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Stationary probabilities for a simple immigration-birth-death process under the influence of total catastrophes

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  • Kyriakidis, E. G.

Abstract

In this note a simple immigration--birth--death process is considered, which is influenced by total catastrophes that are introduced with constant rate. The stationary probabilities are derived using a renewal argument.

Suggested Citation

  • Kyriakidis, E. G., 1994. "Stationary probabilities for a simple immigration-birth-death process under the influence of total catastrophes," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 239-240, June.
    • Handle: RePEc:eee:stapro:v:20:y:1994:i:3:p:239-240
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    Citations

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    Cited by:

    1. Economou, Antonis & Fakinos, Demetrios, 2003. "A continuous-time Markov chain under the influence of a regulating point process and applications in stochastic models with catastrophes," European Journal of Operational Research, Elsevier, vol. 149(3), pages 625-640, September.
    2. Spiros Dimou & Antonis Economou, 2013. "The Single Server Queue with Catastrophes and Geometric Reneging," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 595-621, September.
    3. Román Zapién-Campos & Michael Sieber & Arne Traulsen, 2020. "Stochastic colonization of hosts with a finite lifespan can drive individual host microbes out of equilibrium," PLOS Computational Biology, Public Library of Science, vol. 16(11), pages 1-20, November.
    4. Antonis Economou & Athanasia Manou, 2013. "Equilibrium balking strategies for a clearing queueing system in alternating environment," Annals of Operations Research, Springer, vol. 208(1), pages 489-514, September.
    5. Di Crescenzo, A. & Giorno, V. & Nobile, A.G. & Ricciardi, L.M., 2008. "A note on birth-death processes with catastrophes," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2248-2257, October.
    6. Vijay Rajan Lumb & Indra Rani, 2022. "Analytically simple solution to discrete-time queue with catastrophes, balking and state-dependent service," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 783-817, April.
    7. Economou, Antonis, 2003. "On the control of a compound immigration process through total catastrophes," European Journal of Operational Research, Elsevier, vol. 147(3), pages 522-529, June.

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