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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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References

Chow, Y. S., Robbins, H., and Siegmund, D. (1971). Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, New York.Google Scholar
DeGroot, M. H. (1970). Optimal Statistical Decisions. McGraw-Hill, New York.Google Scholar
Hsiau, S.-R., and Yang, J.-R. (2002). Selecting the last success in Markov-dependent trials. J. Appl. Prob. 39, 271–281.Google Scholar
Ross, S. (1983). Introduction to Stochastic Dynamic Programming. Academic Press, New York.Google Scholar
Sakaguchi, M., and Tamaki, M. (1982). On the optimal parking problem in which spaces appear randomly. Bull. Inf. Cybernet. 20, 1–10.Google Scholar
Tamaki, M. (1982). An optimal parking problem. J. Appl. Prob. 19, 803–814.Google Scholar
Tamaki, M. (1985). Adaptive approach to some stopping problems. J. Appl. Prob. 22, 644–652.Google Scholar
Tamaki, M. (1988). Optimal stopping in the parking problem with U-turn. J. Appl. Prob. 25, 363–374.Google Scholar
Woodroofe, M., Lerche, R., and Keener, R. (1994). A generalized parking problem. In Statistical Decision Theory and Related Topics, V (West Lafayette, IN, 1992), Springer, New York, pp. 523–532.Google Scholar