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We examine various realistic generalizations of the basic cellular automaton model describing traffic flow along a highway. In particular, we introduce a {\em slow-to-start} rule which simulates a possible delay before a car pulls away from…
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion…
Periodicity and relaxation are investigated for the trajectories of the states in one-dimensional finite cellular automata with rule-90 and 150. The time evolutions are described with matrices. Eigenvalue analysis is applied to clarify the…
It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal…
We derive the critical behavior of a CA traffic flow model using an order parameter breaking the symmetry of the jam-free phase. Random braking appears to be the symmetry-breaking field conjugate to the order parameter. For $v_{\max}=2$, we…
We consider the diffusion-advection problem in two simple cellular flow models (often invoked as examples for subdiffusive tracer's motion) and concentrate on the intermediate time range, in which the tracer's motion indeed may show…
The rule 184 fuzzy cellular automaton is regarded as a mathematical model of traffic flow because it contains the two fundamental traffic flow models, the rule 184 cellular automaton and the Burgers equation, as special cases. We show that…
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. We present…
The main motivation of this work is to assess the validity of a LWR traffic flow model to model measurements obtained from trajectory data, and propose extensions of this model to improve it. A formulation for a discrete dynamical system is…
A new cellular automaton (CA) traffic model is presented. The focus is on mechanical restrictions of vehicles realized by limited acceleration and deceleration capabilities. These features are incorporated into the model in order to…
There have been several highway traffic models proposed based on cellular automata. The simplest one is elementary cellular automaton rule 184. We extend this model to city traffic with cellular automata coupled at intersections using only…
The dynamics of affective decision making is considered for an intelligent network composed of agents with different types of memory: long-term and short-term memory. The consideration is based on probabilistic affective decision theory,…
In this paper, we consider a simple cellular automaton with two particles of different speeds that annihilate on contact. Following a previous work by K\r urka et al., we study the asymptotic distribution, starting from a random…
We propose a stochastic model for the intersection of two urban streets. The vehicular traffic at the intersection is controlled by a set of traffic lights which can be operated subject to fix-time as well as traffic adaptive schemes.…
We introduce and study a deterministic lattice model describing the motion of an infinite system of oppositely charged particles under the action of a constant electric field. As an application this model represents a traffic flow of cars…
Traffic flow is a very prominent example of a driven non-equilibrium system. A characteristic phenomenon of traffic dynamics is the spontaneous and abrupt drop of the average velocity on a stretch of road leading to congestion. Such a…
A new kind of cellular automaton (CA) for the study of the dynamics of urban systems is proposed. The state of a cell is not described using a finite set, but by means of continuum variables. A population sector is included, taking into…
We present results on the modeling of on- and off-ramps in cellular automata for traffic flow, especially the Nagel-Schreckenberg model. We study two different types of on-ramps that cause qualitatively the same effects. In a certain…
Cellular automata have turned out to be important tools for the simulation of traffic flow. They are designed for an efficient impletmentation on the computer, but hard to treat analytically. Here we discuss several approaches for an…
Periodicity and relaxation are investigated for the trajectories of the states in cylindrical linear cellular automata. The time evolutions are described with matrices. The eigenvalue analysis is applied to obtain the maximum values of…