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Statistical Analysis with Little's Law

Author

Listed:
  • Song-Hee Kim

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Ward Whitt

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027,)

Abstract

The theory supporting Little's Law (L=(lambda)W) is now well developed, applying to both limits of averages and expected values of stationary distributions, but applications of Little's Law with actual system data involve measurements over a finite-time interval, which are neither of these. We advocate taking a statistical approach with such measurements. We investigate how estimates of L and (lambda) can be used to estimate W when the waiting times are not observed. We advocate estimating confidence intervals. Given a single sample-path segment, we suggest estimating confidence intervals using the method of batch means, as is often done in stochastic simulation output analysis. We show how to estimate and remove bias due to interval edge effects when the system does not begin and end empty. We illustrate the methods with data from a call center and simulation experiments.

Suggested Citation

  • Song-Hee Kim & Ward Whitt, 2013. "Statistical Analysis with Little's Law," Operations Research, INFORMS, vol. 61(4), pages 1030-1045, August.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:4:p:1030-1045
    DOI: 10.1287/opre.2013.1193
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    References listed on IDEAS

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    1. Christos Alexopoulos & Nilay Tanık Argon & David Goldsman & Gamze Tokol & James R. Wilson, 2007. "Overlapping Variance Estimators for Simulation," Operations Research, INFORMS, vol. 55(6), pages 1090-1103, December.
    2. Ali Tafazzoli & James Wilson, 2011. "Skart: A skewness- and autoregression-adjusted batch-means procedure for simulation analysis," IISE Transactions, Taylor & Francis Journals, vol. 43(2), pages 110-128.
    3. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
    4. Otis B. Jennings & Avishai Mandelbaum & William A. Massey & Ward Whitt, 1996. "Server Staffing to Meet Time-Varying Demand," Management Science, INFORMS, vol. 42(10), pages 1383-1394, October.
    5. Christos Alexopoulos & Nilay Tanık Argon & David Goldsman & Natalie M. Steiger & Gamze Tokol & James R. Wilson, 2007. "Efficient Computation of Overlapping Variance Estimators for Simulation," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 314-327, August.
    6. Stephen G. Eick & William A. Massey & Ward Whitt, 1993. "Mt/G/\infty Queues with Sinusoidal Arrival Rates," Management Science, INFORMS, vol. 39(2), pages 241-252, February.
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    Citations

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    Cited by:

    1. 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.
    2. Aleksander Król & Małgorzata Król, 2019. "A Stochastic Simulation Model for the Optimization of the Taxi Management System," Sustainability, MDPI, vol. 11(14), pages 1-22, July.
    3. Ward Whitt & Xiaopei Zhang, 2019. "Periodic Little’s Law," Operations Research, INFORMS, vol. 67(1), pages 267-280, January.
    4. Rosa Hendijani, 2021. "Analytical thinking, Little's Law understanding, and stock‐flow performance: two empirical studies," System Dynamics Review, System Dynamics Society, vol. 37(2-3), pages 99-125, April.
    5. Tsiligianni, Christiana & Tsiligiannis, Aristeides & Tsiliyannis, Christos, 2023. "A stochastic inventory model of COVID-19 and robust, real-time identification of carriers at large and infection rate via asymptotic laws," European Journal of Operational Research, Elsevier, vol. 304(1), pages 42-56.
    6. 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.
    7. Ward Whitt, 2016. "Heavy-traffic fluid limits for periodic infinite-server queues," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 111-143, October.

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