Robust Analysis for Wireless Sensor Networks under Distance Uncertainty

The distance between nodes in a wireless sensor network (WSN) can be determinant in the effectiveness of many applications. However, in many cases the distance values are subject to uncertainty as they might have been indirectly estimated through signal strength or have changed because of node movement. In this paper we propose optimization models that account for this uncertainty in distance for an important design and operating problem in WSNs, yielding solutions that are insensitive to this uncertainty. We consider the problem of minimizing the energy consumed to transmit a given amount of information through a WSN. We formulate this problem with distance uncertainty using the robust optimization methodology and show that solving for the robust solution is just as difficult as solving the deterministic problem. Our computational results show that as the uncertainty increases a robust solution for this problem provides a significant improvement in worst case performance at the expense of a small loss in optimality when compared to the optimal solution of a fixed scenario. We further investigate the performance of the robust solution in practice and its sensitivity of different problem parameters.