Analysis Of Unreliable Multi-Server Queueing System With Breakdowns Spread And Quarantine

We consider an unreliable multi-server queue in which the rate of servers’ breakdowns increases when the number of broken servers grows. To prevent quick degradation of the system, it is proposed to switch to a quarantine regime when the number of broken servers exceeds some threshold and to maintain this regime until the number of broken servers becomes less than another threshold. During the quarantine, service of customers is stopped, new breakdowns do not arrive while the broken servers continue recovering. Under the fixed values of the thresholds, behavior of the system is described by the multi-dimensional continuous time Markov chain. The steady state distribution of the chain and the key performance measures of the system are computed as the functions of the thresholds. Possibility of the optimal choice of the thresholds providing the minimal value of an economical criterion is numerically illustrated.