Analysis of an M[X]/(G1, G2)/1 retrial queueing system with balking, optional re-service under modified vacation policy and service interruption

This paper deals with the steady state analysis of batch arrival retrial queueing system with two types of service under modified vacation policy, where each type consists of an optional re-service. An arriving batch may balk the system at some particular times. After the completion of each types of service the customers may re-service of the same type without joining the orbit or may leave the system. If the orbit is empty at the service completion of each types of service, the server takes at most J vacations until at least one customer is received in the orbit when the server returns from a vacation. Busy server may breakdown at any instance and the service channel will fail for a short interval of time. The steady state probability generating function for system/orbit size is obtained by using the supplementary variable method. Some system performance measures and numerical illustrations are discussed.