On a single server queue fed by scheduled traffic with Pareto perturbations

Abstract

A“scheduled” arrival process is one in which the nth arrival is scheduled for time n, but instead occurs at n+ ξn , where the ξj’s are i.i.d. 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 perturbations 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 parameters of the form pn∼cn-α as n→ ∞, for c> 0 and α> 1. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.