On the Minimization of the Instantaneous Temperature for Periodic Real-Time Tasks ∗

While there is a tradeoff between the energy consumption and the satisfaction of task deadlines, the management of the processor temperature is of paramount important to the survival of the processor and the reduction of packing cost. This paper explores the scheduling of periodic real-time tasks with temperatureaware considerations in a uniprocessor or homogeneous multiprocessor environment. By modeling the cooling process approximately according to Fourier’s Law, a 2.719-approximation algorithm is shown for the minimization of the maximum temperature for processors with continuous processor speeds. When the processor is with discrete speeds only, we extend the 2.719approximation algorithm to manage the voltage/speed transition so that the maximum temperature can be minimized. For homogeneous multiprocessor systems, we show that the largest-taskfirst strategy has a 3.072-approximation bound in the minimization of the maximum temperature when all of the processors are on a chip. When each processor is on a chip, the approximation bound in the minimization of the maximum temperature is 6.444. When jobs might complete earlier than their worst-case estimation, dynamic scheduling is further explored to reduce the maximum temperature.