On Characterizing the Delay-Performance of Wireless Scheduling Algorithms

In this paper we study the problem of characterizing the delay performance of wireless scheduling algorithms. In wireless networks operated under these wireless scheduling algorithms, there often exists a tight coupling between the service-rate process, the system backlog process, the arrival process and the channel variations. Although one can use sample-path large-deviation techniques to form an estimate of the delay-violation probability under a given offered load, the formulation leads to a multi-dimensional calculus of variations problem that is often very difficult to solve. In this paper, we present a new technique for addressing this complexity issue. Using ideas from the Lyapunov function approach in control theory, this technique maps the complex multi-dimensional calculus of variations problem to a one-dimensional calculus of variations problem, and the latter is often much easier to solve. We believe that this technique can potentially be used to study the delay-performance of a large class of wireless scheduling algorithms.