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A motorist drives his car along a one-way street toward his destination and looks for a parking place. If he finds an unoccupied parking place, he must decide either park there and walk the distance t...o his destination or continue driving expecting to find another opportunity of parking nearer to the destination. Unoccupied parking places are assumed to appear in accordance with a Poisson process along the street. Also the location of the destination is a random variable with a known probability distribution. The objective of the optimal parking problem is to find a parking policy which minimizes the expected time to reach the destination. We derive the optimal parking policy and the minimum expected cost is obtained. Moreover a two-person game version is treated in which the objective of each player is to maximize the probability of being the first to reach the destination common to both players. The equilibrium strategy is derived explicitly.show more
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