Analysis of the remaining busy time in a retrial system

In this paper, we consider a retrial queueing system with state-dependent rates and perform an analysis of the reaming service time in that system. We consider a multi-server system with customers arriving according to the Poisson process During service, the interruptions occur according to the Poisson process and are followed by the random time of the server's recovery. We focus on the process which reflects the busy time of the server and derive the expressions for moments of the stationary remaining generalized service time which includes unavailable periods of the server.