Equilibrium strategies in an observable queue with single exponential vacation

We consider an observable queue with single exponential vacation. Whenever the system becomes empty, the server begins a vacation at the instant. And when the vacation ends, if there are customers in the queue, the server begins work. Otherwhise, the server stays idle until the next customer arrives. A customer arriving at an idle server does not wait, while a customer arriving during a server´s vacation must wait until the end of the vacation. We assume both the fully and almost observable cases, then derive equilibrium threshold strategies for the customers and analyze the stationary behavior of the systems under these strategies. We also illustrate the equilibrium thresholds via numerical experiments.