Analysis of the m/m/1 Queue Model with Multiple Vacations and Server Break-Down

Abstract

Analysis of M/M/1 queue model with multiple vacations and server breakdown is the specific queuing model where the server takes a
vacation as soon as it becomes idle. The vacation ends, if there are customers arrive in the queue, the server activates; otherwise, another vacation is taken. Once service begins, the service mechanism is subject to breakdowns which occur at a constant rate. The service mechanism then goes through a repair process of random duration, and when repair is completed, the server returns to the customers whose services were interrupted. In this paper we have obtained the queue length for both cases i.e. for vacations and break down. Also for these two cases we have discussed the model for the numerical values and further value of queue length has been obtained for some fix values and variable parameter.