The Page-R{\'e}nyi parking process

TL;DR

This paper analyzes the Page-Rényi parking process, proving that the coverage approaches 1-exp(-2) as the interval size grows, and explores a related process on the infinite line.

Contribution

The paper provides a probabilistic proof of the asymptotic coverage and investigates a new variant of the process on the infinite line.

Findings

Coverage converges to 1-exp(-2) for large intervals

New consequences derived from the probabilistic proof

Studied a version of the process on the infinite line

Abstract

In the Page parking (or packing) model on a discrete interval (also known as the discrete R{\'e}nyi packing problem or the unfriendly seating problem), cars of length two successively park uniformly at random on pairs of adjacent places, until only isolated places remain. We give a probabilistic proof of the (known) fact that the proportion of the interval covered by cars goes to 1-exp(-2) , when the length of the interval goes to infinity. We obtain some new consequences, and also study a version of this process defined on the infinite line.