Queueing Systems

, Volume 91, Issue 1–2, pp 15–47 | Cite as

A central-limit-theorem version of the periodic Little’s law

  • Ward Whitt
  • Xiaopei ZhangEmail author


We establish a central-limit-theorem (CLT) version of the periodic Little’s law (PLL) in discrete time, which complements the sample-path and stationary versions of the PLL we recently established, motivated by data analysis of a hospital emergency department. Our new CLT version of the PLL extends previous CLT versions of LL. As with the LL, the CLT version of the PLL is useful for statistical applications.


Little’s law \(L = \lambda W\) Periodic queues Central limit theorem Emergency departments Weak convergence in \((\ell _1)^d\) 

Mathematics Subject Classification

60F05 60F25 60K25 90B22 



Support was received from NSF grants CMMI 1634133.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Industrial Engineering and Operations Research DepartmentColumbia UniversityNew YorkUSA

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