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On Markov-dependent parking problems

Part of: Stochastic processes Sequential methods

Published online by Cambridge University Press:  14 July 2016

Jiing-Ru Yang  and
Shoou-Ren Hsiau
Jiing-Ru Yang*
Affiliation:
National Changhua University of Education
Shoou-Ren Hsiau*
Affiliation:
National Changhua University of Education
*
∗ Postal address: Department of Mathematics, National Changhua University of Education, Changhua, Taiwan 50058, R.O.C.
∗ Postal address: Department of Mathematics, National Changhua University of Education, Changhua, Taiwan 50058, R.O.C.
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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.

Keywords

Markov dependentparking problemoptimal stoppingbackward induction

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 62L15: Optimal stopping
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 2 , June 2004 , pp. 579 - 586
Copyright
Copyright © Applied Probability Trust 2004 

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