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Under an average delay constraint, we investigate the energy-efficient scheduling problem in multi-access wireless sensor networks. With the objective to minimize the transmission energy cost under average packet delay constraint, we formulate the problem as a constrained stochastic dynamic programming problem, and compute the constrained optimal policies. Superior to the existing strategies, the proposed scheduling does not require any noncausal information. It determines the scheduled sensor node as well as the transmission duration of the scheduled packet only by current backlogs at the sensor nodes. We also present the simulation results to analyze the proposed scheduling for different transmission scenarios.