Rate allocation and network lifetime problems for wireless sensor networks

An important performance consideration for wireless sensor networks is the amount of information collected by all the nodes in the network over the course of network lifetime. Since the objective of maximizing the sum of rates of all the nodes in the network can lead to a severe bias in rate allocation among the nodes, we advocate the use of lexicographical max-min (LMM) rate allocation. To calculate the LMM rate allocation vector, we develop a polynomial-time algorithm by exploiting the parametric analysis (PA) technique from linear program (LP), which we call serial LP with Parametric Analysis (SLP-PA). We show that the SLP-PA can be also employed to address the LMM node lifetime problem much more efficiently than a state-of-the-art algorithm proposed in the literature. More important, we show that there exists an elegant duality relationship between the LMM rate allocation problem and the LMM node lifetime problem. Therefore, it is sufficient to solve only one of the two problems. Important insights can be obtained by inferring duality results for the other problem.