2019 journal article

Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes

INFORMS JOURNAL ON COMPUTING, 31(2), 347–366.

By: R. Liu *, M. Kuhl*, Y. Liu n & J. Wilson n

author keywords: nonstationary arrival process; non-poisson process; time-dependent arrival rate; dispersion radio; index of dispersion for counts
TL;DR: 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 ... (via Semantic Scholar)
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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. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0828 .