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Dominant poles and tail asymptotics in the critical Gaussian many-sources regime

Author

Listed:
  • A. J. E. M. Janssen

    (Eindhoven University of Technology)

  • J. S. H. van Leeuwaarden

    (Eindhoven University of Technology)

Abstract

The dominant pole approximation (DPA) is a classical analytic method to obtain from a generating function asymptotic estimates for its underlying coefficients. We apply DPA to a discrete queue in a critical many-sources regime, in order to obtain tail asymptotics for the stationary queue length. As it turns out, this regime leads to a clustering of the poles of the generating function, which renders the classical DPA useless, since the dominant pole is not sufficiently dominant. To resolve this, we design a new DPA method, which might also find application in other areas of mathematics, like combinatorics, particularly when Gaussian scalings related to the central limit theorem are involved.

Suggested Citation

  • A. J. E. M. Janssen & J. S. H. van Leeuwaarden, 2016. "Dominant poles and tail asymptotics in the critical Gaussian many-sources regime," Queueing Systems: Theory and Applications, Springer, vol. 84(3), pages 211-236, December.
    • Handle: RePEc:spr:queues:v:84:y:2016:i:3:d:10.1007_s11134-016-9499-5
    DOI: 10.1007/s11134-016-9499-5
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    References listed on IDEAS

    as
    1. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    2. Janssen, A.J.E.M. & van Leeuwaarden, J.S.H., 2007. "Cumulants of the maximum of the Gaussian random walk," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1928-1959, December.
    3. J. S. H. van Leeuwaarden, 2006. "Delay Analysis for the Fixed-Cycle Traffic-Light Queue," Transportation Science, INFORMS, vol. 40(2), pages 189-199, May.
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