System level optimization in wireless networks with uncertain customer arrival rates

Abstract

We consider a system-level approach to interference management in a cellular broadband system operating in an interference-limited and highly dynamic regime, as put forth. Here, base stations in neighboring cells (partially) coordinate their transmission schedules in an attempt to avoid simultaneous transmission to their mutual cell edge. Limits on communication overhead and use of the backhaul require base station coordination to occur at a slower time scale than the arriving customers. Depending on the overhead restrictions, the slower time scale could be on the scale of minutes or even hours. Thus base stations coordinate using only the statistics of customer arrival, while they serve users based on the actual realizations. The central challenge is to properly structure coordination decisions at the slow time scale, as these subsequently restrict the actions of each base station until the next coordination period. A further challenge comes from the fact that over longer coordination intervals, the statistics of the arriving customers, e.g., the load, may themselves vary or be only approximately known. Indeed, we show through simulation that while the approach is effective for a broad range of arriving load, performance rapidly degrades as the variation of the arriving load from the nominal (or assured) arriving load grows. We show this is true even when the variations are neutral, namely when the aggregate load is fixed, but there are local variations. In this paper we show that a two-stage robust optimization framework is a natural way to model two time-scale decision problems. We provide tractable formulations for the base- station coordination problem, and show that our formulation is robust to fluctuations (uncertainties) in the arriving load. This tolerance to load fluctuation also serves to reduce the need for frequent re-optimization across base stations, thus helping minimize the communication overhead required for system level interference reduction. Building in robustness to load variation comes at the potential cost of somewhat degraded performance when variations happen to be very small. Our robust optimization formulations are flexible, allowing us to control the conservatism of the solution. Our simulations show that we can build in robustness without significant degradation of nominal performance.