Most likely parking outcome under alternative boundary conditions

Determine the most likely outcome permutation of the probabilistic parking process under the periodic or closed boundary conditions described in the paper.

Background

The paper proposes two boundary conditions not treated in its main analysis: periodic boundary conditions, in which the probabilistic parking process runs on a cycle, and closed boundary conditions, in which a car attempting to leave the finite interval remains in place. The authors note that determining the distribution of the outcome permutation under these boundary conditions is of interest. They explicitly identify as unresolved which parking outcome is most likely.