Asymptotic normality in a discrete analog of the parking problem

In this article, the authors study the behavior of the central moments of higher orders in a discrete version of the “parking problem”. For these moments, asymptotic behavior is obtained when the length of the filled segment increases indefinitely. This made it possible to prove the asymptotic normality of the total length of the allocated intervals of length $ l $ on an interval of length $ n $ for any fixed $ l \ge 2 $, when $ n $ increases unboundedly.