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The processing and communication capabilities of the smart grid provide a solid foundation for enhancing its efficiency and reliability. These capabilities allow utility companies to adjust their offerings in a way that encourages consumers to reduce their peak hour consumption, resulting in a more efficient system. In this paper, we propose a method for scheduling a community's power consumption such that it becomes almost flat. Our methodology utilizes distributed schedulers that allocate time slots to soft loads probabilistically based on precalculated and predistributed demand forecast information. This approach requires no communication or coordination between scheduling nodes. Furthermore, the computation performed at each scheduling node is minimal. Obtaining a relatively constant consumption makes it possible to have a relatively constant billing rate and eliminates operational inefficiencies. We also analyze the fairness of our proposed approach, the effect of the possible errors in the demand forecast, and the participation incentives for consumers.