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Semi-Markov modulated Poisson process: probabilistic and statistical analysis

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  • S. Özekici
  • R. Soyer

Abstract

We consider a Poisson process that is modulated in such a way that the arrival rate at any time depends on the state of a semi-Markov process. This presents an interesting generalization of Poisson processes with important implications in real life applications. Our analysis concentrates on the transient as well as the long term behaviour of the arrival count and the arrival time processes. We discuss probabilistic as well as statistical issues related to various quantities of interest. Copyright Springer-Verlag 2006

Suggested Citation

  • S. Özekici & R. Soyer, 2006. "Semi-Markov modulated Poisson process: probabilistic and statistical analysis," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 125-144, August.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:1:p:125-144
    DOI: 10.1007/s00186-006-0067-3
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    References listed on IDEAS

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    1. Ozekici, S. & Soyer, R., 2003. "Reliability of software with an operational profile," European Journal of Operational Research, Elsevier, vol. 149(2), pages 459-474, September.
    2. Erdem, Asli Sencer & Ozekici, Suleyman, 2002. "Inventory models with random yield in a random environment," International Journal of Production Economics, Elsevier, vol. 78(3), pages 239-253, August.
    3. S. Özekici & R. Soyer, 2003. "Bayesian analysis of Markov Modulated Bernoulli Processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(1), pages 125-140, April.
    4. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
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    Cited by:

    1. Ramírez-Cobo, Pepa, 2017. "Findings about the two-state BMMPP for modeling point processes in reliability and queueing systems," DES - Working Papers. Statistics and Econometrics. WS 24622, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Ahmadi, Reza & Newby, Martin, 2011. "Maintenance scheduling of a manufacturing system subject to deterioration," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1411-1420.
    3. Ahmadi, Reza & Fouladirad, Mitra, 2017. "Maintenance planning for a deteriorating production process," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 108-118.
    4. Landon, Joshua & Özekici, Süleyman & Soyer, Refik, 2013. "A Markov modulated Poisson model for software reliability," European Journal of Operational Research, Elsevier, vol. 229(2), pages 404-410.

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