IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v88y2018i1d10.1007_s11134-017-9549-7.html
   My bibliography  Save this article

Many-server scaling of the N-system under FCFS–ALIS

Author

Listed:
  • Dongyuan Zhan

    (University College London)

  • Gideon Weiss

    (The University of Haifa)

Abstract

The N-system with independent Poisson arrivals and exponential server-dependent service times under the first come first served and assign to the longest idle server policy has an explicit steady-state distribution. We scale the arrival rate and the number of servers simultaneously, and obtain the fluid and central limit approximation for the steady state. This is the first step toward exploring the many-server scaling limit behavior of general parallel service systems.

Suggested Citation

  • Dongyuan Zhan & Gideon Weiss, 2018. "Many-server scaling of the N-system under FCFS–ALIS," Queueing Systems: Theory and Applications, Springer, vol. 88(1), pages 27-71, February.
    • Handle: RePEc:spr:queues:v:88:y:2018:i:1:d:10.1007_s11134-017-9549-7
    DOI: 10.1007/s11134-017-9549-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-017-9549-7
    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/s11134-017-9549-7?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. Itay Gurvich & Ward Whitt, 2009. "Queue-and-Idleness-Ratio Controls in Many-Server Service Systems," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 363-396, May.
    2. Ivo Adan & Gideon Weiss, 2012. "Exact FCFS Matching Rates for Two Infinite Multitype Sequences," Operations Research, INFORMS, vol. 60(2), pages 475-489, April.
    3. Itai Gurvich & Ward Whitt, 2010. "Service-Level Differentiation in Many-Server Service Systems via Queue-Ratio Routing," Operations Research, INFORMS, vol. 58(2), pages 316-328, April.
    4. Linda Green, 1985. "A Queueing System with General-Use and Limited-Use Servers," Operations Research, INFORMS, vol. 33(1), pages 168-182, February.
    5. Melanie Rubino & Barış Ata, 2009. "Dynamic Control of a Make-to-Order, Parallel-Server System with Cancellations," Operations Research, INFORMS, vol. 57(1), pages 94-108, February.
    6. Samim Ghamami & Amy R. Ward, 2013. "Dynamic Scheduling of a Two-Server Parallel Server System with Complete Resource Pooling and Reneging in Heavy Traffic: Asymptotic Optimality of a Two-Threshold Policy," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 761-824, November.
    7. Mor Armony & Amy R. Ward, 2010. "Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems," Operations Research, INFORMS, vol. 58(3), pages 624-637, June.
    8. Amy R. Ward & Mor Armony, 2013. "Blind Fair Routing in Large-Scale Service Systems with Heterogeneous Customers and Servers," Operations Research, INFORMS, vol. 61(1), pages 228-243, February.
    9. Tolga Tezcan & J. G. Dai, 2010. "Dynamic Control of N -Systems with Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic," Operations Research, INFORMS, vol. 58(1), pages 94-110, 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. Gideon Weiss, 2022. "Parallel multi-type many server conjecture," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 269-271, April.
    2. Adan, Ivo J.B.F. & Boon, Marko A.A. & Weiss, Gideon, 2019. "Design heuristic for parallel many server systems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 259-277.

    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. Adan, Ivo J.B.F. & Boon, Marko A.A. & Weiss, Gideon, 2019. "Design heuristic for parallel many server systems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 259-277.
    2. Jinsheng Chen & Jing Dong & Pengyi Shi, 2020. "A survey on skill-based routing with applications to service operations management," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 53-82, October.
    3. Wyean Chan & Ger Koole & Pierre L'Ecuyer, 2014. "Dynamic Call Center Routing Policies Using Call Waiting and Agent Idle Times," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 544-560, October.
    4. Ari Arapostathis & Guodong Pang, 2018. "Infinite-Horizon Average Optimality of the N-Network in the Halfin–Whitt Regime," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 838-866, August.
    5. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    6. Arapostathis, Ari & Pang, Guodong, 2019. "Infinite horizon asymptotic average optimality for large-scale parallel server networks," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 283-322.
    7. Jeunghyun Kim & Ramandeep S. Randhawa & Amy R. Ward, 2018. "Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems," Manufacturing & Service Operations Management, INFORMS, vol. 20(2), pages 285-301, May.
    8. Amy R. Ward & Mor Armony, 2013. "Blind Fair Routing in Large-Scale Service Systems with Heterogeneous Customers and Servers," Operations Research, INFORMS, vol. 61(1), pages 228-243, February.
    9. Merve Bodur & James R. Luedtke, 2017. "Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty," Management Science, INFORMS, vol. 63(7), pages 2073-2091, July.
    10. Heng-Li Liu & Quan-Lin Li, 2023. "Matched Queues with Flexible and Impatient Customers," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    11. Siqiao Li & Ger Koole & Xiaolan Xie, 2020. "An adaptive priority policy for radiotherapy scheduling," Flexible Services and Manufacturing Journal, Springer, vol. 32(1), pages 154-180, March.
    12. J. G. Dai & Pengyi Shi, 2019. "Inpatient Overflow: An Approximate Dynamic Programming Approach," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 894-911, October.
    13. Carri W. Chan & Linda V. Green & Suparerk Lekwijit & Lijian Lu & Gabriel Escobar, 2019. "Assessing the Impact of Service Level When Customer Needs Are Uncertain: An Empirical Investigation of Hospital Step-Down Units," Management Science, INFORMS, vol. 65(2), pages 751-775, February.
    14. Mor Armony & Avishai Mandelbaum, 2011. "Routing and Staffing in Large-Scale Service Systems: The Case of Homogeneous Impatient Customers and Heterogeneous Servers," Operations Research, INFORMS, vol. 59(1), pages 50-65, February.
    15. 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.
    16. Ragavendran Gopalakrishnan & Sherwin Doroudi & Amy R. Ward & Adam Wierman, 2016. "Routing and Staffing When Servers Are Strategic," Operations Research, INFORMS, vol. 64(4), pages 1033-1050, August.
    17. Zhong, Zhiheng & Cao, Ping, 2023. "Balanced routing with partial information in a distributed parallel many-server queueing system," European Journal of Operational Research, Elsevier, vol. 304(2), pages 618-633.
    18. Cao, Ping & Zhong, Zhiheng & Huang, Junfei, 2021. "Dynamic routing in a distributed parallel many-server service system: The effect of ξ-choice," European Journal of Operational Research, Elsevier, vol. 294(1), pages 219-235.
    19. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    20. Francisco Castro & Hamid Nazerzadeh & Chiwei Yan, 2020. "Matching queues with reneging: a product form solution," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 359-385, December.

    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:1:d:10.1007_s11134-017-9549-7. 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.