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This paper addresses the problem of extending the lifetime of a battery-powered mobile host in a client-server wireless network by using task migration and remote processing. This problem is solved by first constructing a stochastic model of the client-server system based on the theory of continuous-time Markovian decision processes. Next the dynamic power management problem with task migration is formulated as a policy optimization problem and solved exactly by using a linear programming approach. Based on the off-line optimal policy derived in this way, an on-line adaptive policy is proposed, which dynamically monitors the channel conditions and the server behavior and adopts a client-side power management policy with task migration that results in optimum energy consumption in the client. Experimental results demonstrate that the proposed method outperforms existing heuristic methods by as much as 35% in terms of the overall energy savings.