Multiserver retrial queue with setup time and its application to data centers

Abstract

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. Otherwise, if all the servers are not available upon arrival, the job is blocked and retries in a random time. A server needs some setup time during which the server cannot process a job but consumes energy. We formulate this model using a threedimensional continuous-time Markov chain obtaining the stability condition via Foster-Lyapunov criteria. Interestingly, the stability condition is different from that of the corresponding non-retrial queue. Furthermore, exploiting the special structure of the Markov chain together with a heuristic technique, we develop an efficient algorithm for computing the stationary distribution. Numerical results reveal that under the ON-OFF policy, allowing retrials is more power-saving than buffering jobs. Furthermore, we obtain a new insight that if the setup time is relatively long, setting an appropriate retrial time could reduce both power consumption and the mean response time of jobs.

Admission control for finite capacity queueing model with general retrial times and state-dependent rates

“…The supplementary variable technique (SVT) developed by Cox [10] to analyze the M/G/1 queueing model has been extensively implemented by several researchers to study the non-Markovian queueing system in different frameworks. Some researchers have contributed to the analysis of retrial queueing models in different structures [8,32]. An M/G/1 retrial queueing model was investigated by Moreno [30] by considering general retrial times.…”

Performance analysis and system optimization of an energy-saving mechanism in cloud computing with correlated traffic

“…As the construction size and power consumption of cloud data centers worldwide dramatically increases, a considerable amount of greenhouse gases will be emitted into the environment [1], [14]. Not surprisingly, the energy efficiency of these cloud data centers has been receiving significant attention recently [22].…”