Non Markovian retrial queue, balking, disaster under working breakdown and working vacation

Abstract

Any arriving customer who arrives and finds that the server is free, enters the service station and the remaining customers connect into the orbit. When the normal busy server is running, the system may at any time become defective due to a disaster. All users are forced to quit the system due to a disaster, which also brings about the failure of the main server. When a primary server breaks, it is shipped out for repair, and the repair process starts instantly. The server stops running as soon as the orbit is empty at a typical service finish instant. During the working breakdown or working vacation, the replacement server offers arriving customers a lower level of service. The arriving customer receives service instantly if the server is idle. If not, he will choose whether to leave the system without service or returning to receive service. Using the supplementary variable technique, we calculate the steady state PGF for system and orbit sizes. We generate performance measures and particular cases. With the use of specific numerical examples, we analyse the model.