverse non-linear dynamical phenomena observed in freeway traffic.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html and http://www.theo2.physik.uni-stuttgart.de/treiber.htm

Statistical Physics of Vehicular Traffic and Some Related Systems

In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the way the vehicles influence each others' movement. Therefore, vehicular traffic, modeled as a system of interacting "particles" driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called "particle-hopping" models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata.Comment: 170 pages, Latex, figures include