Robust Maximum Lifetime Routing and Energy Allocation in Wireless Sensor Networks

We consider the maximum lifetime routing problem in wireless sensor networks in two settings: (a) when nodes’ initial energy is given, and (b) when it is subject to optimization. The optimal solution and objective value provide optimal flows and the corresponding predicted lifetime, respectively. We stipulate that there is uncertainty in various network parameters (available energy and energy depletion rates). In setting (a) we show that for specific, yet typical network topologies, the actual network lifetime will reach the predicted value with a probability that converges to zero as the number of nodes grows large. In setting (b) the same result holds for all topologies. We develop a series of robust problem formulations, ranging from pessimistic 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 is achieved. We establish a number of properties for the robust network flows and energy allocations and provide numerical results to highlight the trade-off between predicted lifetime and the probability it is achieved. Further, we analyze an interesting limiting regime of massively deployed sensor networks and essentially solve a continuous version of the problem.