Limiting Properties of Overloaded Multiuser Wireless Systems With Throughput-Optimal Scheduling

Throughput-optimal scheduling has been widely discussed due to its capability to stabilize single-hop multiuser wireless systems if possible. However, most of the previous discussions focused on the underloaded scenario, i.e., the arrival rate lies inside the achievable rate region. The behavior of throughput-optimal scheduling in overloaded multiuser wireless systems is the focus of this paper. We first show that, with the infinite buffer assumption, although all the queues are unstable, both the average throughput and a function of queue length converge as time evolves. In addition, the average throughput is the solution to a convex optimization problem whose objective is determined by the scheduling algorithm. By investigating the average throughput of two special throughput-optimal scheduling algorithms, i.e., the generalized MaxWeight and Log-Rule, we find that users can be prioritized by tuning the parameters associated with the scheduling algorithm, but the fairness is not likely to be guaranteed and some users may starve. Second, by studying the finite buffer system, we show that whether the buffer is dedicated to each queue or shared among queues has a great impact on the system performance, and the potential user starvation problem can be alleviated by a proper design.