Ergodic properties of a simple deterministic traffic flow model re(al)visited

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dc.creatorBlank, Michael
dc.date2002-06-19
dc.date.accessioned2026-07-07T04:49:13Z
dc.date.available2026-07-07T04:49:13Z
dc.descriptionWe study statistical properties of a family of maps acting in the space of integer valued sequences, which model dynamics of simple deterministic traffic flows. We obtain asymptotic (as time goes to infinity) properties of trajectories of those maps corresponding to arbitrary initial configurations in terms of statistics of densities of various patterns and describe weak attractors of these systems and the rate of convergence to them. Previously only the so called regular initial configurations (having a density with only finite fluctuations of partial sums around it) in the case of a slow particles model (with the maximal velocity 1) have been studied rigorously. Applying ideas borrowed from substitution dynamics we are able to reduce the analysis of the traffic flow models corresponding to the multi-lane traffic and to the flow with fast particles (with velocities greater than 1) to the simplest case of the flow with the one-lane traffic and slow particles, where the crucial technical step is the derivation of the exact life-time for a given cluster of particles. Applications to the optimal redirection of the multi-lane traffic flow are discussed as well.
dc.description20 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0206194
dc.identifierhttp://arxiv.org/abs/math/0206194
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64340
dc.subjectDynamical Systems
dc.subjectMathematical Physics
dc.subjectProbability
dc.titleErgodic properties of a simple deterministic traffic flow model re(al)visited
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