In this paper, we study the equilibrium strategies in the M/M/1 queue with partial and total failures. The state of the server is modulated by a random environment. Based on different precision levels of system information, we study separately the threshold strategies for the fully observable case and mixed strategies for the fully unobservable case. In addition, we illustrate the effect of several parameters on equilibrium behavior via numerical examples. Some possible generalizations are also discussed.
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