Robustness Analysis for Simultaneous Resource Allocation and Route Optimization Problems

This paper presents the robustness analysis for an algorithm that solves simultaneous resource allocation and route optimization problem (SARO). These problems appear in the context of multi-hop routing applications in sensor networks, which require placement of multiple resource nodes and determining routes from each sensor location to a common data destination center via these resource nodes. In [1], we proposed an algorithm based on Maximum Entropy Principle that addressed the determination of locations of these resource nodes and the corresponding multi-hop routing problem such that the total communication cost is minimized. Such placement of resource nodes is sensitive to multiple parameters such as sensor locations, destination center location, communication costs between sensor and resource nodes, between resource nodes, and between resource nodes and destination center. This paper studies the sensitivity of the solution from the algorithm to these parameters. This robustness analysis is necessary since some of these parameters are typically not known precisely, the sensitivity analysis helps the network design by identifying the hierarchy in parameters in terms of how they affect the algorithm solution, and therefore also indicate how precisely these parameters need to be estimated. In this direction, we propose a modification of our algorithm to account for the uncertainty in sensor locations; here a probability distribution of sensor locations instead of their precise locations is assumed to be known. We also present and characterize a phase-transition aspect of the algorithm, where the number of distinct locations of resource nodes increase at certain critical values of annealing variable — a parameter in the algorithm. Simulations are provided that corroborate our analysis and instantiate relative sensitivities between different parameters.