Optimal control of two-phase M/M/1 queueing system with server Start-up, N-Policy, unreliable server and Balking

---------------------------------------------------------------ABSTRACT-----------------------------------------------------In this paper, an M/M/1 queueing system with server Start-up, N-Policy, breakdowns at two phases of service and Balking is analyzed. Customers arrive at the system according to a Poisson process. They receive the first phase service as a batch followed by second essential phase of individual service. Arriving customers may balk with a certain probability and may depart without getting service due to impatience. Lack of service occurs when the server is on vacation, busy during the service mode or due to the sudden breakdowns of the server. For this model the probability generating functions for the number of customers present in the system at various states of the server are derived and obtained the closed-form expressions for various performance measures of interest. Further a total expected cost model is formulated to determine the optimal threshold of N at a minimum cost. Finally, numerical examples are given.