IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v21y2019i1d10.1007_s11009-018-9643-2.html
   My bibliography  Save this article

Batch Renewal Arrival Process Subject to Geometric Catastrophes

Author

Listed:
  • F. P. Barbhuiya

    (Indian Institute of Technology Kharagpur)

  • Nitin Kumar

    (Indian Institute of Technology Kharagpur)

  • U. C. Gupta

    (Indian Institute of Technology Kharagpur)

Abstract

We consider a stochastic model where a population grows in batches according to renewal arrival process. The population is prone to be affected by catastrophes which occur according to Poisson process. The catastrophe starts the destruction of the population sequentially, with one individual at a time, with probability p. This process comes to an end when the first individual survives or when the entire population is eliminated. Using supplementary variable and difference equation method we obtain explicit expressions of population size distribution in steady-state at pre-arrival and arbitrary epochs, in terms of roots of the associated characteristic equation. Besides, we prove that the distribution at pre-arrival epoch is asymptotically geometric. Based on our theoretical work we present few numerical results to demonstrate the efficiency of our methodology. We also investigate the impact of different parameters on the behavior of the model through some numerical examples.

Suggested Citation

  • F. P. Barbhuiya & Nitin Kumar & U. C. Gupta, 2019. "Batch Renewal Arrival Process Subject to Geometric Catastrophes," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 69-83, March.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:1:d:10.1007_s11009-018-9643-2
    DOI: 10.1007/s11009-018-9643-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-018-9643-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-018-9643-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Epaminondas G. Kyriakidis & Theodosis D. Dimitrakos, 2005. "Computation of the Optimal Policy for the Control of a Compound Immigration Process through Total Catastrophes," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 97-118, March.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nitin Kumar & U. C. Gupta, 2020. "A Renewal Generated Geometric Catastrophe Model with Discrete-Time Markovian Arrival Process," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1293-1324, September.
    2. Veena Goswami & Gopinath Panda, 2024. "Analysis of Renewal Batch Arrival Queues with Multiple Vacations and Geometric Abandonment," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-27, June.
    3. Nitin Kumar & Umesh Chandra Gupta, 2022. "Markovian Arrival Process Subject to Renewal Generated Binomial Catastrophes," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2287-2312, December.
    4. Nitin Kumar & F. P. Barbhuiya & U. C. Gupta, 2020. "Unified killing mechanism in a single server queue with renewal input," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 246-259, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nitin Kumar & Umesh Chandra Gupta, 2022. "Markovian Arrival Process Subject to Renewal Generated Binomial Catastrophes," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2287-2312, December.
    2. 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.
    3. Antonio Di Crescenzo & Virginia Giorno & Balasubramanian Krishna Kumar & Amelia G. Nobile, 2018. "A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation," Mathematics, MDPI, vol. 6(5), pages 1-23, May.
    4. Dimitrios Logothetis & Antonis Economou, 2023. "The impact of information on transportation systems with strategic customers," Production and Operations Management, Production and Operations Management Society, vol. 32(7), pages 2189-2206, July.
    5. Nitin Kumar & U. C. Gupta, 2020. "Analysis of batch Bernoulli process subject to discrete-time renewal generated binomial catastrophes," Annals of Operations Research, Springer, vol. 287(1), pages 257-283, April.
    6. Di Crescenzo, Antonio & Giorno, Virginia & Nobile, Amelia G., 2016. "Constructing transient birth–death processes by means of suitable transformations," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 152-171.
    7. Ye Jingjing & Liu Liwei & Jiang Tao, 2016. "Analysis of a Single-Sever Queue with Disasters and Repairs Under Bernoulli Vacation Schedule," Journal of Systems Science and Information, De Gruyter, vol. 4(6), pages 547-559, December.
    8. Zhang Xiaoyan & Liu Liwei & Jiang Tao, 2015. "Analysis of an M/G/1 Stochastic Clearing Queue in a 3-Phase Environment," Journal of Systems Science and Information, De Gruyter, vol. 3(4), pages 374-384, August.
    9. Nitin Kumar & U. C. Gupta, 2020. "A Renewal Generated Geometric Catastrophe Model with Discrete-Time Markovian Arrival Process," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1293-1324, September.
    10. Junping Li, 2024. "Birth–Death Processes with Two-Type Catastrophes," Mathematics, MDPI, vol. 12(10), pages 1-17, May.
    11. Altay, Nezih & Green III, Walter G., 2006. "OR/MS research in disaster operations management," European Journal of Operational Research, Elsevier, vol. 175(1), pages 475-493, November.
    12. Epaminondas G. Kyriakidis & Theodosis D. Dimitrakos, 2005. "Computation of the Optimal Policy for the Control of a Compound Immigration Process through Total Catastrophes," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 97-118, March.
    13. Gopinath Panda & Veena Goswami & Abhijit Datta Banik, 2016. "Equilibrium and Socially Optimal Balking Strategies in Markovian Queues with Vacations and Sequential Abandonment," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-34, October.
    14. 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.
    15. Paula R. Bouzas & Nuria Ruiz-Fuentes & Carmen Montes-Gijón & Juan Eloy Ruiz-Castro, 2021. "Forecasting counting and time statistics of compound Cox processes: a focus on intensity phase type process, deletions and simultaneous events," Statistical Papers, Springer, vol. 62(1), pages 235-265, February.
    16. Giorno, Virginia & Nobile, Amelia G., 2022. "On some integral equations for the evaluation of first-passage-time densities of time-inhomogeneous birth-death processes," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    17. Antonio Crescenzo & Virginia Giorno & Balasubramanian Krishna Kumar & Amelia G. Nobile, 2012. "A Double-ended Queue with Catastrophes and Repairs, and a Jump-diffusion Approximation," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 937-954, December.
    18. 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.
    19. Kyritsis, Ioannis E. & Tabakis, Nikolaos M., 2009. "A Generalized Model for Birth and Death Mathematical Procedures in the Visitor Management: Evidence from a Protected Area," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 8(2).
    20. Giorno, Virginia & Nobile, Amelia G., 2020. "On a class of birth-death processes with time-varying intensity functions," Applied Mathematics and Computation, Elsevier, vol. 379(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:21:y:2019:i:1:d:10.1007_s11009-018-9643-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.