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A "scheduled" arrival process is one in which the n th arrival is scheduledfor time n, but instead occurs at a different time. The difference between thescheduled time and the arrival time is called the perturbation. The sequence ofperturbations is assumed to be iid. We describe here the behavior of a singleserver queue fed by such traffic in which the processing times aredeterministic. A particular focus is on perturbation with Pareto-like tails butwith finite mean. We obtain tail approximations for the steady-state workloadin both cases where the queue is critically loaded and under a heavy-trafficregime. A key to our approach is our analysis of the tail behavior of a sum ofindependent Bernoulli random variables with success probability following apower law with parameter strictly larger than 1.

On a Single Server Queue Fed by a Scheduled Traffic with Pareto Perturbations