IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v13y2011i2d10.1007_s11009-009-9149-z.html
   My bibliography  Save this article

Maximum Level and Hitting Probabilities in Stochastic Fluid Flows Using Matrix Differential Riccati Equations

Author

Listed:
  • Bruno Sericola

    (INRIA Rennes—Bretagne Atlantique)

  • Marie-Ange Remiche

    (Université Libre de Bruxelles)

Abstract

In this work, we expose a clear methodology to analyze maximum level and hitting probabilities in a Markov driven fluid queue for various initial condition scenarios and in both cases of infinite and finite buffers. Step by step we build up our argument that finally leads to matrix differential Riccati equations for which there exists a unique solution. The power of the methodology resides in the simple probabilistic argument used that permits to obtain analytic solutions of these differential equations. We illustrate our results by a comprehensive fluid model that we exactly solve.

Suggested Citation

  • Bruno Sericola & Marie-Ange Remiche, 2011. "Maximum Level and Hitting Probabilities in Stochastic Fluid Flows Using Matrix Differential Riccati Equations," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 307-328, June.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:2:d:10.1007_s11009-009-9149-z
    DOI: 10.1007/s11009-009-9149-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-009-9149-z
    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/s11009-009-9149-z?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. Fabrice Guillemin & Bruno Sericola, 2007. "Stationary Analysis of a Fluid Queue Driven by Some Countable State Space Markov Chain," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 521-540, December.
    2. V. Ramaswami, 2006. "Passage Times in Fluid Models with Application to Risk Processes," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 497-515, December.
    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. Andreas Löpker, 2016. "On the overflow time of a fluid model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 59-92, August.

    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. Yonit Barron & Dror Hermel, 2017. "Shortage decision policies for a fluid production model with MAP arrivals," International Journal of Production Research, Taylor & Francis Journals, vol. 55(14), pages 3946-3969, July.
    2. Yonit Barron & David Perry & Wolfgang Stadje, 2016. "A make-to-stock production/inventory model with MAP arrivals and phase-type demands," Annals of Operations Research, Springer, vol. 241(1), pages 373-409, June.
    3. Cheung, Eric C.K. & Landriault, David, 2010. "A generalized penalty function with the maximum surplus prior to ruin in a MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 127-134, February.
    4. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
    5. A. S. Dibu & M. J. Jacob & Apostolos D. Papaioannou & Lewis Ramsden, 2021. "Delayed Capital Injections for a Risk Process with Markovian Arrivals," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 1057-1076, September.
    6. Yonit Barron, 2023. "Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements," Mathematics, MDPI, vol. 11(4), pages 1-35, February.
    7. Albrecher, Hansjörg & Badescu, Andrei & Landriault, David, 2008. "On the dual risk model with tax payments," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1086-1094, June.
    8. Yonit Barron, 2022. "A probabilistic approach to the stochastic fluid cash management balance problem," Annals of Operations Research, Springer, vol. 312(2), pages 607-645, May.
    9. Hédi Nabli & Itidel Abdallah, 2023. "Stochastic Fluid Models with Upward Jumps and Phase Transitions," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    10. Ahn, Soohan & Badescu, Andrei L. & Cheung, Eric C.K. & Kim, Jeong-Rae, 2018. "An IBNR–RBNS insurance risk model with marked Poisson arrivals," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 26-42.
    11. Yonit Barron, 2016. "Performance analysis of a reflected fluid production/inventory model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 1-31, February.
    12. Barron, Yonit, 2016. "Clearing control policies for MAP inventory process with lost sales," European Journal of Operational Research, Elsevier, vol. 251(2), pages 495-508.
    13. V. Ramaswami & Douglas Woolford & David Stanford, 2008. "The erlangization method for Markovian fluid flows," Annals of Operations Research, Springer, vol. 160(1), pages 215-225, April.
    14. Nigel Bean & Małgorzata O’Reilly, 2008. "Performance measures of a multi-layer Markovian fluid model," Annals of Operations Research, Springer, vol. 160(1), pages 99-120, April.
    15. Mehmet Akif Yazici & Nail Akar, 2017. "The finite/infinite horizon ruin problem with multi-threshold premiums: a Markov fluid queue approach," Annals of Operations Research, Springer, vol. 252(1), pages 85-99, May.
    16. Yonit Barron, 2016. "Performance analysis of a reflected fluid production/inventory model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 1-31, February.
    17. Jin, Can & Li, Shuanming & Wu, Xueyuan, 2016. "On the occupation times in a delayed Sparre Andersen risk model with exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 304-316.

    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:13:y:2011:i:2:d:10.1007_s11009-009-9149-z. 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.