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Computation of Autocorrelations of Interdeparture Times by Numerical Transform Inversion

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  • Blanc, J.P.C.

    (Tilburg University, Center For Economic Research)

Abstract

The generating function of the autocorrelations of the interdeparture times in stationary M/G/1 and GI/M/1 systems involves the probability generating function of the number of customers served in a busy period. The latter function is implicitly determined as a solution to a functional equation. Standard methods for the numerical inversion of generating functions require the values of these functions at many complex arguments. A recently discovered substitution method for contour integrals allows the numerical inversion of implicitly determined generating functions without the numerical solution of the functional equations. Copyright Kluwer Academic Publishers 2002
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Blanc, J.P.C., 2001. "Computation of Autocorrelations of Interdeparture Times by Numerical Transform Inversion," Discussion Paper 2001-75, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:5caf9835-fcf1-4278-914b-9fd6b53890ed
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    References listed on IDEAS

    as
    1. Blanc, J.P.C., 2001. "On the Numerical Inversion of Busy-Period Related Transforms," Other publications TiSEM 6c859c40-8d0b-4b3b-9526-a, Tilburg University, School of Economics and Management.
    2. Jian-Qiang Hu, 1996. "The Departure Process of the GI / G /1 Queue and Its MacLaurin Series," Operations Research, INFORMS, vol. 44(5), pages 810-815, October.
    3. Charles D. Pack, 1975. "The Output of an M / D /1 Queue," Operations Research, INFORMS, vol. 23(4), pages 750-760, August.
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