IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v59y2011i3p536-549.html

OR FORUM---Little's Law as Viewed on Its 50th Anniversary

Author

Listed:
  • John D. C. Little

    (MIT Sloan School of Management, Cambridge, Massachusetts 02139)

Abstract

Fifty years ago, the author published a paper in Operations Research with the title, “A proof for the queuing formula: L = (lambda)W ” [Little, J. D. C. 1961. A proof for the queuing formula: L = (lambda)W . Oper. Res. 9 (3) 383--387]. Over the years, L = (lambda)W has become widely known as “Little's Law.” Basically, it is a theorem in queuing theory. It has become well known because of its theoretical and practical importance. We report key developments in both areas with the emphasis on practice. In the latter, we collect new material and search for insights on the use of Little's Law within the fields of operations management and computer architecture.

Suggested Citation

  • John D. C. Little, 2011. "OR FORUM---Little's Law as Viewed on Its 50th Anniversary," Operations Research, INFORMS, vol. 59(3), pages 536-549, June.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:3:p:536-549
    DOI: 10.1287/opre.1110.0940
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1110.0940
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1110.0940?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. Dimitris Bertsimas & Daisuke Nakazato, 1995. "The Distributional Little's Law and Its Applications," Operations Research, INFORMS, vol. 43(2), pages 298-310, April.
    2. Daniel P. Heyman & Shaler Stidham, 1980. "The Relation between Customer and Time Averages in Queues," Operations Research, INFORMS, vol. 28(4), pages 983-994, August.
    3. John D. C. Little, 1961. "A Proof for the Queuing Formula: L = (lambda) W," Operations Research, INFORMS, vol. 9(3), pages 383-387, June.
    4. Shaler Stidham, 2002. "Analysis, Design, and Control of Queueing Systems," Operations Research, INFORMS, vol. 50(1), pages 197-216, 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. Rouba Ibrahim & Mor Armony & Achal Bassamboo, 2017. "Does the Past Predict the Future? The Case of Delay Announcements in Service Systems," Management Science, INFORMS, vol. 63(6), pages 1762-1780, June.
    2. Yee Lam Elim Thompson & Gary M. Levine & Weijie Chen & Berkman Sahiner & Qin Li & Nicholas Petrick & Jana G. Delfino & Miguel A. Lago & Qian Cao & Frank W. Samuelson, 2024. "Applying queueing theory to evaluate wait-time-savings of triage algorithms," Queueing Systems: Theory and Applications, Springer, vol. 108(3), pages 579-610, December.
    3. Fajardo, Val Andrei & Drekic, Steve, 2015. "Controlling the workload of M/G/1 queues via the q-policy," European Journal of Operational Research, Elsevier, vol. 243(2), pages 607-617.
    4. Moshe Haviv & Binyamin Oz, 2021. "A busy period approach to some queueing games," Queueing Systems: Theory and Applications, Springer, vol. 97(3), pages 261-277, April.
    5. Barış Ata & Xiaoshan Peng, 2020. "An Optimal Callback Policy for General Arrival Processes: A Pathwise Analysis," Operations Research, INFORMS, vol. 68(2), pages 327-347, March.
    6. Shaler Stidham, 2002. "Analysis, Design, and Control of Queueing Systems," Operations Research, INFORMS, vol. 50(1), pages 197-216, February.
    7. George C. Mytalas & Michael A. Zazanis, 2022. "Service with a queue and a random capacity cart: random processing batches and E-limited policies," Annals of Operations Research, Springer, vol. 317(1), pages 147-178, October.
    8. Hossein Abouee-Mehrizi & Opher Baron, 2016. "State-dependent M/G/1 queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 121-148, February.
    9. Gabriel Zayas‐Cabán & Emmett J. Lodree & David L. Kaufman, 2020. "Optimal Control of Parallel Queues for Managing Volunteer Convergence," Production and Operations Management, Production and Operations Management Society, vol. 29(10), pages 2268-2288, October.
    10. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.
    11. Yifan Liu & Lawrence M. Wein, 2008. "A Queueing Analysis to Determine How Many Additional Beds Are Needed for the Detention and Removal of Illegal Aliens," Management Science, INFORMS, vol. 54(1), pages 1-15, January.
    12. Opher Baron & Oded Berman & Dmitry Krass & Jianfu Wang, 2017. "Strategic Idleness and Dynamic Scheduling in an Open-Shop Service Network: Case Study and Analysis," Manufacturing & Service Operations Management, INFORMS, vol. 19(1), pages 52-71, February.
    13. Zhuang, Weifen & Li, Michael Z.F., 2012. "Monotone optimal control for a class of Markov decision processes," European Journal of Operational Research, Elsevier, vol. 217(2), pages 342-350.
    14. Andreas Klein, 2011. "Die Entwicklung eines agentenbasierten Basismodells zur Bestimmung der deckungsbeitragsmaximierenden Anzahl von Außendienstmitarbeitern," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 21(2), pages 189-210, January.
    15. Opher Baron & Oded Berman & Dmitry Krass & Jianfu Wang, 2014. "Using Strategic Idleness to Improve Customer Service Experience in Service Networks," Operations Research, INFORMS, vol. 62(1), pages 123-140, February.
    16. W. Rogiest & K. Laevens & J. Walraevens & H. Bruneel, 2015. "Random-order-of-service for heterogeneous customers: waiting time analysis," Annals of Operations Research, Springer, vol. 226(1), pages 527-550, March.
    17. Fermín Mallor & Cristina Azcárate & Julio Barado, 2016. "Control problems and management policies in health systems: application to intensive care units," Flexible Services and Manufacturing Journal, Springer, vol. 28(1), pages 62-89, June.
    18. Marco Cello & Giorgio Gnecco & Mario Marchese & Marcello Sanguineti, 2015. "Narrowing the Search for Optimal Call-Admission Policies Via a Nonlinear Stochastic Knapsack Model," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 819-841, March.
    19. Kristen Gardner & Rhonda Righter, 2020. "Product forms for FCFS queueing models with arbitrary server-job compatibilities: an overview," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 3-51, October.
    20. Mehrdad Moshtagh & Jafar Fathali & James MacGregor Smith & Nezam Mahdavi-Amiri, 2019. "Finding an optimal core on a tree network with M/G/c/c state-dependent queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 115-142, February.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:inm:oropre:v:59:y:2011:i:3:p:536-549. 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.