IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v44y1998i7p971-981.html
   My bibliography  Save this article

On Pooling in Queueing Networks

Author

Listed:
  • Avishai Mandelbaum

    (Faculty of Industrial Engineering and Management, Technion, Haifa, Israel)

  • Martin I. Reiman

    (Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974)

Abstract

We view each station in a Jackson network as a queue of tasks, of a particular type, which are to be processed by the associated specialized server. A complete pooling of queues, into a single queue, and servers, into a single server, gives rise to an M/PH/1 queue, where the server is flexible in the sense that it processes all tasks. We assess the value of complete pooling by comparing the steady-state mean sojourn times of these two systems. The main insight from our analysis is that care must be used in pooling. Sometimes pooling helps, sometimes it hurts, and its effect (good or bad) can be unbounded. Also discussed briefly are alternative pooling scenarios, for example complete pooling of only queues which results in an M/PH/S system, or partial pooling which can be devastating enough to turn a stable Jackson network into an unstable Bramson network. We conclude with some possible future research directions.

Suggested Citation

  • Avishai Mandelbaum & Martin I. Reiman, 1998. "On Pooling in Queueing Networks," Management Science, INFORMS, vol. 44(7), pages 971-981, July.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:7:p:971-981
    DOI: 10.1287/mnsc.44.7.971
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.44.7.971
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.44.7.971?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. Michael H. Rothkopf & Paul Rech, 1987. "Perspectives on Queues: Combining Queues is Not Always Beneficial," Operations Research, INFORMS, vol. 35(6), pages 906-909, December.
    2. Paul S. Adler & Avi Mandelbaum & Viên Nguyen & Elizabeth Schwerer, 1995. "From Project to Process Management: An Empirically-Based Framework for Analyzing Product Development Time," Management Science, INFORMS, vol. 41(3), pages 458-484, March.
    3. J. G. Dai & Thomas G. Kurtz, 1995. "A multiclass Station with Markovian Feedback in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 721-742, August.
    4. James R. Jackson, 1957. "Networks of Waiting Lines," Operations Research, INFORMS, vol. 5(4), pages 518-521, August.
    5. Hammer, Michael & Champy, James, 1993. "Reengineering the corporation: A manifesto for business revolution," Business Horizons, Elsevier, vol. 36(5), pages 90-91.
    6. Martin I. Reiman & Burton Simon, 1989. "Open Queueing Systems in Light Traffic," Mathematics of Operations Research, INFORMS, vol. 14(1), pages 26-59, February.
    7. J. Michael Harrison, 1975. "A Priority Queue with Discounted Linear Costs," Operations Research, INFORMS, vol. 23(2), pages 260-269, April.
    8. Loch, Christoph, 1998. "Operations management and reengineering," European Management Journal, Elsevier, vol. 16(3), pages 306-317, June.
    9. Joel M. Calabrese, 1992. "Optimal Workload Allocation in Open Networks of Multiserver Queues," Management Science, INFORMS, vol. 38(12), pages 1792-1802, December.
    10. John A. Buzacott, 1996. "Commonalities in Reengineered Business Processes: Models and Issues," Management Science, INFORMS, vol. 42(5), pages 768-782, May.
    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. Andradóttir, Sigrún & Ayhan, Hayriye & Down, Douglas G., 2017. "Resource pooling in the presence of failures: Efficiency versus risk," European Journal of Operational Research, Elsevier, vol. 256(1), pages 230-241.
    2. Tanja Mlinar & Philippe Chevalier, 2016. "Pooling heterogeneous products for manufacturing environments," 4OR, Springer, vol. 14(2), pages 173-200, June.
    3. Rummel, Jeffrey L. & Walter, Zhiping & Dewan, Rajiv & Seidmann, Abraham, 2005. "Activity consolidation to improve responsiveness," European Journal of Operational Research, Elsevier, vol. 161(3), pages 683-703, March.
    4. Suri Gurumurthi & Saif Benjaafar, 2004. "Modeling and analysis of flexible queueing systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(5), pages 755-782, August.
    5. Nilay Tanık Argon & Sigrún Andradóttir, 2017. "Pooling in tandem queueing networks with non-collaborative servers," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 345-377, December.
    6. Evrim D. Günec{s} & O. Zeynep Akc{s}in, 2004. "Value Creation in Service Delivery: Relating Market Segmentation, Incentives, and Operational Performance," Manufacturing & Service Operations Management, INFORMS, vol. 6(4), pages 338-357, May.
    7. Hummy Song & Anita L. Tucker & Karen L. Murrell, 2015. "The Diseconomies of Queue Pooling: An Empirical Investigation of Emergency Department Length of Stay," Management Science, INFORMS, vol. 61(12), pages 3032-3053, December.
    8. Reijers, H. A. & Liman Mansar, S., 2005. "Best practices in business process redesign: an overview and qualitative evaluation of successful redesign heuristics," Omega, Elsevier, vol. 33(4), pages 283-306, August.
    9. Bitran, Gabriel R. & Morabito, Reinaldo., 1994. "Open queueing networks : optimization and performance evaluation models for discrete manufacturing systems," Working papers 3743-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    10. Ward Whitt, 1999. "Partitioning Customers into Service Groups," Management Science, INFORMS, vol. 45(11), pages 1579-1592, November.
    11. Wil M. P. Aalst & Marcello La Rosa & Flávia Maria Santoro, 2016. "Business Process Management," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 58(1), pages 1-6, February.
    12. 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.
    13. Seidmann, Abraham & Sundararajan, Arun, 1997. "The effects of task and information asymmetry on business process redesign," International Journal of Production Economics, Elsevier, vol. 50(2-3), pages 117-128, June.
    14. Wil Aalst & Marcello La Rosa & Flávia Santoro, 2016. "Business Process Management," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 58(1), pages 1-6, February.
    15. Toppen, R. & Smits, M.T. & Ribbers, P.M.A., 1998. "Improving process performance through market network design : A study of the impact of electronic markets in the financial securities sector," Other publications TiSEM c3c8d2ea-7727-475e-83cf-d, Tilburg University, School of Economics and Management.
    16. Sigrún Andradóttir & Hayriye Ayhan & Douglas G. Down, 2001. "Server Assignment Policies for Maximizing the Steady-State Throughput of Finite Queueing Systems," Management Science, INFORMS, vol. 47(10), pages 1421-1439, October.
    17. V.K. Gupta, 2016. "Strategic framework for managing forces of continuity and change in innovation and risk management in service sector: a study of service industry in India," International Journal of Services and Operations Management, Inderscience Enterprises Ltd, vol. 23(1), pages 1-17.
    18. Harry Hummels & Patrick Nullens, 2022. "‘Other-wise’ Organizing. A Levinasian Approach to Agape in Work and Business Organisations," Humanistic Management Journal, Springer, vol. 7(2), pages 211-232, October.
    19. Tina George Karippacheril & Soonhee Kim & Robert P. Jr. Beschel & Changyong Choi, 2016. "Bringing Government into the 21st Century," World Bank Publications - Books, The World Bank Group, number 24579.
    20. Stephan Kudyba, 2006. "Enhancing Organisational Information Flow And Knowledge Creation In Re-Engineering Supply Chain Systems: An Analysis Of The U.S. Automotive Parts And Supplies Model," International Journal of Innovation Management (ijim), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 163-173.

    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:inm:ormnsc:v:44:y:1998:i:7:p:971-981. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.