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تسجيل مستخدم جديدWhere Should You Park Your Car? The $frac{1}{2}$ Rule
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We investigate parking in a one-dimensional lot, where cars enter at a rate $lambda$ and each attempts to park close to a target at the origin. Parked cars also depart at rate 1. An entering driver cannot see beyond the parked cars for more desirable open spots. We analyze a class of strategies in which a driver ignores open spots beyond $tau L$, where $tau$ is a risk threshold and $L$ is the location of the most distant parked car, and attempts to park at the first available spot encountered closer than $tau L$. When all drivers use this strategy, the probability to park at the best available spot is maximal when $tau=frac{1}{2}$, and parking at the best available spot occurs with probability $frac{1}{4}$.
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