Lifetime Bounds, Optimal Node Distributions and Flow Patterns for Wireless Sensor Networks

In this paper we investigate the expected lifetime and information capacity of a data-gathering wireless sensor network. The information capacity is defined as the maximum amount of data (bits) transferred before the first sensor node death due to energy depletion, while ignoring various signaling overheads, such as MAC and routing. We develop a fluid-flow based computational framework that extends existing approaches, which are based on precise knowledge of the layout/deployment of the network, i.e., exact sensor positions. Our method, on the other hand, computes the expected information capacity for a given distribution of sensor node layout and sensor data rates, rather than any particular instance of sensor deployment. Our flow model assumes a a continuous density of sensor deployment, and is particularly appropriate for sensor environments characterized by highly dense node deployments. This continuous-space flow model is then discretized into grids and solved using a linear programming approach. Numerical studies show that this model produces very accurate results, compared to averaging over results from random instances of deployment, with significantly less computation. We then use our model to determine optimal node distributions for a linear network and the properties of optimal routing that maximizes the lifetime of the network.