A Continuous Version of the Selfish Parking Problem

A new model of the random filling of a segment of large length with intervals of smaller length is studied. A new statement of the problem is considered. A model in which unit intervals are placed on a segment only if the segment being filled has a length of at least 2 is considered. The position of the interval to be placed is subject to a uniform distribution law. The behavior of the average number of intervals placed is studied depending on the length of the segment to be filled. An exact expression is obtained for the analog of Rényi’s constant.