Where should you park your car? The12rule

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 = 1/2, and parking at the best available spot occurs with probability 1/4.