An $M^{[X]}/G(a,b)/1$ queue with unreliable server, re-service on server's decision, balking and Bernoulli vacation schedule under multiple vacation policy

This paper deals with a non-Markovian batch arrival bulk service queue with unreliable server, re-service on server's decision, Bernoulli vacation schedule under multiple vacation and balking. We consider that the server is unreliable and may stop working due to failure. When this happens, the service is interrupted and restarted after repair. The service time, vacation time, re-service time and repair time assume to follow a general (arbitrary) distribution. In the proposed model, we derived the probability distribution of queue size at a random and departure epoch using supplementary variable techniques. Finally, some performance measures, particular cases and numerical results are obtained.