On robust maximum lifetime routing in wireless sensor networks

We consider the maximum lifetime routing problem in wireless sensor networks, which has been formulated as a linear programming problem in the literature (Chang and Tassiulas [1]). The optimal value and optimal solution of this problem provide optimal flows for the network and the corresponding predicted lifetime, respectively. We study the situation when there is uncertainty in various network parameters (available energy and energy depletion rates). We show that for specific, yet typical, network topologies the actual lifetime will reach the predicted value with a probability that converges to zero as the number of nodes grows large. We develop a series of alternative robust problem formulations, ranging from worst-case to optimistic. A set of parameters enable the tuning of the conservatism of the formulation to obtain network flows with a desirably high probability that the corresponding lifetime prediction will be achieved. We establish a number of properties for the robust network flows and provide an illustrative set of numerical results to highlight the trade-off between predicted lifetime and the probability it is achieved.