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Numerical approximations for compound geometric distributions with applications in queueing theory

Published online by Cambridge University Press:  14 July 2016

L. E. N. Delbrouck
L. E. N. Delbrouck*
Affiliation:
Bell-Northern Research, Ottawa, Ontario
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Abstract

A two-step procedure is described to approximate first come first served delay distributions in M/G/1 and GI/G/1 systems. The procedure consists in formulating a coarse initial approximation for the distribution sought, and then correcting this approximation by means of a suitable integral transformation. Examples are displayed.

Keywords

DELAY DISTRIBUTIONSQUEUESPOLLACZEK FORMULAWIENER-HOPF EQUATIONEXPONENTIAL APPROXIMANTSASYMPTOTIC BEHAVIORTWO-STEP COMPUTATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 1 , March 1978 , pp. 202 - 208
Copyright
Copyright © Applied Probability Trust 1978 

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References

[1] Borovkov, A. A. (1970) Factorization identities and properties of the distribution of the supremum of sequential sums. Theory Prob. Appl. 15, 359–402.Google Scholar
[2] Delbrouck, L. E. N. (1975) Convexity properties, moment inequalities, and asymptotic exponential approximations for delay distributions in GI/G/1 systems. Stoch. Proc. Appl. 3, 193–207.Google Scholar
[3] Kühn, P. (1976) Tables on Delay Systems. Institute of Switching and Data Technics, Stuttgart.Google Scholar
[4] Lindley, D. V. (1952) Theory of queues with a single server. Proc. Camb. Phil. Soc. 48, 277–289.Google Scholar
[5] Marchal, W. G. and Harris, C. M. (1976) A modified Erlang approach to approximating GI/G/1 queues. J. Appl. Prob. 13, 118–126.Google Scholar
[6] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar