Some generalizations of “parking” problem

Abstract

In the original Renyi statement of the “parking” problem open intervals of unit length fill a segment of large size. The asymptotic behaviour of the mean of the number of placed intervals is studied. We study two generalizations of “parking” problem. The first generalization is the case where the length of placed intervals is a random value. In this case both the asymptotic behaviour of the mean of the number of placed intervals and the asymptotic behaviour of the mean of the measure of occupied part of large segment are studied. The second generalization is the case where a random position of unit interval is a random variable with not uniform distribution. Two different problems are studied in the second generalization. Refs 5.