# zbMATH — the first resource for mathematics

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
Full Text:
##### References:
 [1] DOI: 10.1109/TCOM.1980.1094582 · Zbl 0431.60089 · doi:10.1109/TCOM.1980.1094582 [2] DOI: 10.1016/0167-6377(82)90033-5 · Zbl 0538.90025 · doi:10.1016/0167-6377(82)90033-5 [3] DOI: 10.2307/3214189 · Zbl 0602.60082 · doi:10.2307/3214189 [4] DOI: 10.1016/0377-2217(84)90232-7 · Zbl 0547.90025 · doi:10.1016/0377-2217(84)90232-7 [5] Tijms, Stochastic modelling and analysis: A computational approach (1986) [6] Seelen, Tables for multiserver queues (1985) · Zbl 0626.60090 [7] Blanc, Proceedings of the CWI Symposium on Mathematics and Computer Science pp 139– (1986) [8] DOI: 10.1016/0167-6377(84)90024-5 · Zbl 0553.60088 · doi:10.1016/0167-6377(84)90024-5 [9] Krämer, Proceedings of the 8th International Teletraffic Congress pp 235– (1976) [10] DOI: 10.1016/0377-2217(86)90222-5 · Zbl 0584.90028 · doi:10.1016/0377-2217(86)90222-5 [11] Kleinrock, Queueing systems, Vol. 1. (1975) [12] Fredericks, Bell System Technical Journal 61 pp 295– (1982) · Zbl 0482.60093 · doi:10.1002/j.1538-7305.1982.tb03408.x [13] Neuts, Matrix-geometric solutions in stochastic models-an algorithmic approach (1981) · Zbl 0469.60002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.