Server farms with batch arrival and staggered setup
Tuan Phung-Duc · 2014
Cloud computing is a new paradigm where a company makes money by selling computer resources including both software and hardware. The core part of cloud computing is a data center where a huge number of servers are available. These servers consume a large amount of energy to run and to keep cool. Therefore, a reduction of a few percent of the power consumption means saving a large amount of money and the environment. In the current technology, an idle server still consumes about 60% of its peak processing a job. Thus, the only way to save energy is to turn off servers which are not processing a job. However, when there are some waiting jobs, we have to turn on the OFF servers. A server needs some setup time to be active during which it consumes energy but cannot process a job. Therefore, there exists a trade-off between power consumption and delay performance. In [8, 9], the authors analyze this tradeoff using an M/M/c queue with setup time for which they present a decomposition property by solving difference equations. In this paper, using an alternative simple approach, we obtain generating functions for the joint stationary distribution of the number of active servers and that of jobs in the system for a more general model with batch arrivals. We further obtain moments for the queue size. Numerical results show some insights in to the performance of the system.