Abstract: This paper studies the M/M/1 constant retrial queueing model with Bernoulli vacations and server unreliability, where the server breaks down at different rates in normal and idle states. The system has no waiting space and service starts immediately if the arriving customer finds the server is idle. Otherwise, if the system is busy, on vacation, and in a breakdown state, the customer decides whether or not to join the orbit based on the different levels of information provided by the system. After each completed service, the system starts to go on vacation or remains available. The system rejects new customers from entering the system in the event of server breakdown. Based on the different levels of information provided by the system, we study the steady-state indicators in the almost unobservable case and fully unobservable case, as well as the equilibrium strategies of customers in both cases based on the reward-cost structure. Finally, we use numerical examples to show that revealing server status information does not increase the social benefit.

Key words: retrial queues, breakdowns, Bernoulli vacations, equilibrium strategy, social benefit