Optimal stopping in the parking problem with U-turn

Optimal stopping in the parking problem with U-turn

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Article ID: iaor1988617
Country: Israel
Volume: 25
Issue: 2
Start Page Number: 363
End Page Number: 374
Publication Date: Jun 1988
Journal: Journal of Applied Probability
Authors:
Keywords: programming: dynamic
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 rë(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.

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