Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T09:49:08.607Z Has data issue: false hasContentIssue false
  • English
  • Français

A Moment-Iteration Method for Approximating the Waiting-Time Characteristics of the GI/G/1 Queue

Published online by Cambridge University Press:  27 July 2009

A. G. De Kok
A. G. De Kok
Affiliation:
Nederlandse Philips Bedrijven B. V. Center for Quantitative Methods The Netherlands
Get access Rights & Permissions [Opens in a new window]

Extract

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.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 2 , April 1989 , pp. 273 - 287
Copyright
Copyright © Cambridge University Press 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ackroyd, M.H. (1980). Computing the waiting-time distribution for the Gl/G/l queue by signal-processing methods. IEEE Transactions on Communication 28: 52–58.CrossRefGoogle Scholar
Blanc, J.P.C. & Van, Doom E.Q. (1986). Relaxation times for queueing systems. In Proceedings of the CWI Symposium on Mathematics and Computer Science. CWI Monograph 1, North-Holland, pp. 139–162.Google Scholar
Bux, W. (1979). Single-server queues with general interarrival and phase-type service times distributions. In Proceedings of the 9th International Teletraffic Congress, Torremolinos, Paper 413.Google Scholar
De, Kok A.G. (1987). Approximations for the waiting-time characteristics of the GI/G/l queue with impatience. CQM-note Centre for Quantitative Methods, Philips, Eindhoven, The Netherlands.Google Scholar
De, Kok A.G. (1987). Computing optimal (m,M) control rules for production-inventory models with compound Poisson demand. CQM-note 55, paper presented at EURO VIII, 1986, Lisbon, Portugal.Google Scholar
Fredericks, A.A. (1982). A class of approximations for the waiting-time distribution in a GI/G/1 queueing system. Bell System Technical Journal 61: 295–325.CrossRefGoogle Scholar
Kleinrock, L. (1975). Queueing systems, Vol. 1. New York: Wiley.Google Scholar
Krämer, W. & Langenbach-Belz, M. (1976). Approximate formulae for the delay in the queueing System GI/G/1. In Proceedings of the 8th International Teletraffic Congress, Melbourne, 235–1/8.Google Scholar
Neuts, M.F. (1981). Matrix-geometric solutions in stochastic models-an algorithmic approach. Baltimore, Maryland: The John Hopkins University Press.Google Scholar
Seelen, L.P. (1986). An algorithm for Ph/Ph/c queues. European Journal of Operations Research 23: 118–127.CrossRefGoogle Scholar
Seelen, L.P. & Tijms, H.C. (1984). Approximations for the conditional waiting times in the GI/G/c queue. Operations Research Letters 3: 183–190.Google Scholar
Seelen, L.P., Tijms, H.C., & Van, Hoorn M.H. (1985). Tables for multiserver queues. Amsterdam: North-Holland.Google Scholar
Tijms, H.C. (1986). Stochastic modelling and analysis: A computational approach. New York: Wiley.Google Scholar
Tijms, H.C. & Groenevelt, H. (1984). Simple approximations for the reorder point in periodic and continuous review (s, S) inventory systems with service-level constraints. European Journal of Operations Research 17: 175–190.CrossRefGoogle Scholar
Tijms, H.C. (1987). Private communication.Google Scholar
Van, Hoorn M.H. & Seelen, L.P. (1986). Approximations for the GI/G/c queue. Journal of Applied Probabilities 23: 484–494.Google Scholar
Whitt, W. (1982). Refining diffusion approximations for queues. Operations Research Letters 5: 165–169.Google Scholar