Periodic Little’s Law

Ward Whitt () and Xiaopei Zhang ()
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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

Operations Research, 2019, vol. 67, issue 1, 267-280

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.

Keywords: Little’s law; L = λ W; periodic queues; service systems; data analysis; emergency departments (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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