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1. M. E. Gebrehiwot, S. Aalto and P. Lassila, Energy-performance trade-off for processor sharing queues with setup delay, Operations Research Letters, vol. 44, pp. 101-106, 2016 (link)(bib)

   Abstract: Despite the extensive literature available on determining energy efficient control mechanisms for servers, only few studies address the processor sharing discipline. We assume jobs are served in the busy period using the processor sharing service discipline. Once the server becomes idle, depending on the applied control policy, the system may wait for an arriving job in the idle state before it is switched to a sleep state eventually. We study the energy-performance trade-off in an energy-aware M/G/1-PS system using the Energy Respose time Weighted Sum (ERWS) and Energy Response time Product (ERP) cost metrics. By analysing the integral equation related to the mean conditional response time, in both cases, the optimal policy is found to be a simple control that either leaves the server idle, or puts it to sleep immediately whenever it becomes idle.