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Numerical Transform Inversion for Autocorrelations of Waiting Times

In: Operations Research Proceedings 2004

Author

Listed:
  • Hans Blanc

    (Tilburg University)

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.

Suggested Citation

  • Hans Blanc, 2005. "Numerical Transform Inversion for Autocorrelations of Waiting Times," Operations Research Proceedings, in: Hein Fleuren & Dick Hertog & Peter Kort (ed.), Operations Research Proceedings 2004, pages 297-304, Springer.
    • Handle: RePEc:spr:oprchp:978-3-540-27679-1_37
    DOI: 10.1007/3-540-27679-3_37
    as

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