Maximizing network utilization with max-min fairness in wireless sensor networks

The state-of-the-art for optimal data-gathering in wireless sensor networks is to use additive increase algorithms to achieve fair rate allocation while implicity trying to maximize network utilization. For the quantification of the problem we present a receiver capacity model to capture the interference existing in a wireless network. We also provide empirical evidence to motivate the applicability of this model to a real CSMA based wireless network. Using this model, we explicitly formulate the problem of maximizing the network utilization subject to a max-min fair rate allocation constraint in the form of two coupled linear programs. We first show how the max-min rate can be computed efficiently for a given network. We then adopt a dual-based approach to maximize the network utilization. The analysis of the dual shows the sub-optimality of previously proposed additive increase algorithms with respect to bandwidth efficiency. Although in theory a dual-based sub-gradient search algorithm can take a long time to converge, we find empirically that setting all shadow prices to an equal and small constant value, results in near-optimal solutions within one iteration (within 2% of the optimum in 99.65% of the cases). This results in a fast heuristic distributed algorithm that has a nice intuitive explanation-rates are allocated sequentially after rank ordering flows based on the number of downstream receivers whose bandwidth they consume. We also investigate the near optimal performance of this heuristic by comparing the rank ordering of the source rates obtained from the heuristic to the solutions obtained by solving the linear program.