Michael Blank
Ergodic properties of a simple deterministic traffic flow model re(al)visited
(74K, LATeX 2e)
ABSTRACT. We 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.