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This is a study of localised structures in one-dimensional cellular automata, with the elementary cellular automaton Rule 54 as a guiding example. A formalism for particles on a periodic background is derived, applicable to all…

Cellular Automata and Lattice Gases · Physics 2019-07-16 Markus Redeker

We investigate a one-dimensional system of $N$ particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the $N$ particles do…

Mathematical Physics · Physics 2018-03-14 Joceline Lega , Sunder Sethuraman , Alexander L Young

We consider the Follow-The-Leader approximation of the Aw-Rascle-Zhang (ARZ) model for traffic flow in a multi-population formulation. We prove rigorous convergence to weak solutions of the ARZ system in the many particle limit in presence…

Analysis of PDEs · Mathematics 2016-08-16 M. Di Francesco , S. Fagioli , M. D. Rosini

The aim of this work is to introduce a two-dimensional macroscopic traffic model for multiple populations of vehicles. Starting from the paper [20], where a two-dimensional model for a single class of vehicles is proposed, we extend the…

Numerical Analysis · Mathematics 2020-11-04 Caterina Balzotti , Simone Göttlich

In this paper, a particle method is used to approximate the solutions of a "fluid-like" macroscopic traffic flow model for automated vehicles. It is shown that this method preserves certain differential inequalities that hold for the…

Numerical Analysis · Mathematics 2024-01-23 George Titakis , Iasson Karafyllis , Dionysis Theodosis , Ioannis Papamichail , Markos Papageorgiou

Modeling and control of agent-based models is twice cursed by the dimensionality of the problem, as both the number of agents and their state space dimension can be large. Even though the computational barrier posed by a large ensemble of…

Optimization and Control · Mathematics 2025-07-16 Giacomo Albi , Sara Bicego , Dante Kalise

We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. We demonstrate how…

Cellular Automata and Lattice Gases · Physics 2023-12-18 Henryk Fukś , Andrew Skelton

A two-dimensional cellular automaton model of traffic flow with open boundaries are investigated by computer simulations. The outflow of cars from the system and the average velocity are investigated. The time sequences of the outflow and…

adap-org · Physics 2009-10-28 Shin-ichi Tadaki

This paper studies the optimal solution of the classical problem of detecting the location of multiple image occurrences in a two-dimensional, noisy measurement. Assuming the image occurrences do not overlap, we formulate this task as a…

Image and Video Processing · Electrical Eng. & Systems 2024-07-31 Simon Anuk , Tamir Bendory , Amichai Painsky

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…

Cellular Automata and Lattice Gases · Physics 2007-05-23 Janne V. Kujala , Tuomas J. Lukka

The one-parameter two-dimensional cellular automaton with the Margolus neighbourhood is analyzed based on the considering the projection of the stochastic movements of a single particle. Introducing the auxiliary random variable associated…

Probability · Mathematics 2023-04-18 Anton Kulagin , Alexander Shapovalov

In recent years the modelling of traffic flow using methods from statistical physics, especially cellular automata models have allowed simulations of large traffic networks faster than real time. In this paper, we study a probabilistic…

Soft Condensed Matter · Physics 2007-05-23 M. E. Larraga , J. A. del Rio

Summary: Traffic light coordination is a complex problem. In this paper, we extend previous work on an abstract model of city traffic to allow for multiple street intersections. We test a self-organizing method in our model, showing that it…

Adaptation and Self-Organizing Systems · Physics 2011-04-15 Carlos Gershenson , David A. Rosenblueth

Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…

Cellular Automata and Lattice Gases · Physics 2007-05-23 Andres Moreira , Nino Boccara , Eric Goles

We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g. cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion…

Statistical Mechanics · Physics 2015-06-25 M. R. Evans , N. Rajewsky , E. R. Speer

A traffic model on an open one-dimensional lattice is considered. At any discrete time moment, with prescribed probability, a particle arrives to the leftmost cell of the lattice, and, with prescribed probability, the arriving particle…

Probability · Mathematics 2024-11-20 Marina V. Yashina , Alexander G. Tatashev

Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models,…

Physics and Society · Physics 2009-11-13 Dirk Helbing , Mehdi Moussaid

It is shown that a variety of deterministic cellular automaton models of highway traffic flow obey a variational principle which states that, for a given car density, the average car flow is a non-decreasing function of time. This result is…

Disordered Systems and Neural Networks · Physics 2016-12-21 Nino Boccara

This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the…

adap-org · Physics 2009-10-30 Nino Boccara , Henryk Fuks

In this work we consider the problem of finding the minimum-weight loop cover of an undirected graph. This combinatorial optimization problem is called 2-matching and can be seen as a relaxation of the traveling salesman problem since one…

Disordered Systems and Neural Networks · Physics 2018-08-28 Sergio Caracciolo , Andrea Di Gioacchino , Enrico M. Malatesta