Equilibrium balking behavior in the Geo/Geo/1Geo/Geo/1 queueing system with multiple vacations

This paper studies the equilibrium behavior of customers in the Geo/Geo/1Geo/Geo/1 queueing system under multiple vacation policy. The server leaves for repeated vacations as soon as the system becomes empty. Customers decide for themselves whether to join or to balk, which is more sensible than the classical viewpoint in queueing theory. Equilibrium customer behavior is considered under four cases: fully observable, almost observable, almost unobservable and fully unobservable, which cover all the levels of information. Based on the reward-cost structure, we obtain the equilibrium balking strategies in all cases. Furthermore, the stationary system behavior is analyzed and a variety of performance measures are developed under the corresponding strategies. Finally, we present several numerical experiments that demonstrate the effect of the information level as well as several parameters on the equilibrium behavior and social benefit. The research results not only offer the customers optimal strategies but also provide the managers with a good reference to discuss the pricing problem in the queueing system.