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A moment-iteration method for approximating the waiting-time characteristics of the \(GI/G/1\) queue. (English) Zbl 1134.60414
Summary: 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 \(GI/G/1\) 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.

MSC:
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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