Throughput optimality of delay-driven MaxWeight scheduler for a wireless system with flow dynamics

We consider a wireless downlink shared by a dynamic population of flows. The flows of random size (bits) arrive at the base station at random times, and leave when they have been completely transmitted. The transmission rate supported by the wireless channel of each flow while the flow awaits transmission varies randomly over time and is independent of that of the other flows. The scheduling problem in this context is to select a flow for transmission based on the current system state (e.g., backlogs, wait times, and channel states of the contending flows). It has recently been shown that for such a system, the well-known (backlog-driven) MaxWeight scheduler is not throughput optimal. That is to say, the MaxWeight scheduler will not stabilize a given system even though it is possible to construct a stabilizing scheduler using the various flow- and channel-related statistics. However, in this paper, we show that the delay-driven MaxWeight scheduler is, nevertheless, throughput optimal for such a system. The delay-driven MaxWeight, like its backlog-driven version, does not require any knowledge of the flow- or channel-related statistics.