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Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?
, 2013
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manuscript (Please, provide the mansucript number!) Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named journal. INFORMS journal templates are for the exclusive purpose of submitting to an INFORMS journal and should not be used to distribute the papers in print or online or to submit the papers to another publication.
Extending the FCLT version of L = λW
"... The functional central limit theorem (FCLT) version of Little’s law (L = λW) established by Glynn and Whitt is extended to show that a bivariate FCLT for the number in system and the waiting times implies the joint FCLT for all processes. It is based on a converse to the preservation of convergence ..."
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The functional central limit theorem (FCLT) version of Little’s law (L = λW) established by Glynn and Whitt is extended to show that a bivariate FCLT for the number in system and the waiting times implies the joint FCLT for all processes. It is based on a converse to the preservation of convergence by the composition map with centering on the function space containing the sample paths, exploiting monotonicity. Keywords: Little’s law, L = λW, functional central limit theorem, confidence intervals, continuous mapping theorem, composition with centering 1.
Contents lists available at SciVerse ScienceDirect Statistics and Probability Letters
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Appendix to Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?
, 2013
"... Service systems such as call centers and hospitals typically have strongly timevarying arrivals. A natural model for such an arrival process is a nonhomogeneous Poisson process (NHPP), but that should be tested by applying appropriate statistical tests to arrival data. Assuming that the NHPP has a ..."
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Service systems such as call centers and hospitals typically have strongly timevarying arrivals. A natural model for such an arrival process is a nonhomogeneous Poisson process (NHPP), but that should be tested by applying appropriate statistical tests to arrival data. Assuming that the NHPP has a rate that is piecewiseconstant, a KolmogorovSmirnov (KS) statistical test of a Poisson process (PP) can be applied to test for a NHPP, by combining data from separate subintervals, exploiting the classical conditionaluniform property. In this paper we apply KS tests to call center and hospital arrival data and show that they are consistent with the NHPP property, but only if that data is analyzed carefully. Initial testing rejected the NHPP null hypothesis, because it failed to take account of three common features of arrival data: (i) data rounding, e.g., to seconds, (ii) overdispersion caused by combining data from multiple days that do not have the same arrival rate, and (iii) choosing subintervals over which the rate varies too much. In the main paper we investigate how to address these three problems. This appendix