On the numerical inversion of busy-period related transforms

Authors:
J. P. C Blanc
Affiliations:
Department of Econometrics & Operations Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands
Venue:
Operations Research Letters
Year:
2002

Citing 4
Cited 2

The Fourier-series method for inverting transforms of probability distributions

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Calculating the M/G/1 busy-period density and LIFO waiting-time distribution by direct numerical transform inversion

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Abstract

Many quantities of interest in queueing theory can be determined in the form of transforms. Methods for numerically inverting those transforms are well developed. However, some transforms such as that of the busy period distribution can only be characterized implicitly via functional equations. Algorithms for inversion require the evaluation of transforms at many complex arguments. Although this is possible it may be computationally quite involved. In this paper, we show that the original contour integral with the implicitly determined transform as part of the integrand can be replaced by alternative contour integrals with only known transforms as part of the integrand via simple substitutions. The alternative contour integrals can be evaluated by the same techniques as the original ones.