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The hierarchical architecture has been proven effective for solving the scalability problems in large-scale ad hoc networks. The stability of the hierarchical architecture is a key factor in determining the network performance. Although many solutions have been proposed to construct stable clusters, the maximum stability achievable in the mobile environments is still unknown. In this paper, the authors define three metrics to measure the network stability: the cluster lifetime, the inter-cluster link lifetime, and the end-to-end path lifetime. They model and analyze the maximum of these lifetimes under the constraint of random node mobility.
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