Result: Stochastic stability of traffic maps

Title:
Stochastic stability of traffic maps
Authors:
BLANK, Michael
Source:
Nonlinearity (Bristol. Print). 25(12):3389-3408
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 27 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Probabilités et statistiques, Probability and statistics, Théorie des probabilités et processus stochastiques, Probability theory and stochastic processes, Processus particuliers (théorie du renouvellement, processus de renouvellement markoviens, processus semi-markoviens, modèles de la mécanique statistique, applications diverses), Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications), Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Probabilités et statistiques numériques, Numerical methods in probability and statistics, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Chaîne Markov, Markov chain, Cadena Markov, Ecoulement trafic, Traffic flow, Flujo tráfico, Entropie topologique, Topological entropy, Entropía topológica, Espace séquence, Sequence space, Espacio sequencia, Estimation moyenne, Mean estimation, Estimación promedio, Fonction densité, Density function, Función densidad, Mesure invariante, Invariant measure, Medida invariante, Mouvement, Motion, Movimiento, Moyenne, Average, Promedio, Nombre réel, Real number, Número real, Physique mathématique, Mathematical physics, Física matemática, Stabilité stochastique, Stochastic stability, Estabilidad estocástica, Trafic, Traffic, Tráfico, Treillis, Lattice, Enrejado, Véhicule, Vehicle, Vehículo, 06Bxx, 28C10, 60J10, 60K30, 65C40, Séquence réelle, Real sequence
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Institute for Information Transmission Problems, Russian Academy of Science, Russian Federation
ISSN:
0951-7715
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=26755536
Rights:
Copyright 2014 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Theoretical physics
Accession Number:
edscal.26755536
Database:
PASCAL Archive

Further Information

We study the ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using connections to topological Markov chains we obtain nontrivial invariant measures, prove their stochastic stability and calculate the topological entropy. Technically these results in the deterministic setting are related to the construction of measures of maximal entropy via measures uniformly distributed on periodic points of a given period, while in the random setting we construct (spatially) Markov invariant measures directly. In distinction to conventional results the limiting measures in the non-lattice case are non-ergodic. The average velocity of individual 'vehicles' as a function of their density and its stochastic stability is studied as well.