Robust control of an M/G/1 processor sharing queue with applications to energy management

The Internet contains many devices that must process multiple jobs at the same time. For many purposes, such devices can be modelled as M/G/1-PS queues. This report investigates such a queue. We consider single-pass, lossless, queueing systems at steady-state subject to Poisson job arrivals at an unknown rate. Service rates are in general allowed to depend on the number of jobs in the system, i.e. speed-scaling. A general goal is to control the state dependent service rates such that both energy consumption and delay are kept low. As there is a tradeoff between the two, a sensible performance measure is a linear combination of the mean job delay and energy consumption, where power is generally assumed to be an increasing polynomial function of the speed. We consider both the ''architecture'' of the system, which we define as a specification of the number of speeds that the system can choose from, and the ''design'' of the system, which we define as the actual speeds available. Previous work has illustrated, that when the arrival rate is precisely known, there is little benefit in introducing complex (multi-speed) architectures, yet in view of parameter uncertainty, allowing a variable number of speeds improves robustness. In the current report, we numerically quantify the tradeoffs of architecture specification with respect to robustness.