Timing Analysis on a Processor with Temperature-Controlled Speed Scaling

Several recent works consider the problem of temperature-constrained scheduling of jobs. In such attempts, speed of the processor and the execution of jobs is software-controlled such that temperature and performance constraints are met. An alternative approach is to use measurements from temperature sensors to actuate the speed of the processor as a feedback control loop. Though such a solution explicitly and independently meets the thermal constraints, the analysis of the real-time properties of tasks served by such a processor is not straightforward. In this paper, we study this problem for a variable stream of jobs characterized by an input arrival rate. We show that an intuitive notion of monotonicity extends to such a processor. Using this property, we present an analytical technique to determine the worst-case delay suffered by jobs. The presented technique efficiently and tightly determines the delay as a function of the initial temperature. The simplicity of this analysis motivates further analysis and mainstream use of such systems.