Energy-aware scheduling algorithms for network stability

A key problem in the control of packet-switched data networks is to schedule the data so that the queue sizes remain bounded over time. Scheduling algorithms have been developed in a number of different models that ensure network stability as long as no queue is inherently overloaded. However, this literature typically assumes that each server runs at a fixed maximum speed. Although this is optimal for clearing queue backlogs as fast as possible, it may be suboptimal in terms of energy consumption. Indeed, a lightly loaded server could operate at a lower rate, at least temporarily, to save energy. Within an energy-aware framework, a natural question arises: "What is the minimum energy that is required to keep the network stable?" In this paper, we demonstrate the following results towards answering that question. Starting with the simplest case of a single server in isolation, we consider three types of rate adaptation policies: a heuristic policy, which sets server speed depending on queue size only, and two more complex ones that exhibit a tradeoff between queue size and energy usage. We also present a lower bound on the best such tradeoff that can possibly be achieved. Next, we study a general network environment and investigate two scenarios. In a temporary sessions scenario, where connection paths can rapidly change over time, we propose a combination of the above rate adaptation policies with the standard Farthest-to Go scheduling algorithm. This approach provides stability in the network setting, while using an amount of energy that is within a bounded factor of the optimum. In a permanent sessions scenario, where connection paths are fixed, we examine an analogue of the well-known Weighted Fair Queueing scheduling policy and show how delay bounds are affected under rate adaptation.