Bio: https://www.aub.edu.lb/pages/profile.aspx?memberId=va03&id=1&id=1
Abstract: A scheduled traffic model is one in which customer n is scheduled to arrive at time nh, but actually arrives at time nh + ξ_n, where the ξ_i's are iid. In this talk, we compare the behavior of these arrival models to renewal traffic. We do that by describing the behavior of a single server queue when fed by such traffic in which the processing times are deterministic. In particular, such queue can be stable even at the same time that the queue fed by the time-reversed scheduled traffic model is unstable. When the perturbations have 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. We also discuss functional limit theorems for scheduled traffic models as the ξ_i's become successively more and more heavy-tailed, with limit processes that transition from fractional Brownian motion with H < 1/2 into the realm of Brownian motion as the tail gets heavier.
(Joint work with Peter Glynn)
