IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v124y2014i5p1741-1772.html
   My bibliography  Save this article

The stochastic fluid–fluid model: A stochastic fluid model driven by an uncountable-state process, which is a stochastic fluid model itself

Author

Listed:
  • Bean, Nigel G.
  • O’Reilly, Małgorzata M.

Abstract

We introduce the Stochastic Fluid–Fluid Model, which offers powerful modeling ability for a wide range of real-life systems of significance. We first derive the infinitesimal generator, with respect to time, of the driving stochastic fluid model. We then use this to derive the infinitesimal generator of a particular Laplace–Stieltjes transform of the model, which is the foundation of our analysis. We develop expressions for the Laplace–Stieltjes transforms of various performance measures for the transient and limiting analysis of the model. This work is the first direct analysis of a stochastic fluid model that is Markovian on a continuous state space.

Suggested Citation

  • Bean, Nigel G. & O’Reilly, Małgorzata M., 2014. "The stochastic fluid–fluid model: A stochastic fluid model driven by an uncountable-state process, which is a stochastic fluid model itself," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1741-1772.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:5:p:1741-1772
    DOI: 10.1016/j.spa.2013.12.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414913003037
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2013.12.006?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. Bean, Nigel G. & O'Reilly, Malgorzata M. & Taylor, Peter G., 2005. "Hitting probabilities and hitting times for stochastic fluid flows," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1530-1556, September.
    2. 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.
    3. D. R. Bellwood & T. P. Hughes & C. Folke & M. Nyström, 2004. "Confronting the coral reef crisis," Nature, Nature, vol. 429(6994), pages 827-833, 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. Samuelson, Aviva & Haigh, Andrew & O'Reilly, Małgorzata M. & Bean, Nigel G., 2017. "Stochastic model for maintenance in continuously deteriorating systems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1169-1179.
    2. Nigel Bean & Angus Lewis & Giang T. Nguyen & Małgorzata M. O’Reilly & Vikram Sunkara, 2022. "A Discontinuous Galerkin Method for Approximating the Stationary Distribution of Stochastic Fluid-Fluid Processes," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2823-2864, December.
    3. Nikki Sonenberg & Peter G. Taylor, 2019. "Networks of interacting stochastic fluid models with infinite and finite buffers," Queueing Systems: Theory and Applications, Springer, vol. 92(3), pages 293-322, 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. O’Reilly, Małgorzata M., 2014. "Multi-stage stochastic fluid models for congestion control," European Journal of Operational Research, Elsevier, vol. 238(2), pages 514-526.
    2. Samuelson, Aviva & Haigh, Andrew & O'Reilly, Małgorzata M. & Bean, Nigel G., 2017. "Stochastic model for maintenance in continuously deteriorating systems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1169-1179.
    3. Teh, Louise S.L. & Teh, Lydia C.L. & Rashid Sumaila, U., 2014. "Time preference of small-scale fishers in open access and traditionally managed reef fisheries," Marine Policy, Elsevier, vol. 44(C), pages 222-231.
    4. Yutaka Sakuma & Onno Boxma & Tuan Phung-Duc, 2021. "An M/PH/1 queue with workload-dependent processing speed and vacations," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 373-405, August.
    5. Yu-Rong Cheng & Chi-Hsiang Chin & Ding-Fa Lin & Chao-Kang Wang, 2020. "The Probability of an Unrecoverable Coral Community in Dongsha Atoll Marine National Park Due to Recurrent Disturbances," Sustainability, MDPI, vol. 12(21), pages 1-20, October.
    6. Conrad W Speed & Russ C Babcock & Kevin P Bancroft & Lynnath E Beckley & Lynda M Bellchambers & Martial Depczynski & Stuart N Field & Kim J Friedman & James P Gilmour & Jean-Paul A Hobbs & Halina T Ko, 2013. "Dynamic Stability of Coral Reefs on the West Australian Coast," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-12, July.
    7. Wamukota, A. & Brewer, T.D. & Crona, B., 2014. "Market integration and its relation to income distribution and inequality among fishers and traders: The case of two small-scale Kenyan reef fisheries," Marine Policy, Elsevier, vol. 48(C), pages 93-101.
    8. Reiji Masuda, 2020. "Tropical fishes vanished after the operation of a nuclear power plant was suspended in the Sea of Japan," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-13, May.
    9. Christine Bergman & Rochelle Good & Andrew Moreo, 2022. "Influencing Hotel Patrons to Use Reef-Safe Sunscreen," Tourism and Hospitality, MDPI, vol. 3(3), pages 1-22, June.
    10. Chambers, Paul E. & Glenn Dutcher, E. & Mark Isaac, R., 2018. "Improving Environmental Quality Through Aid: An Experimental Analysis of Aid Structures With Heterogeneous Agents," Ecological Economics, Elsevier, vol. 146(C), pages 435-446.
    11. Srinivasan, Venkatraman & Kumar, Praveen, 2015. "Emergent and divergent resilience behavior in catastrophic shift systems," Ecological Modelling, Elsevier, vol. 298(C), pages 87-105.
    12. Pittman, S.J. & Christensen, J.D. & Caldow, C. & Menza, C. & Monaco, M.E., 2007. "Predictive mapping of fish species richness across shallow-water seascapes in the Caribbean," Ecological Modelling, Elsevier, vol. 204(1), pages 9-21.
    13. Matthew J. Powell-Palm & E. Michael Henley & Anthony N. Consiglio & Claire Lager & Brooke Chang & Riley Perry & Kendall Fitzgerald & Jonathan Daly & Boris Rubinsky & Mary Hagedorn, 2023. "Cryopreservation and revival of Hawaiian stony corals using isochoric vitrification," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    14. Brathwaite, Angelique & Pascal, Nicolas & Clua, Eric, 2021. "When are payment for ecosystems services suitable for coral reef derived coastal protection?: A review of scientific requirements," Ecosystem Services, Elsevier, vol. 49(C).
    15. Muko, Soyoka & Arakaki, Seiji & Tamai, Reiko & Sakai, Kazuhiko, 2014. "An individual-based model for population viability analysis of the brooding coral Seriatopora hystrix," Ecological Modelling, Elsevier, vol. 277(C), pages 68-76.
    16. Alexandre C. Siqueira & Wolfgang Kiessling & David R. Bellwood, 2022. "Fast-growing species shape the evolution of reef corals," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    17. Gábor Horváth & Miklós Telek, 2017. "Matrix-analytic solution of infinite, finite and level-dependent second-order fluid models," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 325-343, December.
    18. Bean, Nigel G. & Nguyen, Giang T. & Nielsen, Bo F. & Peralta, Oscar, 2022. "RAP-modulated fluid processes: First passages and the stationary distribution," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 308-340.
    19. Meixia Zhao & Haiyang Zhang & Yu Zhong & Dapeng Jiang & Guohui Liu & Hongqiang Yan & Hongyu Zhang & Pu Guo & Cuitian Li & Hongqiang Yang & Tegu Chen & Rui Wang, 2019. "The Status of Coral Reefs and Its Importance for Coastal Protection: A Case Study of Northeastern Hainan Island, South China Sea," Sustainability, MDPI, vol. 11(16), pages 1-13, August.
    20. Jan Tebben & James R Guest & Tsai M Sin & Peter D Steinberg & Tilmann Harder, 2014. "Corals Like It Waxed: Paraffin-Based Antifouling Technology Enhances Coral Spat Survival," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-8, January.

    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:eee:spapps:v:124:y:2014:i:5:p:1741-1772. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.