On a single serve queue fed by a scheduled traffic with Pareto perturbation

Abstract

A scheduled arrival process is one in which the arrival is scheduled for time n, but occurs instead at some random time after or before n. The difference between the arrival times and the scheduled times are called perturbations and are iid. We describe here the behavior of a single server queue fed by such traffic in which the processing times are deterministic. A particular focus is on perturbation with Pareto-like tails but with finite mean. We obtain tail approximations for the steady-state workload in both cases where the queue is critically loaded and under a heavy-traffic regime. A key to our approach is our analysis of the tail behavior of a sum of independent Bernoulli random variables with probabilities following a power law with a parameter strictly larger than one.

Keywords: Scheduled traffic, Heavy-tailed distributions, Limit theorems, queueing system, Bernoulli sums