Energy-aware SRPT server with batch arrivals: Analysis and optimization

We consider the optimal energy-aware control of a single server with batch arrivals and applying the SRPT scheduling rule. The server is modeled as an M^X∕G∕1 queue with a particular control policy that puts the server to a sleep mode to save energy with an additional delay cost, the setup delay, after the server is turned on again. We first consider an ordinary M^X∕G∕1-SRPT system that does not go to sleep, and derive the mean response time equation. We then consider the more elaborate energy-aware M^X∕G∕1-SRPT system, and show that the mean response time can be decomposed into two parts: the mean response time of an ordinary M^X∕G∕1-SRPT, and an additional penalty term for switching the server to a sleep state. Furthermore, we study the energy-performance optimization of the system and prove that, for the Energy Response time Weighted Sum (ERWS) and Energy Response time Product (ERP) cost metrics, the optimal control either puts the server into a sleep state immediately when it becomes idle or keeps it idling until the next job arrives.