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Periodic Little’s Law

Author

Listed:
  • Ward Whitt

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

  • Xiaopei Zhang

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

Abstract

Motivated by our recent study of patient flow data from an Israeli emergency department (ED), we establish a sample path periodic Little’s law (PLL), which extends the sample path Little’s law (LL). The ED data analysis led us to propose a periodic stochastic process to represent the aggregate ED occupancy level, with the length of a periodic cycle being 1 week. Because we conducted the ED data analysis over successive hours, we construct our PLL in discrete time. The PLL helps explain the remarkable similarities between the simulation estimates of the average hourly ED occupancy level over a week using our proposed stochastic model fit to the data and direct estimates of the ED occupancy level from the data. We also establish a steady-state stochastic PLL, similar to the time-varying LL.

Suggested Citation

  • Ward Whitt & Xiaopei Zhang, 2019. "Periodic Little’s Law," Operations Research, INFORMS, vol. 67(1), pages 267-280, January.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:1:p:267-280
    DOI: 10.1287/opre.2018.1766
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    References listed on IDEAS

    as
    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. Song-Hee Kim & Ward Whitt, 2013. "Statistical Analysis with Little's Law," Operations Research, INFORMS, vol. 61(4), pages 1030-1045, August.
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    Citations

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    Cited by:

    1. Morgan, Lucy E. & Barton, Russell R., 2022. "Fourier trajectory analysis for system discrimination," European Journal of Operational Research, Elsevier, vol. 296(1), pages 203-217.
    2. Karl Sigman & Ward Whitt, 2019. "Marked point processes in discrete time," Queueing Systems: Theory and Applications, Springer, vol. 92(1), pages 47-81, June.
    3. Hung, Ying-Chao & PakHai Lok, Horace & Michailidis, George, 2022. "Optimal routing for electric vehicle charging systems with stochastic demand: A heavy traffic approximation approach," European Journal of Operational Research, Elsevier, vol. 299(2), pages 526-541.

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