Per-site occupancy in the discrete parking problem
Statistics & Probability Letters , Volume 120 p. 141- 146
We consider the classical discrete parking problem, in which cars arrive uniformly at random on any two adjacent sites out of n sites on a line. An arriving car parks if there is no overlap with previously parked cars, and leaves otherwise. This process continues until there is no more space available for cars to park, at which point we may compute the jamming density En/n, which represents the expected fraction of occupied sites. We extend the classical results by not just considering the total expected number of cars parked, but also the probability of each site being occupied by a car. This we then use to provide an alternative derivation of the jamming density.