Kernel Density Estimation for Interdeparture Time of GI/G/1 Queues

The departure process of a single queue has been studied since the 1960s. Due to its inherent complexity, closed form solutions for the distribution of the departure process are nearly intractable. In this study, kernel type estimators of the density of interdeparture time in a GI/G/1 queue are studied. Uniform strong consistency of the estimators in a GI/G/1 queue and their rates of convergence are obtained. The stochastic processes are shown to satisfy the strong mixing condition with random instants of sampling. With the analysis presented, we provide a novel analytic tool for studying the departure process in a general queueing model.