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 $\frac{1}{4}$.

中文翻译：

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你应该把车停在哪里？$\frac{1}{2}$ 规则

我们研究在一维停车场停车，其中汽车以 $\lambda$ 的速度进入，每辆车都试图靠近原点的目标停车。停放的汽车也以速率 1 离开。进入的驾驶员无法看到停放的汽车以外的更理想的开放位置。我们分析了一类策略，其中驾驶员忽略 $\tau L$ 以外的空位，其中 $\tau$ 是风险阈值，$L$ 是最远停放汽车的位置，并尝试在第一个停车遇到的可用点比 $\tau L$ 更近。当所有司机都采用这种策略时，当$\tau=\frac{1}{2}$时，在最佳可用位置停车的概率最大，而在最佳可用位置停车的概率为$\frac{1}{1}{ 4}$。