Abstract
In this investigation, single repairable server queueing system with bulk input and state dependent rates is analyzed by considering the general distributions for the repair, delay to repair and service processes. The server is capable of rendering two stages of the service in which the first stage service is essential and the second stage service is optional. During the repair, the server has to undergo through m-different compulsory phases of the repair. To examine the steady state behavior and to obtain the various performance indices of the system, the probability generating functions of the queue size distributions are derived by using the supplementary variable technique. By setting the appropriate parameters, some special cases are discussed. The sensitivity analysis is performed by facilitating the numerical results for the suitable illustration.
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