IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v83y2013i3p718-723.html
   My bibliography  Save this article

Functional strong law of large numbers for loads in a planar network model

Author

Listed:
  • Torrisi, Giovanni Luca

Abstract

In this note we consider a planar network with three bins located at the vertices of an equilateral triangle and customers which are uniformly distributed on the triangle and have Poisson arrival times and general sojourn times. We show that the allocation which minimizes the bin loads and that one which affiliates each customer to its less costly bin satisfy the same functional strong law of large numbers.

Suggested Citation

  • Torrisi, Giovanni Luca, 2013. "Functional strong law of large numbers for loads in a planar network model," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 718-723.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:718-723
    DOI: 10.1016/j.spl.2012.11.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212004294
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2012.11.013?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. Iglehart, Donald L., 1973. "Weak convergence of compound stochastic process, I," Stochastic Processes and their Applications, Elsevier, vol. 1(1), pages 11-31, January.
    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. Eugene Furman & Adam Diamant & Murat Kristal, 2021. "Customer Acquisition and Retention: A Fluid Approach for Staffing," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4236-4257, November.
    2. J. G. Dai & Tolga Tezcan, 2011. "State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 271-320, May.
    3. Pang, Guodong & Zhou, Yuhang, 2018. "Functional limit theorems for a new class of non-stationary shot noise processes," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 505-544.
    4. Iksanov, Alexander, 2013. "Functional limit theorems for renewal shot noise processes with increasing response functions," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 1987-2010.
    5. Avishai Mandelbaum & Petar Momčilović, 2012. "Queues with Many Servers and Impatient Customers," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 41-65, February.

    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:stapro:v:83:y:2013:i:3:p:718-723. 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/622892/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.