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

A“scheduled” arrival process is one in which the nth scheduled for time n, but instead occurs at \(n+\xi _n\) , where \(\xi _j\)’s are i.i.d. We describe here behavior of a single server queue fed by such traffic processing times deterministic. A particular focus on perturbations with Pareto-like tails finite mean. obtain tail approximations steady-state workload both cases critically loaded and under heavy-traffic regime. key to our approach analysis sum independent Bernoulli random variables parameters form \(p_n\sim c \,n^{-\alpha }\) as \(n\rightarrow \infty \), \(c>0\) \(\alpha >1\).