On a Single Server Queue Fed by a Scheduled Traffic with Pareto PerturbationsVictor F. Araman, Hong Chen, Peter W. Glynn, and Li Xia Queueing Systems, Volume 100, Issue 1 (2022). 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 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 parameters of the form pn ∼ c n−α as n → ∞, for c > 0 and α > 1. |