Opportunistic schedulers and asymptotic price for fairness

Abstract

We consider the well-known wireless fair opportunistic schedulers (mainly the alpha-fair schedulers) and analyze their price of fairness (PoF). Efficient scheduler, designed from the system perspective, maximizes the sum of accumulated utilities of all the agents, accumulated over several time slots. On the other hand, the fair schedulers deviate from such a schedule to provide a given level of fairness to various customers utilizing the system. This obviously results in a lower (total) accumulated utility. We study this loss, using the well-known performance measure, the price of fairness. Previous studies show that the PoF mostly increases, as the number of agents increases. We have very different results for opportunistic schedulers. We group agents into finite classes, each class having identical utilities and QoS requirements (inspired by wireless cellular networks), to obtain the asymptotic PoF (APoF). This is always below one. Further, in many cases, the PoF actually decreases to zero/negligible value as the number of agents increases. We also consider the case of multiple resources with bounded utilities. We again have zero/small APoF, depending upon the distributions of the utilities and the relative proportions of various classes. We derive closed-form/easily computable expressions for the APoF, using extreme-value theory, center-order statistics and the maximum theorem.