Journal ArticleDOI
A cellular automaton model for freeway traffic
Kai Nagel,Michael Schreckenberg +1 more
TLDR
A stochastic discrete automaton model is introduced to simulate freeway traffic and shows a transition from laminar traffic flow to start-stop- waves with increasing vehicle density, as is observed in real freeway traffic.Abstract:
We introduce a stochastic discrete automaton model to simulate freeway traffic. Monte-Carlo simulations of the model show a transition from laminar traffic flow to start-stop- waves with increasing vehicle density, as is observed in real freeway traffic. For special cases analytical results can be obtained.read more
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Journal ArticleDOI
Dynamical pair approximation for cellular automata with shuffle update
David A. Smith,R. Eddie Wilson +1 more
TL;DR: In this article, the random shuffle update method for the asymmetric exclusion process (ASEP) is introduced, and the dynamical pair technique is extended in order to analyse its dynamics.
Journal ArticleDOI
Metric properties of discrete time exclusion type processes in continuum
Michael Blank,Michael Blank +1 more
TL;DR: In this paper, a new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied, and their connections to other statistical quantities, in particular to the particle density (the so called Fundamental Diagram) are analyzed rigorously.
Journal ArticleDOI
Cycle Equivalence of Graph Dynamical Systems
TL;DR: In this article, the authors studied cycle equivalence of GDSs in which the vertex functions are applied sequentially through an update sequence and showed that the number of components in these graphs, denoted as κ(Y) and δ(Y), bound the possible long-term behavior that can be generated by varying the update sequence.
Journal ArticleDOI
Linear and nonlinear stability analysis of a car-following model considering velocity difference of two adjacent lanes
TL;DR: In this paper, an improved optimal velocity model, which considers the velocity difference of two adjacent lanes, is presented, and the stability criterion of the new model is obtained and the neutral stability curves are plotted.
Journal ArticleDOI
A min-plus derivation of the fundamental car-traffic law
TL;DR: From the fundamental law that links the flow to the density of vehicles on the road, the mean speed is derived as an eigenvalue of the min-plus matrix describing the dynamics of the system in the deterministic case and as the Lyapunov exponent of a min- plus stochastic matrix in the Stochastic case.