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Optimal stopping in the parking problem with U-turn

Published online by Cambridge University Press:  14 July 2016

Mitsushi Tamaki
Mitsushi Tamaki*
Affiliation:
Aichi University
*
∗Postal address: Department of Law and Economics, Aichi University, Miyoshi, Aichi, Japan.
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Abstract

A motorist drives his car toward his destination along a street and looks for a motor pool. Motor pools are assumed to occur independently, with probability p. Observing whether there exists a motor pool or not, the driver decides either to stop (i.e., return to the latest motor pool observed so far and park there) or continue driving. Once the driver stops, he walks the remaining distance to his destination. Let r, 0 < r < 1, be the relative speed of driving a car compared with that on foot. Then the time duration required to reach the destination is measured by r · (distance driven) + (distance on foot) and the objective of the driver is to find a parking policy which minimizes the expected time duration. It is shown that, under an optimal policy, a U-turn never occurs before the destination, but may occur beyond the destination. Moreover, the expected time is computed and some comparisons are made between our problem and the classical parking problem.

Keywords

DYNAMIC PROGRAMMING
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 363 - 374
Copyright
Copyright © Applied Probability Trust 1988 

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References

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