Equilibrium Strategies in the Almost Unobservable Queues with Catastrophes and Repairs

We consider customers' strategic behavior in the almost unobservable queue with catastrophes and repairs, where only the state of the server is observable. Whenever a catastrophes occurs, all customers are forced to abandon the system, the server breaks down and is repaired immediately. By using the method of probability generating function, the stationary distribution is derived. Based on a natural reward-cost structure, the utility function of the customer is constructed, and customers' equilibrium balking strategies are determined. Finally, numerical examples are illustrated the effect of catastrophes on the behavior of the customers.