1,995 research outputs found
A stochastic cellular automaton model for traffic flow with multiple metastable states
A new stochastic cellular automaton (CA) model of traffic flow, which
includes slow-to-start effects and a driver's perspective, is proposed by
extending the Burgers CA and the Nagel-Schreckenberg CA model. The flow-density
relation of this model shows multiple metastable branches near the transition
density from free to congested traffic, which form a wide scattering area in
the fundamental diagram. The stability of these branches and their velocity
distributions are explicitly studied by numerical simulations.Comment: 11 pages, 20 figures, submitted for publicatio
Analytical Studies on a Modified Nagel-Schreckenberg Model with the Fukui-Ishibashi Acceleration Rule
We propose and study a one-dimensional traffic flow cellular automaton model
of high-speed vehicles with the Fukui-Ishibashi-type (FI) acceleration rule for
all cars, and the Nagel-Schreckenberg-type (NS) stochastic delay mechanism. By
using the car-oriented mean field theory, we obtain analytically the
fundamental diagrams of the average speed and vehicle flux depending on the
vehicle density and stochastic delay probability. Our theoretical results,
which may contribute to the exact analytical theory of the NS model, are in
excellent agreement with numerical simulations.Comment: 3 pages previous; now 4 pages 2 eps figure
Cellular Automata Models of Road Traffic
In this paper, we give an elaborate and understandable review of traffic
cellular automata (TCA) models, which are a class of computationally efficient
microscopic traffic flow models. TCA models arise from the physics discipline
of statistical mechanics, having the goal of reproducing the correct
macroscopic behaviour based on a minimal description of microscopic
interactions. After giving an overview of cellular automata (CA) models, their
background and physical setup, we introduce the mathematical notations, show
how to perform measurements on a TCA model's lattice of cells, as well as how
to convert these quantities into real-world units and vice versa. The majority
of this paper then relays an extensive account of the behavioural aspects of
several TCA models encountered in literature. Already, several reviews of TCA
models exist, but none of them consider all the models exclusively from the
behavioural point of view. In this respect, our overview fills this void, as it
focusses on the behaviour of the TCA models, by means of time-space and
phase-space diagrams, and histograms showing the distributions of vehicles'
speeds, space, and time gaps. In the report, we subsequently give a concise
overview of TCA models that are employed in a multi-lane setting, and some of
the TCA models used to describe city traffic as a two-dimensional grid of
cells, or as a road network with explicitly modelled intersections. The final
part of the paper illustrates some of the more common analytical approximations
to single-cell TCA models.Comment: Accepted for publication in "Physics Reports". A version of this
paper with high-quality images can be found at: http://phdsven.dyns.cx (go to
"Papers written"
Collective traffic-like movement of ants on a trail: dynamical phases and phase transitions
The traffic-like collective movement of ants on a trail can be described by a
stochastic cellular automaton model. We have earlier investigated its unusual
flow-density relation by using various mean field approximations and computer
simulations. In this paper, we study the model following an alternative
approach based on the analogy with the zero range process, which is one of the
few known exactly solvable stochastic dynamical models. We show that our theory
can quantitatively account for the unusual non-monotonic dependence of the
average speed of the ants on their density for finite lattices with periodic
boundary conditions. Moreover, we argue that the model exhibits a continuous
phase transition at the critial density only in a limiting case. Furthermore,
we investigate the phase diagram of the model by replacing the periodic
boundary conditions by open boundary conditions.Comment: 8 pages, 6 figure
Non-concave fundamental diagrams and phase transitions in a stochastic traffic cellular automaton
Within the class of stochastic cellular automata models of traffic flows, we
look at the velocity dependent randomization variant (VDR-TCA) whose parameters
take on a specific set of extreme values. These initial conditions lead us to
the discovery of the emergence of four distinct phases. Studying the
transitions between these phases, allows us to establish a rigorous
classification based on their tempo-spatial behavioral characteristics. As a
result from the system's complex dynamics, its flow-density relation exhibits a
non-concave region in which forward propagating density waves are encountered.
All four phases furthermore share the common property that moving vehicles can
never increase their speed once the system has settled into an equilibrium
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