Architecture and robustness tradeoffs in speed-scaled queues with application to energy management

We consider single-pass, lossless, queueing systems at steady-state subject to Poisson job arrivals at an unknown rate. Service rates are allowed to depend on the number of jobs in the system, up to a fixed maximum, and power consumption is an increasing function of speed. The goal is to control the state dependent service rates such that both energy consumption and delay are kept low. We consider a linear combination of the mean job delay and energy consumption as the performance measure. We examine 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. We quantify the tradeoffs of architecture specification with respect to robustness, analysing both global robustness and a newly defined measure which we call local robustness