The Annals of Applied Probability

Saturation in a Makovian Parking Process

Raúl Gouet and F. Javier López

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 11, Number 4 (2001), 1116-1136.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1015345397

Digital Object Identifier
doi:10.1214/aoap/1015345397

Mathematical Reviews number (MathSciNet)
MR1878292

Zentralblatt MATH identifier
1012.60087

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]

Keywords
Random parking interacting particle systems quasi-stationary distributions

Citation

Gouet, Raúl; López, F. Javier. Saturation in a Makovian Parking Process. Ann. Appl. Probab. 11 (2001), no. 4, 1116--1136. doi:10.1214/aoap/1015345397. https://projecteuclid.org/euclid.aoap/1015345397


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