Numerical Transform Inversion for Autocorrelations of Waiting Times

Hans Blanc

A chapter in Operations Research Proceedings 2004, 2005, pp 297-304 from Springer

Abstract: Abstract The generating function of the autocorrelations of successive waiting times in a stationary M/G/l or in a stationary GI/M/1 system can be expressed in terms of the probability generating function of the number of customers served in a busy period. The latter function is only implicitly determined as a solution to a functional equation. More explicit expressions have been obtained with the aid of Lagrange’s theorem on the reversion of power series, but they involve increasingly higher order derivatives of a function which comprises several Laplace-Stieltjes transforms. A recently discovered substitution method for contour integrals allows the numerical inversion of an implicitly determined generating function without the numerical solution of the functional equation for many complex values.

Keywords: Functional Equation; Busy Period; Contour Integral; Probability Generate Function; Service Time Distribution (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-540-27679-1_37

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DOI: 10.1007/3-540-27679-3_37

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