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Computation of Autocorrelations of Interdeparture Times by Numerical Transform Inversion

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  • J.P.C. Blanc

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

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  • J.P.C. Blanc, 2002. "Computation of Autocorrelations of Interdeparture Times by Numerical Transform Inversion," Annals of Operations Research, Springer, vol. 112(1), pages 83-100, April.
    • Handle: RePEc:spr:annopr:v:112:y:2002:i:1:p:83-100:10.1023/a:1020976904635
    DOI: 10.1023/A:1020976904635
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    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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