Where should you park your car? The 12 rule. (14th July 2020)

• Record Type: Journal Article
• Authors: Krapivsky, P L; Redner, S
• Is Part Of: Journal of statistical mechanics. (2020:Jul.)
• Publication Date: 2020-07-14
• Subjects: traffic and crowd dynamics -- stochastic processes -- transport properties; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ab96b7
• Languages: English
• ISSNs: 1742-5468

Abstract

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 .