  We apply the statistical mechanical approach based on the ``flat'' measure
proposed by Edwards and coworkers to the parking lot model, a model that
reproduces the main features of the phenomenology of vibrated granular
materials. We first build the flat measure for the case of vanishingly small
tapping strength and then generalize the approach to finite tapping strengths
by introducing a new ``thermodynamic'' parameter, the available volume for
particle insertion, in addition to the particle density. This description is
able to take into account the various memory effects observed in vibrated
granular media. Although not exact, the approach gives a good description of
the behavior of the parking-lot model in the regime of slow compaction.
