Necessary and Sufficient Conditions for Thermal Schedulability of Periodic Real-Time Tasks

With growing need to address the thermal issues in modern processing platforms various performance throttling schemes have been proposed in literature (DVFS, clock gating etcetera). In real-time systems such methods are often unacceptable as they can result into potentially catastrophic deadline misses. As a result real-time scheduling research has been focused in developing algorithms which meet the compute deadline while satisfying power and thermal constraints. Basic bounds that can determine if a set of tasks can be scheduled or not were established in the 70´s based on computation utilization of processing power and no new results have been forthcoming that deal with thermal effect based bounds. In this paper we address the problem of thermal constraint schedulability of tasks and derive necessary and sufficient conditions for thermal feasibility of periodic task sets for a unicore system. We then extend some of these results to multi-coreprocessing environment. We demonstrate the efficacy of our results through extensive simulations.