Switching Constrained Max-Weight Scheduling for Wireless Networks

We consider the wireless scheduling problem of jointly activating/de-activating base-stations and (opportunistically) scheduling from among the active base stations. Such systems are of increasing relevance in emerging wireless networks with dense overlapping coverage, where it suffices for only a (time-varying) subset of the base-stations to be active at any given time to satisfy traffic demands. In addition to queue stability (to ensure that traffic demands are met), we focus on optimizing for costs arising due to activating base-stations (switching base-station state between active/inactive), and maintaining activation (these costs arising due to energy consumption).We propose two algorithms–LASS-Static and LASS-Dynamic (LASS: Learning Aided Switching and Scheduling), both of which are explore-exploit policies for base-station switching and channel scheduling. In our setting, the switching action consists of two key decisions: when to switch, and what base-station activation state to switch to. Both LASS-Static and LASS-Dynamic determine the resulting switching state (i.e. ‘what to switch to as well as the schedule using current queue-lengths and (estimated) channel states. The crucial difference is in ‘when to switch’–LASS-Static determines these statically (motivated by an epsilon-greedy bandit approach), whereas LASS-Dynamic does so using current queue-lengths (thus correlating switching times, switching states and schedules). For either algorithm, existing Lyapunov-based techniques fail to establish stability, as the switching state dynamics correlate the base-station activation decisions with the channel evolution over time. Using novel drift based techniques, in this paper we derive stability, and provide explicit bounds on the expected cost and queue lengths for both algorithms. Furthermore, we show that adaptively selecting switching times in LASS-Dynamic results in an improved upper-tail of queue lengths compared to LASS-Static.