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We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to…
We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to…
We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to…
Pedestrian dynamics exhibits various collective phenomena. Here we study bidirectional pedestrian flow in a floor field cellular automaton model. Under certain conditions, lane formation is observed. Although it has often been studied…
Traffic models based on cellular automata have high computational efficiency because of their simplicity in describing unrealistic vehicular behavior and the versatility of cellular automata to be implemented on parallel processing. On the…
The density classification task is a famous problem in the theory of cellular automata. It is unsolvable for deterministic automata, but recently solutions for stochastic cellular automata have been found. One of them is a set of stochastic…
We construct a stochastic cellular automata model for the description of vehicular traffic at a roundabout designed at the intersection of two perpendicular streets. The vehicular traffic is controlled by a self-organized scheme in which…
Although traffic simulations with cellular-automata models give meaningful results compared with empirical data, highway traffic requires a more detailed description of the elementary dynamics. Based on recent empirical results we present a…
We present analytical results for first-passage processes in a deterministic one-dimensional cellular automaton (CA) model of traffic flow. Starting at time $t=0$ from a random initial state with car density p, at every time step $t\ge 1$…
A cellular automaton model of traffic flow taking into account velocity anticipation is introduced. The strength of anticipation can be varied which allows to describe different driving schemes. We find phase separation into a free-flow…
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
We investigate a simple multisegment cellular automaton model of traffic flow. With the introduction of segment-dependent deceleration probability, metastable congested states in the intermediate density region emerge, and the initial state…
We propose a stochastic cellular-automaton model for two-lane traffic flow based on the misanthrope process in one dimension. The misanthrope process is a stochastic process allowing for an exact steady-state solution; hence we have an…
We present a new analytical description of the cellular automaton model for single-lane traffic. In contrast to previous approaches we do not use the occupation number of sites as dynamical variable but rather the distance between…
We study the impact of a localized defect in a cellular automaton model for traffic flow which exhibits metastable states and phase separation. The defect is implemented by locally limiting the maximal possible flow through an increase of…
This paper firstly show that a recent model (Tian et al., Transpn. Res. B 71, 138-157, 2015) is not able to well replicate the evolution concavity in traffic flow, i.e. the standard deviation of vehicles increases in a concave/linear way…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open…
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…
We use analytical methods to investigate cellular automata for traffic flow. Two different mean-field approaches are presented, which we call site-oriented and car-oriented, respectively. The car-oriented mean-field theory yields the exact…