A moment-iteration method for approximating the waiting-time characteristics of the G1/G/1 queue

In this paper, a moment-iteration method is introduced. The method is used to solve Lindley's integral equation for the GI/G/l queue. From several forms of this integral equation, we derive the first two moments of the waiting-time distribution, the waiting probability, and the percentiles of the conditional waiting time. Numerical evidence is given that the method yields excellent results. The flexibility of the method provides the opportunity to solve the GI/G/l queue for all interarrival time distributions of practical interest. To show that the moment-iteration method is generally applicable, we give some results for an (s, S)-model with order-size-dependent lead times and finite production capacity of the supplier.