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Power efficiency is an important design issue in mobile devices with limited power supplies. In this paper, we study a reward-based packet scheduling problem in wireless environments. We consider a general scenario in which a transmitter communicates with multiple receivers periodically. To guarantee timely transmission of data, each packet is associated with a delay constraint. The periodic data streams have different importance levels, power functions, and levels of data sizes. The more data a transmitter delivers, the more rewards it obtains. Our objective is to develop schemes that selectively transmit data streams of different data sizes at different transmission rates so that the system reward can be maximized under given time and energy constraints. We show that the problem is NP-hard and develop a dynamic programming algorithm for the optimal solution in pseudopolynomial time. A fast polynomial-time heuristic approach based on clustering of states in state space is presented to achieve close approximation. Simulation results demonstrate the effectiveness of the optimal solution and show that the proposed polynomial-time approach can achieve near-optimal results. Both approaches make a significant improvement over other approaches adapted from existing studies at a marginal runtime overhead.