The condition for the existence of steady-state distribution in the multi-server repairable queue system

In this paper, we analyse the condition for the existence of steady-state distribution in the multi-server repairable queue system. Quasi-birth–death process theory can be used to deal with the state distribution and the multi-server repairable queueing system has been given by the quasi-birth–death process method. In this paper we derive another form of the steady-state condition which has apparent probabilistic significance from the matrix form of the steady-state condition of the queueing system, so we have proved the two different forms of the conditions for the existence of steady-state distribution in the queueing system are consistent.