Analysis of a Two-Phase Queueing System with Impatient Customers and Multiple Vacations

In this paper, we consider a two-phase queueing system with impatient customers and multiple vacations. Customers arrive at the system according to a Poisson process. They receive the first essential service as well as a second optional service. Arriving customers may balk with a certain probability and may depart after joining the queue without getting service due to impatience. Lack of service occurs when the server is on vacation or busy during the first phase of service. We analyze this model and derive the probability generating functions for the number of customers present in the system for various states of the server. We further obtain the closed-form expressions for various performance measures including the mean system sizes for various states of the server, the average rate of balking, the average rate of reneging, and the average rate of loss.

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