Wireless Scheduling with Partial Channel State Information: Large Deviations and Optimality

TL;DR

This paper develops a new scheduling algorithm, Max-Exp, for multi-flow systems with partial channel information, achieving optimal queue overflow decay rates and providing novel large deviations analysis techniques.

Contribution

Introduction of Max-Exp, a joint subset-sampling and scheduling algorithm that optimally manages queues with partial channel information, and development of new large deviations results for such systems.

Findings

Max-Exp achieves the best exponential decay rate of queue overflow among algorithms with partial info.

When no channel info is available, Max-Exp reduces to serving the longest queue, which is large-deviations optimal.

Novel analytical techniques for partial state large deviations are introduced, applicable beyond this context.

Abstract

We consider a server serving a time-slotted queued system of multiple packet-based flows, with exogenous packet arrivals and time-varying service rates. At each time, the server can observe instantaneous service rates for only a subset of flows (from within a fixed collection of observable subsets) before scheduling a flow in the subset for service. We are interested in queue-length aware scheduling to keep the queues short, and develop scheduling algorithms that use only partial service rate information from subsets of channels to minimize the likelihood of queue overflow in the system. Specifically, we present a new joint subset-sampling and scheduling algorithm called Max-Exp that uses only the current queue lengths to pick a subset of flows, and subsequently schedules a flow using the Exponential rule. When the collection of observable subsets is disjoint, we show that Max-Exp achieves the best exponential decay rate, among all scheduling algorithms using partial information, of the tail of the longest queue in the system. Towards this, we employ novel analytical techniques for studying the performance of scheduling algorithms using partial state, which may be of independent interest. These include new sample-path large deviations results for processes obtained by non-random, predictable sampling of sequences of independent and identically distributed random variables. A consequence of these results is that scheduling with partial state information yields a rate function significantly different from scheduling with full channel information. In the special case when the observable subsets are singleton flows, i.e., when there is effectively no a priori channel-state information, Max-Exp reduces to simply serving the flow with the longest queue; thus, our results show that to always serve the longest queue in the absence of any channel-state information is large-deviations optimal.