We consider $\mathbb{Z}$ as an infinite lattice street where cars of
integer length $m \geq 1$ can park. The parking process is described by a
0–1 interacting particle system such that a site $z \in \mathbb{Z}$ is
in state 1 whenever a car has its rear end at z and 0 otherwise. Cars
attempt to park after exponential times with parameter $\lambda$, leave after
exponential times with parameter 1 and are not allowed to touch nor overlap. We
define and study a jamming occupation density for this parking process, using
the quasi-stationary distribution of a Markov chain related to the reversible
measure of the particle system. An extension to a strip in $\mathbb{Z}^2$ is
also investigated.
Publié le : 2001-11-14
Classification:
Random parking,
interacting particle systems,
quasi-stationary distributions,
60K35,
60K30
@article{1015345397,
author = {Gouet, Ra\'ul and L\'opez, F. Javier},
title = {Saturation in a Makovian Parking Process},
journal = {Ann. Appl. Probab.},
volume = {11},
number = {2},
year = {2001},
pages = { 1116-1136},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345397}
}
Gouet, Raúl; López, F. Javier. Saturation in a Makovian Parking Process. Ann. Appl. Probab., Tome 11 (2001) no. 2, pp. 1116-1136. http://gdmltest.u-ga.fr/item/1015345397/