Where should you park your car? The 1 2 rule
P L Krapivsky, S Redner · Journal of Statistical Mechanics Theory and Experiment · 2020
Abstract We investigate parking in a one-dimensional lot, where cars enter at a rate λ 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 τL , where τ 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 τL . When all drivers use this strategy, the probability to park at the best available spot is maximal when τ = 1 2 , and parking at the best available spot occurs with probability 1 4 .