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In this paper, we investigate the problem of the lifetime maximization in a wireless sensor network under the constraint of the target end-to-end transmission success probability, by adopting a cross-layer strategy that considers both physical layer (i.e., power control) and network layer (i.e., routing protocol) jointly. We first present the optimal power allocation algorithm for a given routing path. This allocation determines per-hop success probability for each link along the path in order to minimize the total energy consumption while guaranteeing the reliability constraint. Then, we develop an optimal routing algorithm that maximizes the network lifetime and a heuristic algorithm that has lower and tractable complexity. Simulation results reveal that a trade-off relation exists between the network lifetime maximization and the reliability constraint, and that the proposed routing algorithm combined with the optimal power allocation algorithm increases the network lifetime significantly.