On the numerical inversion of busy-period related transforms
type: Item
instance of: scholarly article
title: On the numerical inversion of busy-period related transforms
zbMATH Open document ID: 1096.90009
DOI: 10.1016/S0167-6377(01)00113-4
author: J. P. C. Blanc
published in: Operations Research Letters
publication date: 2002-08-28T00:00:00Z
review text: Most algorithms for the numerical inversion of integral transforms require the values of the involved transforms at complex arguments. This poses a problem for inverting transforms implicitly defined as solutions of some functional equations. A number of examples of such transforms stem from queueing theory, e.g. the number of customers in a busy period and the busy period distribution. The author shows that the original contour integral with an implicitly defined integrand needed to invert the transform can be replaced by alternative contour integrals with only known transforms as part of the integrand. This method is applied to the two above mentioned queueing problems.
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 65C50
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 65R10
zbMATH DE Number: 1790722
zbMATH Keywords: integral transform
zbMATH Keywords: inversion
zbMATH Keywords: contour integral
zbMATH Keywords: busy period
reviewed by: Ilya S. Molchanov
MaRDI profile type: Publication
cites work: Calculating the \(M/G/1\) busy-period density and LIFO waiting-time distribution by direct numerical transform inversion
cites work: The Fourier-series method for inverting transforms of probability distributions
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cites work: Q3938929
cites work: Queueing output processes
cites work: Evaluating first-passage probabilities for spectrally one-sided Lévy processes
full work available at URL: s0167-6377(01)00113-4
OpenAlex ID: W2150086784
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description: scientific article; zbMATH DE number 1790722