A continuous version of the selfish parking problem

The work is devoted to the study of a new model of random filling of a segment of large length with intervals of smaller length. A new formulation of the problem is considered. We study a model in which unit intervals are placed on a segment only if the segment being filled has a length of at least 2. In this case, the position of the placed interval is subject to a uniform distribution law. The paper investigates the behavior of the average number of placed intervals depending on the length of the filled segment. An exact expression is obtained for the analog of the Renyi constant.