This paper considers the equilibrium behavior of customers in a Markovian queue with two types of breakdowns, where the normal server can get a breakdown at any time. The system does not admit a new arrival once a breakdown happens, and there may exist two independent types of breakdowns: (1) partial breakdown: the server continues to serve the customers on spot at a low rate and is repaired when the system is empty; (2) full breakdown: the server stagnates service and is repaired immediately. When the repair is over, new arrivals will be accepted. Assuming that all the customers have the option of joining or balking in order to maximize their own benefits and basing on a linear reward-cost structure, we analyze the equilibrium joining strategies of the customers and the average social benefits of the system in the fully observable case and the almost unobservable case, respectively. And on this basis, the effect of several parameters on customers’ strategic behavior is presented by some numerical examples.
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