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With the current state of development in demand response (DR) programs in smart grid systems, there have been great demands for automated energy scheduling for residential customers. Recently, energy scheduling in smart grids have focused on the minimization of electricity bills, the reduction of the peak demand, and the maximization of user convenience. Thus, a user convenience model is proposed under the consideration of user waiting times, which is a nonconvex problem. Therefore, the nonconvex is reformulated as convex to guarantee optimal solutions. Moreover, mathematical formulations for DR optimization are derived based on the reformulated convex problem. In addition, two types of pricing policies for electricity bills are designed in the mathematical formulations, i.e., real-time pricing policy and progressive policy. With real-time pricing policy, convexity is guaranteed whereas progressive policy …