Stability Region of Opportunistic Scheduling in Wireless Networks

The stability regions of two opportunistic scheduling policies, i.e., utility-based (UB) scheduling and the channel-rate-based (CRB) scheduling, in wireless networks are discussed, respectively. UB scheduling is a generalized proportional fair scheduling in an unsaturated system, and CRB scheduling is a variant of the UB scheduling. We give the closed-form expression of the stability region of CRB scheduling and a numerical method to obtain the stability region of UB scheduling. Both two scheduling policies are not throughput optimal, and thus, in general, their stability regions are less than the ergodic capacity region. With CRB scheduling, the stability region is a convex hull, whereas with UB scheduling, the stability region is generally even nonconvex and may exhibit some undesirable properties such as decreasing the traffic of one flow leading another flow being unstable and proportionally decreasing the traffic of all flows leading a stable system to be unstable. We further show that, as long as the arrival rate lies inside the ergodic capacity region, we can assign a proper weight to each user, and based on the weighted UB/CRB scheduling policies, the system can be stabilized. Detailed numerical examples and simulations are given to illustrate the stability region of the two policies and validate our analysis.