Abstract: This paper considered the equilibrium balking strategy of customers in the Geo/Geo/1 queue with single vacation. To the authors' knowledge, this is the first time that the vacation policy is introduced into the economics of the discrete-time queue. The customers decide for themselves whether to enter the system or balk based on a natural  reward-cost structure. Using the theory of the quasi-birth-death process and the standard approach for solving difference equation, we obtain the stationary distribution of the system and the mean sojourn time of an arriving customer. Then by introducing appropriate functions, we provide an algorithm to identify the equilibrium balking strategy. Furthermore, the resulting stationary system behavior is explored and the equilibrium social benefit is derived. Finally, we illustrate the effects of the parameters on the equilibrium behavior via numerical experiments.

Key words:  economics of queues, Nash equilibrium, expected net benefit, quasi-birth-death chain, difference equations, stationary distribution,  equilibrium balking strategy, social benefit