Analysis of the Mx/G(M/G)/1 repairable queueing system with single delay vacation (I) – some queueing indices

In this paper we consider a kind of Mx/G(M/G)/1 repairable queueing system with single delay vacation in which the vacation time, service time, repairing time and the delay vacation time are all arbitrary distributions. By using a concise method, we obtain the transient solution, stationary solution and stochastic decomposition of the queue length. Simultaneously we also give out the stochastic decompositions of the queue lengths in some special cases.