Equilibrium Analysis of the Observable Queue with Balking and Delayed Repairs

The equilibrium threshold balking strategies are investigated for the fully observable and partially single-server queues with server breakdowns and delayed repairs. Upon arriving, the customers observe the queue length and status of the server and decide whether to join or balk the queue based on these information, along with the waiting cost and the reward after finishing their service. By using queueing theory and cost analysis, we obtain the stationary distribution of queue size of the queueing systems under consideration and provide algorithms in order to identify the equilibrium strategies for the fully and partially observable model. Finally, the equilibrium threshold balking strategies are derived for the fully observable system and partially observable system respectively, both with server breakdowns and delayed repairs.