Abstract: Queueing theory is vastly used to study service systems arising in management problems, where customers are considered to be indifferent in the sense that the decisions to control a system, are only made by the management and the users are impelled to follow the decisions. However, for a service system to be more realistic, it is essential to consider customers’ decisions about their actions (join or balk, wait or abandon, buy priority or not) which depends on the information provided to them at their arrival epochs. The study of queuing systems with strategic customers was initiated by Naor in 1969. After Naor’s work, an emerging tendency to study customers’ behavior imposing a reward-cost structure on the system took place. In this scenario, customers want to maximize their net benefit against others who have the same objective, which can be viewed as a symmetric game among them. When the system is empty, the server goes on vacation and returns after a random time to serve waiting customers if any.During the server’s vacation, customers continue to arrive at the system and if the present customers did not receive their service in due time, they became impatient and decide sequentially whether they will abandon the system or not upon the availability of a secondary transportation facility. In this presentation, the focus is to study customers’ equilibrium and socially optimal behavior in queuing systems with server vacation. Numerical experiments showing the dependence of performance measures on system parameters is demonstrated via several figures. Finally, a potential application of the model is suggested in managing a perishable inventory store.
School of Mathematical Sciences
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