IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v47y2000i5p440-454.html
   My bibliography  Save this article

Workload distribution of discrete‐time parallel queues with two servers

Author

Listed:
  • P. Patrick Wang

Abstract

We study discrete‐time, parallel queues with two identical servers. Customers arrive randomly at the system and join the queue with the shortest workload that is defined as the total service time required for the server to complete all the customers in the queue. The arrivals are assumed to follow a geometric distribution and the service times are assumed to have a general distribution. It is a no‐jockeying queue. The two‐dimensional state space is truncated into a banded array. The resulting modified queue is studied using the method of probability generating function (pgf) The workload distribution in steady state is obtained in form of pgf. A special case where the service time is a deterministic constant is further investigated. Numerical examples are illustrated. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 440–454, 2000

Suggested Citation

  • P. Patrick Wang, 2000. "Workload distribution of discrete‐time parallel queues with two servers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(5), pages 440-454, August.
    • Handle: RePEc:wly:navres:v:47:y:2000:i:5:p:440-454
    DOI: 10.1002/1520-6750(200008)47:53.0.CO;2-W
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(200008)47:53.0.CO;2-W
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(200008)47:53.0.CO;2-W?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
    ---><---

    References listed on IDEAS

    as
    1. Yiqiang Zhao & Winfried K. Grassmann, 1995. "Queueing Analysis of a Jockeying Model," Operations Research, INFORMS, vol. 43(3), pages 520-529, June.
    2. Kao, Edward P. C. & Lin, Chiunsin, 1990. "A matrix-geometric solution of the jockeying problem," European Journal of Operational Research, Elsevier, vol. 44(1), pages 67-74, January.
    3. B. M. Rao & M. J. M. Posner, 1987. "Algorithmic and approximation analyses of the shorter queue model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 381-398, June.
    4. J. P. C. Blanc, 1992. "The Power-Series Algorithm Applied to the Shortest-Queue Model," Operations Research, INFORMS, vol. 40(1), pages 157-167, February.
    5. Gertsbakh, Ilya, 1984. "The shorter queue problem: A numerical study using the matrix-geometric solution," European Journal of Operational Research, Elsevier, vol. 15(3), pages 374-381, March.
    6. Yiqiang Zhao & W. K. Grassmann, 1990. "The shortest queue model with jockeying," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 773-787, 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. M. Saxena & I. Dimitriou & S. Kapodistria, 2020. "Analysis of the shortest relay queue policy in a cooperative random access network with collisions," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 39-75, February.
    2. Blanc, J.P.C., 2009. "Bad luck when joining the shortest queue," European Journal of Operational Research, Elsevier, vol. 195(1), pages 167-173, May.
    3. Danielle Tibi, 2019. "Martingales and buffer overflow for the symmetric shortest queue model," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 153-190, October.
    4. Sergei A. Dudin & Olga S. Dudina & Olga I. Kostyukova, 2023. "Analysis of a Queuing System with Possibility of Waiting Customers Jockeying between Two Groups of Servers," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    5. Plinio S. Dester & Christine Fricker & Danielle Tibi, 2017. "Stationary analysis of the shortest queue problem," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 211-243, December.
    6. J. P. C. Blanc, 1992. "The Power-Series Algorithm Applied to the Shortest-Queue Model," Operations Research, INFORMS, vol. 40(1), pages 157-167, February.
    7. Partha Chakroborty & Rahul Gill & Pranamesh Chakraborty, 2016. "Analysing queueing at toll plazas using a coupled, multiple-queue, queueing system model: application to toll plaza design," Transportation Planning and Technology, Taylor & Francis Journals, vol. 39(7), pages 675-692, October.
    8. Blanc, J.P.C., 1990. "Performance evaluation of polling systems by means of the power-series algorithm," Research Memorandum FEW 459, Tilburg University, School of Economics and Management.
    9. Herwig Bruneel & Arnaud Devos, 2024. "Explicit Solutions for Coupled Parallel Queues," Mathematics, MDPI, vol. 12(15), pages 1-31, July.
    10. He, Qi-Ming & Chao, Xiuli, 2014. "A tollbooth tandem queue with heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 236(1), pages 177-189.
    11. Simon Martin & Isi Mitrani, 2008. "Analysis of job transfer policies in systems with unreliable servers," Annals of Operations Research, Springer, vol. 162(1), pages 127-141, September.
    12. van den Hout, W.B. & Blanc, J.P.C., 1994. "The power-series algorithm for Markovian queueing networks," Other publications TiSEM 1312893d-c375-4b17-bbbe-3, Tilburg University, School of Economics and Management.
    13. Kevin Granville & Steve Drekic, 2021. "The unobserved waiting customer approximation," Queueing Systems: Theory and Applications, Springer, vol. 99(3), pages 345-396, December.
    14. van den Hout, W.B. & Blanc, J.P.C., 1994. "The Power-Series Algorithm for a Wide Class of Markov Processes," Discussion Paper 1994-87, Tilburg University, Center for Economic Research.
    15. Zhang, Zhongju & Daigle, John, 2012. "Analysis of job assignment with batch arrivals among heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 217(1), pages 149-161.
    16. Li Li & Li Jiang & Liming Liu, 2012. "Service and Price Competition When Customers Are Naive," Production and Operations Management, Production and Operations Management Society, vol. 21(4), pages 747-760, July.
    17. Yina Lu & Andrés Musalem & Marcelo Olivares & Ariel Schilkrut, 2013. "Measuring the Effect of Queues on Customer Purchases," Management Science, INFORMS, vol. 59(8), pages 1743-1763, August.
    18. Nur Sunar & Yichen Tu & Serhan Ziya, 2021. "Pooled vs. Dedicated Queues when Customers Are Delay-Sensitive," Management Science, INFORMS, vol. 67(6), pages 3785-3802, June.
    19. Dieter Fiems & Balakrishna Prabhu & Koen Turck, 2013. "Analytic approximations of queues with lightly- and heavily-correlated autoregressive service times," Annals of Operations Research, Springer, vol. 202(1), pages 103-119, January.
    20. B. M. Rao & M. J. M. Posner, 1987. "Algorithmic and approximation analyses of the shorter queue model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 381-398, June.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:47:y:2000:i:5:p:440-454. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.