53 research outputs found
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
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