IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v88y2018i3d10.1007_s11134-017-9558-6.html
   My bibliography  Save this article

Probabilistic selfish routing in parallel batch and single-server queues

Author

Listed:
  • A. Wang

    (The University of Auckland)

  • I. Ziedins

    (The University of Auckland)

Abstract

We consider a network of parallel queues, operating under probabilistic routing, where users can choose to join either a batch service queue, or one of several FIFO single-server queues. Afimeimounga et al. (Queueing Syst 49:321–334, 2005) considered the 2-queue case, which is known to exhibit the Downs–Thomson paradox, where delays may increase as capacity is increased. We show that in larger parallel systems, with multiple single-server queues, the user equilibrium is always unique when the batch size is sufficiently large relative to the number of queues; no more than three equilibria exist; Braess paradox may appear when adding extra queues.

Suggested Citation

  • A. Wang & I. Ziedins, 2018. "Probabilistic selfish routing in parallel batch and single-server queues," Queueing Systems: Theory and Applications, Springer, vol. 88(3), pages 389-407, April.
    • Handle: RePEc:spr:queues:v:88:y:2018:i:3:d:10.1007_s11134-017-9558-6
    DOI: 10.1007/s11134-017-9558-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-017-9558-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11134-017-9558-6?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
    ---><---

    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. Watling, David, 1996. "Asymmetric problems and stochastic process models of traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 339-357, October.
    2. Colin E. Bell & Shaler Stidham, Jr., 1983. "Individual versus Social Optimization in the Allocation of Customers to Alternative Servers," Management Science, INFORMS, vol. 29(7), pages 831-839, July.
    3. Arvidsson, Niklas, 2013. "The milk run revisited: A load factor paradox with economic and environmental implications for urban freight transport," Transportation Research Part A: Policy and Practice, Elsevier, vol. 51(C), pages 56-62.
    4. Pengfei Guo & Robin Lindsey & Zhe George Zhang, 2014. "On the Downs–Thomson Paradox in a Self-Financing Two-Tier Queuing System," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 315-322, May.
    5. Pengfei Guo & Zhe George Zhang, 2013. "Strategic Queueing Behavior and Its Impact on System Performance in Service Systems with the Congestion-Based Staffing Policy," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 118-131, September.
    6. D. Braess & G. Koch, 1979. "On the Existence of Equilibria in Asymmetrical Multiclass-User Transportation Networks," Transportation Science, INFORMS, vol. 13(1), pages 56-63, February.
    7. F. H. Knight, 1924. "Some Fallacies in the Interpretation of Social Cost," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 38(4), pages 582-606.
    8. Ward Whitt, 1986. "Deciding Which Queue to Join: Some Counterexamples," Operations Research, INFORMS, vol. 34(1), pages 55-62, 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. Ayane Nakamura & Tuan Phung-Duc, 2023. "Equilibrium Analysis for Batch Service Queueing Systems with Strategic Choice of Batch Size," Mathematics, MDPI, vol. 11(18), pages 1-22, September.
    2. Melia, Dr Steve, 2019. "Why did UK governments cut road building in the 1990s and expand it after 2010?," Transport Policy, Elsevier, vol. 81(C), pages 242-253.
    3. Olga Bountali & Antonis Economou, 2019. "Strategic customer behavior in a two-stage batch processing system," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 3-29, October.

    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. Parlakturk, Ali & Kumar, Sunil, 2004. "Self-Interested Routing in Queueing Networks," Research Papers 1782r, Stanford University, Graduate School of Business.
    2. Athanasia Manou & Antonis Economou & Fikri Karaesmen, 2014. "Strategic Customers in a Transportation Station: When Is It Optimal to Wait?," Operations Research, INFORMS, vol. 62(4), pages 910-925, August.
    3. Ali K. Parlaktürk & Sunil Kumar, 2004. "Self-Interested Routing in Queueing Networks," Management Science, INFORMS, vol. 50(7), pages 949-966, July.
    4. Rob Shone & Vincent A. Knight & Paul R. Harper, 2020. "A conservative index heuristic for routing problems with multiple heterogeneous service facilities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 511-543, December.
    5. Han, Linghui & Wang, David Z.W. & Lo, Hong K. & Zhu, Chengjuan & Cai, Xingju, 2017. "Discrete-time day-to-day dynamic congestion pricing scheme considering multiple equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 1-16.
    6. Watling, David, 1998. "Perturbation stability of the asymmetric stochastic equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 155-171, April.
    7. Olga Bountali & Antonis Economou, 2019. "Strategic customer behavior in a two-stage batch processing system," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 3-29, October.
    8. Zhang, Zhe George & Yin, Xiaoling, 2021. "Information and pricing effects in two-tier public service systems," International Journal of Production Economics, Elsevier, vol. 231(C).
    9. Qian, Qu & Zhuang, Weifen, 2017. "Tax/subsidy and capacity decisions in a two-tier health system with welfare redistributive objective," European Journal of Operational Research, Elsevier, vol. 260(1), pages 140-151.
    10. 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.
    11. Terry E. Daniel & Eyran J. Gisches & Amnon Rapoport, 2009. "Departure Times in Y-Shaped Traffic Networks with Multiple Bottlenecks," American Economic Review, American Economic Association, vol. 99(5), pages 2149-2176, December.
    12. 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.
    13. Élodie Bertrand, 2006. "La thèse d'efficience du « théorème de Coase ». Quelle critique de la microéconomie ?," Revue économique, Presses de Sciences-Po, vol. 57(5), pages 983-1007.
    14. 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.
    15. Mehdiloozad, Mahmood & Zhu, Joe & Sahoo, Biresh K., 2018. "Identification of congestion in data envelopment analysis under the occurrence of multiple projections: A reliable method capable of dealing with negative data," European Journal of Operational Research, Elsevier, vol. 265(2), pages 644-654.
    16. Loukas Dimitriou & Theodore Tsekeris, 2009. "Evolutionary game-theoretic model for dynamic congestion pricing in multi-class traffic networks," Netnomics, Springer, vol. 10(1), pages 103-121, April.
    17. De Palma, Andre & Motamedi, Kiarash & Picard, Nathalie & Waddell, Paul, 2007. "Accessibility and environmental quality: inequality in the Paris housing market," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 36, pages 47-74.
    18. Iryo, Takamasa & Watling, David, 2019. "Properties of equilibria in transport problems with complex interactions between users," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 87-114.
    19. Dariusz Kotlewski, 2022. "Przesłanki za wykorzystaniem rachunkowości wzrostu gospodarczego w badaniu specjalizacji regionalnych," Ekonomista, Polskie Towarzystwo Ekonomiczne, issue 2, pages 235-258.
    20. Winston, Clifford & Yan, Jia, 2011. "Can privatization of U.S. highways improve motorists' welfare?," Journal of Public Economics, Elsevier, vol. 95(7), pages 993-1005.

    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:spr:queues:v:88:y:2018:i:3:d:10.1007_s11134-017-9558-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.