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Erschienen in:
20.01.2022
On a single server queue fed by scheduled traffic with Pareto perturbations
Erschienen in: Queueing Systems | Ausgabe 1-2/2022
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Abstract
A“scheduled” arrival process is one in which the nth arrival is scheduled for time n, but instead occurs at \(n+\xi _n\) , where the \(\xi _j\)’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 \(p_n\sim c \,n^{-\alpha }\) as \(n\rightarrow \infty \), for \(c>0\) and \(\alpha >1\).