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This paper deals with the steady state analysis of a single server batch arrival queueing system with three stages of compulsory service. An additional supposition of a fourth stage optional service is well thought-out. The server may take a vacation after completion of service. In this model, the vacation is of predetermined duration. A busy server may break down at any moment. It is tracked by a repair process. Service time, vacation time and repair time follow general distribution. The steady state probability generating function for the system and also system recital measures is obtained by using a supplementary variable technique. Some special cases of the model are also discussed. The model is justified by means of numerical illustrations followed by graphical representation.

No abstract