Rate allocation and network lifetime problems for wireless sensor networks
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In this paper, we consider an overarching problem that encompasses both performance metrics. In particular, we study the network capacity problem under a given network lifetime requirement. Specifically, for a wireless sensor network where each node is provisioned with an initial energy, if all nodes are required to live up to a certain lifetime criterion, 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. Existing System: Our focus in this paper is on the communication energy consumption. A naive approach to the LMM rate allocation problem would be to apply a max-min-like iterative procedure. Under this approach, successive LPs are employed to calculate the maximum rate at each level based on the available energy for the remaining nodes, until all nodes use up their energy. As it turns out, for the LMM rate allocation problem, any iterative rate allocation approach that requires energy reservation at each iteration is incorrect the LMM rate allocation problem, there usually exist non-unique flow routing solutions corresponding to the same rate allocation at each level. Consequently, each of these flow routing solutions will yield different available energy levels on the remaining nodes for future iterations and so forth, leading to a different rate allocation vector, which usually does not coincide with the optimal LMM rate allocation vector.