On saturation effects in coupled speed scaling

Abstract

In coupled speed scaling systems, the speed of the CPU is adjusted dynamically based on the number of jobs present in the system. In this paper, we use Markov chain analysis to study the autoscaling properties of an M/GI/1/PS system. In particular, we study the saturation behaviour of the system under heavy load. Our analytical results show that the mean and variance of system occupancy are not only finite, but tightly bounded by polynomial functions of the system load and the speed scaling exponent. We build upon these results to study the speed, utilization, and mean busy period of the M/GI/1/PS. Discrete-event simulation results confirm the accuracy of our analytical models.