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Where should you park your car? The $\frac{1}{2}$ rule

Where should you park your car? The $\frac{1}{2}$ rule

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 …