Timing Analysis on a Processor with Temperature-Controlled Speed Scaling

Pratyush Kumar and Lothar Thiele.
In In Proc. of the 18th IEEE Real-Time and Embedded Technology and Applications Symposium, RTAS 2012, Beijing, China, April 2012.
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.