Equilibrium strategies of the unobservable M/M/1 queue with balking and delayed repairs

• The balking strategies for a queue with breakdowns and delayed repairs is studied.
• We provide supplement to Wang and Zhang (2011) by studying the unobservable cases.
• The model is viewed as an M/M/1 queue that operates in a random environment.
• From a methodological point of view, the almost unobservable case is interesting.

Wang and Zhang (2011) studied the equilibrium threshold balking strategies for the fully observable and partially observable single-server queues with server breakdowns and delayed repairs. Customers decide whether to join or balk the system based on observation of the queue length and status of the server at their arrival instants. The present paper aims to study the corresponding unobservable cases in which the queue length is unknown to arriving customers. The model under consideration can be viewed as an M/M/1 queue in a random environment. Equilibrium mixed strategies are derived for the almost unobservable and fully unobservable queues. Finally, we illustrate the effect of several system parameters on the equilibrium behavior via numerical examples.