Optimal Scheduling of Heavy Tailed Traffic via Shape Parameter Estimation

In this paper we present a new scheduler, the alpha-scheduler, which performs better on heavy tailed traffic than the foreground-background (FB) scheduler which is known to be optimal in scheduling traffic which has unknown characteristics. The alpha-scheduler is able to provide a closer approximation to the shortest remaining processing time (SRPT) scheduler which is known to provide optimal scheduling in the case when the length of the packets to be scheduled is known. We are able to improve our alpha-scheduler SRPT approximation by basing our expected remaining processing time on an estimate of the shape parameter, alpha, from the standard heavy tailed Pareto complementary probability distribution function, P[X>t]=ct^-alpha. We show that even using the standard sliding window least mean square estimator our scheduler exhibits improved performance over the FB scheduler. The particular scheduling problem we investigate in detail concerns the servicing of a number of ingress flows being fed by heavy tailed distributions. Each flow is characterized as having a distinct shape parameter which may change (slowly) over time. We report on numerical experiments in which we schedule generated samples with the perfect knowledge of {alpha_i } and experiments in which we attempt to use our Pareto shape parameter estimation methods