IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v81y1999i2p299-321.html
   My bibliography  Save this article

Differentiability of functionals of Poisson processes via coupling with applications to queueing theory

Author

Listed:
  • Baccelli, François
  • Hasenfuss, Sven
  • Schmidt, Volker

Abstract

We give some probabilistic conditions based on coupling for a functional of a Poisson point process to be differentiable in the intensity [lambda] of this process in a neighborhood of the origin. These conditions are exemplified on various queueing theory problems, and compared with other conditions of the literature.

Suggested Citation

  • Baccelli, François & Hasenfuss, Sven & Schmidt, Volker, 1999. "Differentiability of functionals of Poisson processes via coupling with applications to queueing theory," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 299-321, June.
    • Handle: RePEc:eee:spapps:v:81:y:1999:i:2:p:299-321
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(98)00101-X
    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. Blaszczyszyn, B., 1995. "Factorial moment expansion for stochastic systems," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 321-335, April.
    2. Martin I. Reiman & Burton Simon, 1989. "Open Queueing Systems in Light Traffic," Mathematics of Operations Research, INFORMS, vol. 14(1), pages 26-59, February.
    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. Ilya Molchanov & Sergei Zuyev, 2000. "Variational Analysis of Functionals of Poisson Processes," Mathematics of Operations Research, INFORMS, vol. 25(3), pages 485-508, 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. Ayhan, Hayriye & Schlegel, Sabine, 2001. "Expansion formulae for characteristics of cumulative cost in finite horizon production models," European Journal of Operational Research, Elsevier, vol. 132(1), pages 50-61, July.
    2. Frey, Andreas & Schmidt, Volker, 1996. "Taylor-series expansion for multivariate characteristics of classical risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 18(1), pages 1-12, May.
    3. Blaszczyszyn, Bartlomiej & Merzbach, Ely & Schmidt, Volker, 1997. "A note on expansion for functionals of spatial marked point processes," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 299-306, December.
    4. Igor Kovalenko, 1997. "Ergodic and light traffic properties of a complex repairable system," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(3), pages 387-409, October.
    5. Avishai Mandelbaum & Martin I. Reiman, 1998. "On Pooling in Queueing Networks," Management Science, INFORMS, vol. 44(7), pages 971-981, July.
    6. Blaszczyszyn, B., 1995. "Factorial moment expansion for stochastic systems," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 321-335, April.
    7. Cao, Xi-Ren, 1996. "Perturbation analysis of discrete event systems: Concepts, algorithms, and applications," European Journal of Operational Research, Elsevier, vol. 91(1), pages 1-13, May.

    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:81:y:1999:i:2:p:299-321. 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.