From Sleeping to Stockpiling: Energy Conservation via Stochastic Scheduling in Wireless Networks.

Abstract

Motivated by the need to conserve energy in wireless networks, we study three stochastic dynamic scheduling problems.

In the first problem, we consider a wireless sensor node that can turn its radio off for fixed durations of time in order to conserve energy. We formulate finite horizon expected cost and infinite horizon average expected cost problems to model the fundamental tradeoff between packet delay and energy consumption. Through analysis of the dynamic programming equations, we derive structural results on the optimal policies for both formulations. For the infinite horizon problem, we identify a threshold decision rule to determine the optimal control action when the queue is empty.

In the second problem, we consider a sensor node with an inaccurate timer in the ultra-low power sleep mode. The loss in timing accuracy in the sleep mode can result in unnecessary energy consumption from two unsynchronized devices trying to communicate. We develop a novel method for the node to calibrate its timer: occasionally waking up to measure the ambient temperature, upon which the timer speed depends. The objective is to dynamically schedule a limited number of temperature measurements in a manner most useful to improving the accuracy of the timer. We formulate optimization problems with both continuous and discrete underlying time scales, and implement a numerical solution to an equivalent reduction of the second formulation.

In the third problem, we consider a single source transmitting data to one or more receivers over a shared wireless channel. Each receiver has a buffer to store received packets before they are drained. The transmitter's goal is to minimize total power consumption by exploiting the temporal and spatial variation of the channel, while preventing the receivers' buffers from emptying. In the case of a single receiver, we show that modified base-stock and finite generalized base-stock policies are optimal when the power-rate curves are linear and piecewise-linear convex, respectively. We also present the sequences of critical numbers that complete the characterizations of the optimal policies when additional technical conditions are satisfied. We then analyze the structure of the optimal policy for the case of two receivers.