IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v61y2003i4p359-371.html
   My bibliography  Save this article

A law of the iterated logarithm for global values of waiting time in multiphase queues

Author

Listed:
  • Minkevicius, Saulius
  • Steisunas, Stasys

Abstract

The target of this research in the queueing theory is to prove the law of the iterated logarithm (LIL) under the conditions of heavy traffic in multiphase queueing systems. In this paper, the LIL for global extreme values (maximum and minimum) is proved in the phases of a queueing system studied for an important probability characteristic of system (waiting time of a customer).

Suggested Citation

  • Minkevicius, Saulius & Steisunas, Stasys, 2003. "A law of the iterated logarithm for global values of waiting time in multiphase queues," Statistics & Probability Letters, Elsevier, vol. 61(4), pages 359-371, February.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:4:p:359-371
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(02)00393-0
    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. Martin I. Reiman, 1984. "Open Queueing Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 441-458, August.
    2. Sakalauskas, L. L. & Minkevicius, S., 2000. "On the law of the iterated logarithm in open queueing networks," European Journal of Operational Research, Elsevier, vol. 120(3), pages 632-640, February.
    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. Saulius Minkevičius & Edvinas Greičius, 2019. "Heavy Traffic Limits for the Extreme Waiting Time in Multi-phase Queueing Systems," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 109-124, March.
    2. Saulius MinkeviÄ ius, 2020. "On the law of the iterated logarithm in hybrid multiphase queueing systems," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 30(4), pages 57-64.
    3. Yongjiang Guo & Yunan Liu & Renhu Pei, 2018. "Functional law of the iterated logarithm for multi-server queues with batch arrivals and customer feedback," Annals of Operations Research, Springer, vol. 264(1), pages 157-191, May.
    4. Edvinas Greičius & Saulius Minkevičius, 2017. "Diffusion limits for the queue length of jobs in multi-server open queueing networks," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(4), pages 71-84.
    5. Saulius Minkevičius & Vladimiras Dolgopolovas & Leonidas L. Sakalauskas, 2016. "A Law of the Iterated Logarithm for the Sojourn Time Process in Queues in Series," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 37-57, March.
    6. Josh Reed & Yair Shaki, 2015. "A Fair Policy for the G / GI / N Queue with Multiple Server Pools," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 558-595, March.
    7. Saulius Minkevičius & Igor Katin & Joana Katina & Irina Vinogradova-Zinkevič, 2021. "On Little’s Formula in Multiphase Queues," Mathematics, MDPI, vol. 9(18), pages 1-15, September.
    8. Amarjit Budhiraja & Chihoon Lee, 2009. "Stationary Distribution Convergence for Generalized Jackson Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 45-56, February.
    9. Budhiraja, Amarjit & Lee, Chihoon, 2007. "Long time asymptotics for constrained diffusions in polyhedral domains," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1014-1036, August.
    10. Zhen Xu & Jiheng Zhang & Rachel Q. Zhang, 2019. "Instantaneous Control of Brownian Motion with a Positive Lead Time," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 943-965, August.
    11. David M. Markowitz & Martin I. Reiman & Lawrence M. Wein, 2000. "The Stochastic Economic Lot Scheduling Problem: Heavy Traffic Analysis of Dynamic Cyclic Policies," Operations Research, INFORMS, vol. 48(1), pages 136-154, February.
    12. I. Venkat Appal Raju & S. Ramasubramanian, 2016. "Risk Diversifying Treaty Between Two Companies with Only One in Insurance Business," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 183-214, November.
    13. Mor Armony & Constantinos Maglaras, 2004. "On Customer Contact Centers with a Call-Back Option: Customer Decisions, Routing Rules, and System Design," Operations Research, INFORMS, vol. 52(2), pages 271-292, April.
    14. Biswas, Anup & Budhiraja, Amarjit, 2011. "Exit time and invariant measure asymptotics for small noise constrained diffusions," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 899-924.
    15. Avi Mandelbaum & Kavita Ramanan, 2010. "Directional Derivatives of Oblique Reflection Maps," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 527-558, August.
    16. David M. Markowitz & Lawrence M. Wein, 2001. "Heavy Traffic Analysis of Dynamic Cyclic Policies: A Unified Treatment of the Single Machine Scheduling Problem," Operations Research, INFORMS, vol. 49(2), pages 246-270, April.
    17. Itai Gurvich, 2014. "Validity of Heavy-Traffic Steady-State Approximations in Multiclass Queueing Networks: The Case of Queue-Ratio Disciplines," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 121-162, February.
    18. Yamada, Keigo, 1999. "Two limit theorems for queueing systems around the convergence of stochastic integrals with respect to renewal processes," Stochastic Processes and their Applications, Elsevier, vol. 80(1), pages 103-128, March.
    19. Ward Whitt & Wei You, 2020. "Heavy-traffic limits for stationary network flows," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 53-68, June.
    20. Atar, Rami & Shadmi, Yonatan, 2023. "Fluid limits for earliest-deadline-first networks," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 279-307.

    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:61:y:2003:i:4:p:359-371. 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.