This paper considers a multiserver queueing system with finite capacity. Customers that find the service facility being fully occupied are blocked and enter a virtual waiting room (called orbit). Blocked customers stay in the orbit for an exponentially distributed time and retry to occupy an idle server again. After completing a service, the server starts an additional job that we call an after-call work. We formulate the queueing system using a continuous-time level-dependent quasi-birth-and-death process, for which a sufficient condition for the ergodicity is derived. We obtain an approximation to the stationary distribution by a direct truncation method whose truncation point is simply determined using an asymptotic analysis of a single server retrial queue. Some numerical examples are presented in order to show the influence of parameters on the performance of the system.

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 three-dimensional 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.