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Today's embedded systems are exposed to variations in load demand due to complex software applications, hardware platforms, and impact of the run-time environments. When these variations are large, and efficiency is required, on-line resource managers may be deployed on the system to help it control its resource usage. An often neglected problem is whether these resource managers are stable, meaning that the resource usage is controlled under all possible scenarios. In this paper we develop mathematical models for the real-time embedded system and we derive conditions which, if satisfied, lead to stable systems. For the developed system models, we also determine bounds on the worst case response times of tasks.