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Efficient simulation of non-Poisson non-stationary point processes to study queueing approximations

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  • Ma, Ni
  • Whitt, Ward

Abstract

A nonstationary point process can be efficiently simulated by exploiting a representation as the composition of a rate-one process and the cumulative arrival rate function, provided that an efficient algorithm is available for generating the rate-one process, as is the case for stationary renewal processes, Markov modulated Poisson processes and many other processes. Overall efficiency can be achieved by constructing a table of the inverse cumulative arrival rate function when it is not explicitly available.

Suggested Citation

  • Ma, Ni & Whitt, Ward, 2016. "Efficient simulation of non-Poisson non-stationary point processes to study queueing approximations," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 202-207.
    • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:202-207
    DOI: 10.1016/j.spl.2015.11.018
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    References listed on IDEAS

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    1. Athanassios N. Avramidis & Alexandre Deslauriers & Pierre L'Ecuyer, 2004. "Modeling Daily Arrivals to a Telephone Call Center," Management Science, INFORMS, vol. 50(7), pages 896-908, July.
    2. Lawrence M. Leemis, 1991. "Nonparametric Estimation of the Cumulative Intensity Function for a Nonhomogeneous Poisson Process," Management Science, INFORMS, vol. 37(7), pages 886-900, July.
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    4. Ira Gerhardt & Barry L. Nelson, 2009. "Transforming Renewal Processes for Simulation of Nonstationary Arrival Processes," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 630-640, November.
    5. Song-Hee Kim & Ward Whitt, 2014. "Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 464-480, July.
    6. Geurt Jongbloed & Ger Koole, 2001. "Managing uncertainty in call centres using Poisson mixtures," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 17(4), pages 307-318, October.
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    Cited by:

    1. Yongkyu Cho & Young Myoung Ko, 2020. "Stabilizing the virtual response time in single-server processor sharing queues with slowly time-varying arrival rates," Annals of Operations Research, Springer, vol. 293(1), pages 27-55, October.
    2. Noa Zychlinski & Avishai Mandelbaum & Petar Momčilović, 2018. "Time-varying tandem queues with blocking: modeling, analysis, and operational insights via fluid models with reflection," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 15-47, June.
    3. Nasr, Walid W. & Elshar, Ibrahim J., 2018. "Continuous inventory control with stochastic and non-stationary Markovian demand," European Journal of Operational Research, Elsevier, vol. 270(1), pages 198-217.
    4. Ward Whitt & Jingtong Zhao, 2017. "Many‐server loss models with non‐poisson time‐varying arrivals," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(3), pages 177-202, April.

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