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Stability Analysis of Routing Strategies for the Maximum Lifetime Problem in One-Dimensional Ad-Hoc Wireless Networks

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In the paper we discuss solutions of the maximum network lifetime problem in one-dimensional, regular ad-hoc wireless networks. For the problem, nodes of the network generate given amount of data and send it possibly via other nodes to the data collector. To extend the network lifetime the data should be transmitted in such a way, that the energy utilized by the most overloaded node is minimized. We assume, that the nodes use the point-to-point data transmission scheme and the cost of transmission of one unit of data is arbitrary superadditive function of a distance between transmitter and receiver. We show that for the one-dimensional network in which the nodes are evenly distributed on the line and each node generates the same amount of data there exists an equal energy solution of the problem. We treat the amount of data generated by each node and the location of the nodes on the line as the initial parameters of the problem. It is known, that solutions of the problem are very sensitive under change of these parameters. It means, that small change in the value of these parameters can change the optimal transmission graph and the solution. In the paper we analyze stability of obtained equal energy solution under modification of these two sets of parameters.