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We investigate the problem of lifetime maximization in a wireless sensor network under the constraint of target end-to-end transmission success probability, by adopting a cross-layer strategy that considers physical layer (i.e., power control), MAC layer (i.e., ARQ control) and network layer (i.e., routing protocol) jointly. We first present a near-optimal retry limit allocation algorithm for a given routing path. This allocation determines the 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 and power control algorithm that maximizes the network lifetime while keeping the network stable, and an alternative 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 constraints and that the network lifetime can be increased significantly by employing the proposed algorithms.