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Estimating Customer and Time Averages

Author

Listed:
  • Peter W. Glynn

    (Stanford University, Stanford, California)

  • Benjamin Melamed

    (NEC Research USA, Inc., Princeton, New Jersey)

  • Ward Whitt

    (AT&T Bell Laboratories, Murray Hill, New Jersey)

Abstract

In this paper we establish a joint central limit theorem for customer and time averages by applying a martingale central limit theorem in a Markov framework. The limiting values of the two averages appear in the translation terms. This central limit theorem helps to construct confidence intervals for estimators and perform statistical tests. It thus helps determine which finite average is a more asymptotically efficient estimator of its limit. As a basis for testing for PASTA (Poisson arrivals see time averages), we determine the variance constant associated with the central limit theorem for the difference between the two averages when PASTA holds.

Suggested Citation

  • Peter W. Glynn & Benjamin Melamed & Ward Whitt, 1993. "Estimating Customer and Time Averages," Operations Research, INFORMS, vol. 41(2), pages 400-408, April.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:2:p:400-408
    DOI: 10.1287/opre.41.2.400
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    Cited by:

    1. Mandjes, M. & Ravner, L., 2021. "Hypothesis testing for a Lévy-driven storage system by Poisson sampling," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 41-73.
    2. Azam Asanjarani & Yoni Nazarathy & Peter Taylor, 2021. "A survey of parameter and state estimation in queues," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 39-80, February.

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