Abstract: This paper studies the time-dependent analysis of an M/M/1 queueing model with single, multiple working vacation, balking and vacation interruptions. Whenever the system becomes empty, the server commences working vacation. During the working vacation period, if the queue length reaches a positive threshold value ‘k’, the working vacation of the server is interrupted and it immediately starts the service in an exhaustive manner. During working vacations, the customers become discouraged due to the slow service and possess balking behavior. The transient system size probabilities of the proposed model are derived explicitly using the method of generating function and continued fraction. The performance indices such as average and variance of system size are also obtained. Further, numerical simulations are presented to analyze the impact of system parameters.

Key words: The M/M/1 queue, Single and multiple working vacation, Balking, Vacation interruption, Continued fractions, Transient probabilities