Impacts of Retrials on Power-Saving Policy in Data Centers

This paper considers a multiserver retrial queue with setup time which is motivated from application in data centers with the ON-OFF policy, where an idle server is immediately turned off. The ON-OFF policy is designed to save energy consumption of idle servers because an idle server still consumes about 60% of its peak consumption processing jobs. Upon arrival, a job is allocated to one of available off-servers and that server is started up. The server needs some setup time during which the server cannot process a job but consumes energy. An arriving job that sees all the servers occupied (active or setup) joins the orbit and retries to enter an unoccupied server after some random time. We formulate this model using a level-dependent quasi birth- and-death process. Using Foster--Lyapunov criteria, we obtain the stability condition. We also propose a heuristic technique to determine the truncation point for the level-dependent quasi birth-and-death process.