Opportunistic scheduling policies for wireless systems with short term fairness constraints

We consider a scheduling problem for packet based wireless systems with time-varying channel conditions. Designing scheduling mechanisms that take advantage of time-varying channel conditions, which are different for different users, is necessary to improve the wireless system performance. Such scheduling mechanisms are called opportunistic. In this paper we formulate an opportunistic scheduling problem with short term processor sharing fairness constraints as an optimization problem where short term refers to the time window on which the fairness is guaranteed. In its most general form, this problem cannot be solved analytically. We first solve the above optimization problem for three special cases. We consider the scheduling problem with long term fairness constraints; then we consider the scheduling problem for the shortest possible window under two sets of assumptions namely, one in which users have identically distributed channel conditions and another in which users have independent channel conditions. Observing the form of the corresponding optimal policies, we define a heuristic policy for our original opportunistic scheduling problem with short term fairness constraints. We show via simulation that our heuristic policy attains a good trade-off by guaranteeing short term fairness while achieving high average system throughput. We also illustrate that the optimal opportunistic scheduling policy with long term fairness constraint is in fact unfair in practical scenarios.