IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v47y1999i3p438-444.html
   My bibliography  Save this article

Optimal Routing of Customers to Two Parallel Heterogeneous Servers: The Case of IHR Service Times

Author

Listed:
  • Esther Frostig

    (University of Haifa, Haifa, Israel)

  • Benny Levikson

    (University of Haifa, Haifa, Israel)

Abstract

We consider here the optimal routing of customers, arriving to a system consisting of two heterogeneous parallel servers. The service times of the two servers have an increasing hazard rate. The arrival process is a general renewal process. The cost of holding x customers in the system per time unit is a nondecreasing and convex function. The objective is to minimize the expected discounted holding cost. We show some monotonicity properties of the optimal policy. Then we show that the optimal policy routes an arriving customer to the fastest server whenever this server has the lowest workload.

Suggested Citation

  • Esther Frostig & Benny Levikson, 1999. "Optimal Routing of Customers to Two Parallel Heterogeneous Servers: The Case of IHR Service Times," Operations Research, INFORMS, vol. 47(3), pages 438-444, June.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:3:p:438-444
    DOI: 10.1287/opre.47.3.438
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.47.3.438
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.47.3.438?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. Johri, Pravin K., 1989. "Optimality of the shortest line discipline with state-dependent service rates," European Journal of Operational Research, Elsevier, vol. 41(2), pages 157-161, July.
    2. 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. Tom F. Tan & Bradley R. Staats, 2020. "Behavioral Drivers of Routing Decisions: Evidence from Restaurant Table Assignment," Production and Operations Management, Production and Operations Management Society, vol. 29(4), pages 1050-1070, April.

    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. P S Ansell & K D Glazebrook & C Kirkbride, 2003. "Generalised ‘join the shortest queue’ policies for the dynamic routing of jobs to multi-class queues," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(4), pages 379-389, April.
    2. 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.
    3. Josh Reed & Yair Shaki, 2015. "A Fair Policy for the G / GI / N Queue with Multiple Server Pools," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 558-595, March.
    4. Parlakturk, Ali & Kumar, Sunil, 2004. "Self-Interested Routing in Queueing Networks," Research Papers 1782r, Stanford University, Graduate School of Business.
    5. 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.
    6. V.D. Dinopoulou & C. Melolidakis, 2001. "Asymptotically optimal component assembly plans in repairable systems and server allocation in parallel multiserver queues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(8), pages 732-746, December.
    7. 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.
    8. Yi Ouyang & Demosthenis Teneketzis, 2022. "Signaling for decentralized routing in a queueing network," Annals of Operations Research, Springer, vol. 317(2), pages 737-775, October.
    9. Yan Chen & Ward Whitt, 2020. "Algorithms for the upper bound mean waiting time in the GI/GI/1 queue," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 327-356, April.
    10. Jazeem Abdul Jaleel & Sherwin Doroudi & Kristen Gardner & Alexander Wickeham, 2022. "A general “power-of-d” dispatching framework for heterogeneous systems," Queueing Systems: Theory and Applications, Springer, vol. 102(3), pages 431-480, December.
    11. 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.
    12. Hong Chen & Heng-Qing Ye, 2012. "Asymptotic Optimality of Balanced Routing," Operations Research, INFORMS, vol. 60(1), pages 163-179, February.
    13. Senthil Veeraraghavan & Laurens Debo, 2009. "Joining Longer Queues: Information Externalities in Queue Choice," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 543-562, April.
    14. 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.
    15. Hyytiä, Esa & Penttinen, Aleksi & Aalto, Samuli, 2012. "Size- and state-aware dispatching problem with queue-specific job sizes," European Journal of Operational Research, Elsevier, vol. 217(2), pages 357-370.
    16. Fernanda Campello & Armann Ingolfsson & Robert A. Shumsky, 2017. "Queueing Models of Case Managers," Management Science, INFORMS, vol. 63(3), pages 882-900, March.
    17. Tolga Tezcan, 2008. "Optimal Control of Distributed Parallel Server Systems Under the Halfin and Whitt Regime," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 51-90, February.
    18. 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.
    19. 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.
    20. Coolen, F. P. A. & Coolen-Schrijner, P., 2003. "A nonparametric predictive method for queues," European Journal of Operational Research, Elsevier, vol. 145(2), pages 425-442, March.

    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:47:y:1999:i:3:p:438-444. 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.