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Indirect Estimation Via L = λ W

Author

Listed:
  • Peter W. Glynn

    (Stanford University, Stanford, California)

  • Ward Whitt

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

Abstract

For a large class of queueing systems, Little's law ( L = λ W ) helps provide a variety of statistical estimators for the long-run time-average queue length L and the long-run customer-average waiting time W . We apply central limit theorem versions of Little's law to investigate the asymptotic efficiency of these estimators. We show that an indirect estimator for L using the natural estimator for W plus the known arrival rate λ is more efficient than a direct estimator for L , provided that the interarrival and waiting times are negatively correlated, thus extending a variance-reduction principle for the GI/G/s model due to A. M. Law and J. S. Carson. We also introduce a general framework for indirect estimation which can be applied to other problems besides L = λ W . We show that the issue of indirect-versus-direct estimation is related to estimation using nonlinear control variables. We also show, under mild regularity conditions, that any nonlinear control-variable scheme is equivalent to a linear control-variable scheme from the point of view of asymptotic efficiency. Finally, we show that asymptotic bias is typically asymptotically negligible compared to asymptotic efficiency.

Suggested Citation

  • Peter W. Glynn & Ward Whitt, 1989. "Indirect Estimation Via L = λ W," Operations Research, INFORMS, vol. 37(1), pages 82-103, February.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:1:p:82-103
    DOI: 10.1287/opre.37.1.82
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    Citations

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    Cited by:

    1. Kenneth W. Bauer & James R. Wilson, 1992. "Control‐variate selection criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 307-321, April.
    2. Ward Whitt & Xiaopei Zhang, 2019. "A central-limit-theorem version of the periodic Little’s law," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 15-47, February.
    3. Rayadurgam Srikant & Ward Whitt, 1999. "Variance Reduction in Simulations of Loss Models," Operations Research, INFORMS, vol. 47(4), pages 509-523, August.
    4. Paul Glasserman & Bin Yu, 2005. "Large Sample Properties of Weighted Monte Carlo Estimators," Operations Research, INFORMS, vol. 53(2), pages 298-312, April.

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