  A "scheduled" arrival process is one in which the n th arrival is scheduled
for time n, but instead occurs at a different time. The difference between the
scheduled time and the arrival time is called the perturbation. The sequence of
perturbations is assumed to be 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 success probability following a
power law with parameter strictly larger than 1.
