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The elastic task model is a powerful model for adapting periodic real-time systems in the presence of uncertainty. This work generalizes the existing elastic scheduling approach in several directions. First, it presents a general framework, which formulates a trade-off between task schedulability and a specific performance metric as an optimization problem. Such a framework allows real-time systems under overloads to graciously adapt by adjusting their performance level. Second, it is shown in this work that the well-known task compression algorithm in fact solves a quadratic programming problem that seeks to minimize the sum of the squared deviation of a task's utilization from initial desired utilization. This finding indicates that the task compression algorithm may be applied to efficiently solve other similar types of problems that often arise in real-time applications. In particular, an iterative approach is proposed to solve the period selection problem for real-time tasks with deadlines less than respective periods. Further, the framework is adapted to solve the deadline selection problem, which is useful in some control systems with fixed periods.