On Markov-dependent parking problems

Abstract

We drive a car along a street towards our destination and look for an available parking place without turning around. Each parking place is associated with a loss which decreases with the distance of the parking place from our destination. Assume that the states (empty or filled) of the parking places form a Markov chain. We want to find an optimal parking strategy to minimize the expected loss. A curious example is constructed and two sufficient conditions for the existence of the threshold-type optimal parking strategy are given.