IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v98y2002i1p1-22.html
   My bibliography  Save this article

Ergodicity of one-dimensional resource sharing systems

Author

Listed:
  • Andjel, Enrique
  • López, F. Javier
  • Sanz, Gerardo

Abstract

We study one-dimensional resource sharing systems which can be seen as interacting particle systems taking values in . We first get, by coupling techniques, an estimate of their invariant measures. Then, for processes having a reversible measure, we show the uniqueness of the invariant measure and conclude that they are ergodic. As a consequence, we prove that every loss network on with calls of bounded length is ergodic.

Suggested Citation

  • Andjel, Enrique & López, F. Javier & Sanz, Gerardo, 2002. "Ergodicity of one-dimensional resource sharing systems," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 1-22, March.
    • Handle: RePEc:eee:spapps:v:98:y:2002:i:1:p:1-22
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(01)00138-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Graham, Carl & Méléard, Sylvie, 1994. "Fluctuations for a fully connected loss network with alternate routing," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 97-115, September.
    2. Satoru Fujishige & Naoki Katoh & Tetsuo Ichimori, 1988. "The Fair Resource Allocation Problem with Submodular Constraints," Mathematics of Operations Research, INFORMS, vol. 13(1), pages 164-173, February.
    3. Hunt, P. J. & Kurtz, T. G., 1994. "Large loss networks," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 363-378, October.
    Full references (including those not matched with items on IDEAS)

    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. Itai Gurvich & Ohad Perry, 2012. "Overflow Networks: Approximations and Implications to Call Center Outsourcing," Operations Research, INFORMS, vol. 60(4), pages 996-1009, August.
    2. Lee, Zu-Hsu & Deng, Shiming & Lin, Beixin & Yang, James G.S., 2010. "Decision model and analysis for investment interest expense deduction and allocation," European Journal of Operational Research, Elsevier, vol. 200(1), pages 268-280, January.
    3. Mor Harchol-Balter, 2021. "Open problems in queueing theory inspired by datacenter computing," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 3-37, February.
    4. Golshid Baharian & Tolga Tezcan, 2011. "Stability analysis of parallel server systems under longest queue first," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 257-279, October.
    5. Khaled Elbassioni & Areg Karapetyan & Trung Thanh Nguyen, 2019. "Approximation schemes for r-weighted Minimization Knapsack problems," Annals of Operations Research, Springer, vol. 279(1), pages 367-386, August.
    6. Ohad Perry & Ward Whitt, 2013. "A Fluid Limit for an Overloaded X Model via a Stochastic Averaging Principle," Mathematics of Operations Research, INFORMS, vol. 38(2), pages 294-349, May.
    7. Harwin De Vries & Lisa E. Swinkels & Luk N. Van Wassenhove, 2021. "Site Visit Frequency Policies for Mobile Family Planning Services," Production and Operations Management, Production and Operations Management Society, vol. 30(12), pages 4522-4540, December.
    8. Renato de Matta & Vernon Ning Hsu & Timothy J. Lowe, 1999. "The selection allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 707-725, September.
    9. Adam Kasperski & Paweł Zieliński, 2009. "A randomized algorithm for the min-max selecting items problem with uncertain weights," Annals of Operations Research, Springer, vol. 172(1), pages 221-230, November.
    10. Ellen Cardinaels & Sem C. Borst & Johan S. H. Leeuwaarden, 2019. "Job assignment in large-scale service systems with affinity relations," Queueing Systems: Theory and Applications, Springer, vol. 93(3), pages 227-268, December.
    11. Debankur Mukherjee & Sem C. Borst & Johan S. H. van Leeuwaarden & Philip A. Whiting, 2020. "Asymptotic Optimality of Power-of- d Load Balancing in Large-Scale Systems," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1535-1571, November.
    12. Chassein, André & Goerigk, Marc & Kasperski, Adam & Zieliński, Paweł, 2018. "On recoverable and two-stage robust selection problems with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 265(2), pages 423-436.
    13. Yiran Liu & Harsha Honnappa & Samy Tindel & Nung Kwan Yip, 2021. "Infinite server queues in a random fast oscillatory environment," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 145-179, June.
    14. Kurt M. Bretthauer & Bala Shetty & Siddhartha Syam, 2003. "A specially structured nonlinear integer resource allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 770-792, October.
    15. Jun Luo & Jiheng Zhang, 2013. "Staffing and Control of Instant Messaging Contact Centers," Operations Research, INFORMS, vol. 61(2), pages 328-343, April.
    16. Ohad Perry & Ward Whitt, 2011. "A Fluid Approximation for Service Systems Responding to Unexpected Overloads," Operations Research, INFORMS, vol. 59(5), pages 1159-1170, October.
    17. Castiel, Eyal & Borst, Sem & Miclo, Laurent & Simatos, Florian & Whiting, Phil, 2020. "Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms," TSE Working Papers 20-1129, Toulouse School of Economics (TSE).
    18. Varun Gupta & Neil Walton, 2019. "Load Balancing in the Nondegenerate Slowdown Regime," Operations Research, INFORMS, vol. 67(1), pages 281-294, January.
    19. Onno Boxma & Offer Kella & Uri Yechiali, 2016. "An ASIP model with general gate opening intervals," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 1-20, October.
    20. Mor Harchol-Balter, 2022. "The multiserver job queueing model," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 201-203, April.

    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:98:y:2002:i:1:p:1-22. 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.