Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes

Ran Liu (), Michael E. Kuhl (), Yunan Liu () and James R. Wilson ()
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Ran Liu: SAS Institute, Cary, North Carolina 27513
Michael E. Kuhl: Department of Industrial and Systems Engineering, Rochester Institute of Technology, Rochester, New York 14623
Yunan Liu: Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, North Carolina 27695-7906
James R. Wilson: Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, North Carolina 27695-7906

INFORMS Journal on Computing, 2019, vol. 31, issue 2, 347-366

Abstract: We develop CIATA, a combined inversion-and-thinning approach for modeling a nonstationary non-Poisson process (NNPP), where the target arrival process is described by a given rate function and its associated mean-value function together with a given asymptotic variance-to-mean (dispersion) ratio. CIATA is based on the following: (i) a piecewise-constant majorizing rate function that closely approximates the given rate function from above; (ii) the associated piecewise-linear majorizing mean-value function; and (iii) an equilibrium renewal process (ERP) whose noninitial interrenewal times have mean 1 and variance equal to the given dispersion ratio. Transforming the ERP by the inverse of the majorizing mean-value function yields a majorizing NNPP whose arrival epochs are then thinned to deliver an NNPP having the specified properties. CIATA-Ph is a simulation algorithm that implements this approach based on an ERP whose noninitial interrenewal times have a phase-type distribution. Supporting theorems establish that CIATA-Ph can generate an NNPP having the desired mean-value function and asymptotic dispersion ratio. Extensive simulation experiments substantiated the effectiveness of CIATA-Ph with various rate functions and dispersion ratios. In all cases, we found approximate convergence of the dispersion ratio to its asymptotic value beyond a relatively short warm-up period.

Keywords: nonstationary arrival process; non-Poisson process; time-dependent arrival rate; dispersion ratio; index of dispersion for counts (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:31:y:2019:i:2:p:347-366

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