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An optimal parking problem

Published online by Cambridge University Press:  14 July 2016

Mitsushi Tamari
Mitsushi Tamari*
Affiliation:
Otemon-Gakuin University
*
∗ Postal address: School of Economics, Otemon-Gakuin University, Ai, lbaraki City, Osaka, Japan.
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Abstract

The decision-maker drives a car along a straight highway towards his destination and looks for a parking place. When he finds a parking place, he can either park there and walk the distance to his destination or continue driving. Parking places are assumed to occur in accordance with a Poisson process along the highway. The decision-maker does not know the distance Y to his destination exactly in advance. Only an a priori distribution is assumed for Y and cases of typically important distribution are examined. When we take as loss the distance the decision-maker must walk and wish to minimize the expected loss, the optimal stopping rule and the minimum expected loss are obtained. In Section 3 a generalization to the cases of a non-homogeneous Poisson process and a renewal process is considered.

Keywords

DYNAMIC PROGRAMMINGOLA POLICYOPTIMAL STOPPING PROBLEMMARKOVIAN DECISION PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 4 , December 1982 , pp. 803 - 814
Copyright
Copyright © Applied Probability Trust 1982 

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