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Renewal processes of phase type

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  • Marcel F. Neuts

Abstract

This paper discusses a class of analytically and numerically tractable renewal processes, which generalize the Poisson process. When used to describe interarrival or service times in queues, these renewal processes lead to computationally explicit solutions which involve only real arithmetic. Previous modifications of the Poisson process, based on the Erlang or the hyperexponential distributions, appear as particular cases.

Suggested Citation

  • Marcel F. Neuts, 1978. "Renewal processes of phase type," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 25(3), pages 445-454, September.
    • Handle: RePEc:wly:navlog:v:25:y:1978:i:3:p:445-454
    DOI: 10.1002/nav.3800250307
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    Cited by:

    1. Edward P. C. Kao & Marion Spokony Smith, 1992. "On excess‐, current‐, and total‐life distributions of phase‐type renewal processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(6), pages 789-799, October.
    2. Bountzis, P. & Papadimitriou, E. & Tsaklidis, G., 2020. "Earthquake clusters identification through a Markovian Arrival Process (MAP): Application in Corinth Gulf (Greece)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. L. G. Afanaseva & S. A. Grishunina, 2020. "Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 213-241, April.

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