Optimal Balking Strategies in a Markovian Queue with a Single Vacation

摘要

We consider the optimal balking strategies in a Markovian queue with a single exponential vacation. Whenever the system becomes empty, the server begins to take a vacation. And when the server finishes his vacation, if there are customers waiting in the queue, the server begins to work. Otherwise, the server stays idle until the next customer arrives. Arriving customers decide either to enter the system or to balk, based on their desire for service, or their unwillingness for waiting. We consider that the system states are the fully unobservable and partially observable respectively. We first analyze the stationary behavior of the system, and then derive the equilibrium mixed strategies and social benefit for all customers. For the fully unobservable case, we obtain socially optimal strategies and provide numerical examples.