Stochastic stability of traffic maps

被引:2
作者
Blank, Michael [1 ]
机构
[1] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 117901, Russia
基金
俄罗斯基础研究基金会;
关键词
ZERO-RANGE PROCESS; CELLULAR-AUTOMATON; STATIONARY MEASURE; EXCLUSION PROCESS; MODELS; TASEP; FLOW;
D O I
10.1088/0951-7715/25/12/3389
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 nonergodic. The average velocity of individual 'vehicles' as a function of their density and its stochastic stability is studied as well.
引用
收藏
页码:3389 / 3408
页数:20
相关论文
共 27 条
[1]   THE TASEP SPEED PROCESS [J].
Amir, Gideon ;
Angel, Omer ;
Valko, Benedek .
ANNALS OF PROBABILITY, 2011, 39 (04) :1205-1242
[2]   The stationary measure of a 2-type totally asymmetric exclusion process [J].
Angel, O .
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2006, 113 (04) :625-635
[3]  
[Anonymous], METHODS SYMBOLIC DYN
[4]  
[Anonymous], GRADUATE TEXTS MATH
[5]   Invariant measures and convergence properties for cellular automaton 184 and related processes [J].
Belitsky, V ;
Ferrari, PA .
JOURNAL OF STATISTICAL PHYSICS, 2005, 118 (3-4) :589-623
[6]  
Billingsley P., 1965, ERGODIC THEORY INFOR
[7]   Hysteresis phenomenon in deterministic traffic flows [J].
Blank, M .
JOURNAL OF STATISTICAL PHYSICS, 2005, 120 (3-4) :627-658
[8]   Ergodic properties of a simple deterministic traffic flow model [J].
Blank, M .
JOURNAL OF STATISTICAL PHYSICS, 2003, 111 (3-4) :903-930
[9]  
Blank M, 1997, MONOGRAPH AM MATH SO
[10]   Exclusion-type spatially heterogeneous processes in continua [J].
Blank, Michael .
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2011,