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.
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Blanc, J. Computation of Autocorrelations of Interdeparture Times by Numerical Transform Inversion. Annals of Operations Research 112, 83–100 (2002). https://doi.org/10.1023/A:1020976904635
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DOI: https://doi.org/10.1023/A:1020976904635