Saturation in a Makovian Parking Process

We consider Z as an infinite lattice street where cars of integer length m.1 can park. The parking process is described by a 0.1 interacting particle system such that a site z.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 ., 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 Z2 is also investigated.