Discretization of the parking problem

The present work consider a natural discretization of Rényi’s so-called “parking problem”. Let l, n, i be integers satisfying l ≥ 2, n ≥ 0 and 0 ≤ i ≤ n − l. We place an open interval (i, i + l) in the segment [0, n] with i being a random variable taking values 0, 1, 2,...,n − l with equal probability for all n ≥ l. If n