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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…
It is shown that the desire for smooth and comfortable driving is directly responsible for the occurrence of complex spatio-temporal structures (``synchronized traffic'') in highway traffic. This desire goes beyond the avoidance of…
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…
We study the set of strictly periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but they not spatially periodic. This set turns out to be dense for…
While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with…
We analyze the steady-state flow as a function of the initial density for a class of deterministic cellular automata rules (``traffic rules'') with periodic boundary conditions [H. Fuks and N. Boccara, Int. J. Mod. Phys. C 9, 1 (1998)]. We…
A general stochastic traffic cellular automaton (CA) model, which includes slow-to-start effect and driver's perspective, is proposed in this paper. It is shown that this model includes well known traffic CA models such as…
We investigate a cellular automaton (CA) model of traffic on a bi-directional two-lane road. Our model is an extension of the one-lane CA model of {Nagel and Schreckenberg 1992}, modified to account for interactions mediated by passing, and…
In this paper computer simulation results of higher order density correlation for cellular automaton models of traffic flow are presented. The examinations show the jamming transition as a function of both the density and the magnitude of…
We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…
We focus in this work on the study of traffic in open systems using a modified version of an existing cellular automaton model. We demonstrate that the open system is rather different from the closed system in its 'choice' of a unique…
Microscopic traffic models have recently gained considerable importance as a mean of optimising traffic control strategies. Computationally efficient and sufficiently accurate microscopic traffic models have been developed based on the…
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…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…
In this paper a cellular automata model for one-lane traffic flow is presented. A new set of rules is proposed to better capture driver reactions to traffic that are intended to preserve safety on the highway. As a result, drivers behavior…
We study the relation between the average traffic flow and the vehicle density on road networks that we call 2D-traffic fundamental diagram. We show that this diagram presents mainly four phases. We analyze different cases. First, the case…
We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…
We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic…
We study statistical properties of a family of maps acting in the space of integer valued sequences, which model dynamics of simple deterministic traffic flows. We obtain asymptotic (as time goes to infinity) properties of trajectories of…
The cellular automaton model for traffic flow exhibits a jamming transition from a free-flow phase to a congested phase. In the deterministic case this transition corresponds to a critical point with diverging correlation length. In the…