IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v51y2003i5p748-758.html
   My bibliography  Save this article

Necessary and Sufficient Conditions for Delay Moments in FIFO Multiserver Queues with an Application Comparing s Slow Servers with One Fast One

Author

Listed:
  • Alan Scheller-Wolf

    (Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890)

Abstract

In this paper we establish the weakest known sufficient conditions for the existence of stationary delay moments in FIFO GI/GI/s queues, for s (ge)2. These conditions involve not only the service time distribution, as in the classic Kiefer and Wolfowitz conditions, but also the interplay of the traffic intensity and the number of servers in the queue. We then prove the necessity of our conditions for a large class of service times having finite first, but infinite (alpha)th, moment for some finite (alpha). Such service time distributions include many, but not all of, the class of heavy-tailed distributions: The Pareto and Cauchy are members; the Weibull is not.Our results are then applied to provide one answer to the classic question: When are s slow servers (operating at rate 1 /s ) better than one fast server (operating at rate 1)? We consider this question with respect to the rate of decay of the tail of stationary customer delay. In a system characterized by service times that have finite mean but lack some higher moments, such as are often used to model telecommunications traffic, for s greater than a traffic-related constant, the answer is always . Our results help to quantify the benefits of extra servers, while also pointing the way towards the derivation of bounds and asymptotics for the stationary delay distribution of multiserver queues having these types of service times. Such queues are attracting a great deal of academic research, motivated by their practical use modeling telecommunications systems.

Suggested Citation

  • Alan Scheller-Wolf, 2003. "Necessary and Sufficient Conditions for Delay Moments in FIFO Multiserver Queues with an Application Comparing s Slow Servers with One Fast One," Operations Research, INFORMS, vol. 51(5), pages 748-758, October.
  • Handle: RePEc:inm:oropre:v:51:y:2003:i:5:p:748-758
    DOI: 10.1287/opre.51.5.748.16759
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.51.5.748.16759
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.51.5.748.16759?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 Greiner & Manfred Jobmann & Lester Lipsky, 1999. "The Importance of Power-Tail Distributions for Modeling Queueing Systems," Operations Research, INFORMS, vol. 47(2), pages 313-326, April.
    2. Paul Glasserman, 1997. "Bounds and Asymptotics for Planning Critical Safety Stocks," Operations Research, INFORMS, vol. 45(2), pages 244-257, April.
    3. Uday Rao & Alan Scheller-Wolf & Sridhar Tayur, 2000. "Development of a Rapid-Response Supply Chain at Caterpillar," Operations Research, INFORMS, vol. 48(2), pages 189-204, April.
    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. Altendorfer, Klaus & Minner, Stefan, 2011. "Simultaneous optimization of capacity and planned lead time in a two-stage production system with different customer due dates," European Journal of Operational Research, Elsevier, vol. 213(1), pages 134-146, August.
    2. 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.
    3. Daley, D.J. & Goldie, Charles M., 2006. "The moment index of minima (II)," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 831-837, 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. Dimitris Bertsimas & Ioannis Ch. Paschalidis, 2001. "Probabilistic Service Level Guarantees in Make-to-Stock Manufacturing Systems," Operations Research, INFORMS, vol. 49(1), pages 119-133, February.
    2. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2016. "Capacitated Multiechelon Inventory Systems: Policies and Bounds," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 570-584, October.
    3. James A. Rappold & John A. Muckstadt, 2000. "A computationally efficient approach for determining inventory levels in a capacitated multiechelon production‐distribution system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(5), pages 377-398, August.
    4. Wouter van Eekelen & Dick den Hertog & Johan S.H. van Leeuwaarden, 2022. "MAD Dispersion Measure Makes Extremal Queue Analysis Simple," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1681-1692, May.
    5. Anshul Sheopuri & Ganesh Janakiraman & Sridhar Seshadri, 2010. "New Policies for the Stochastic Inventory Control Problem with Two Supply Sources," Operations Research, INFORMS, vol. 58(3), pages 734-745, June.
    6. Frank Schneider & Ulrich W. Thonemann & Diego Klabjan, 2018. "Optimization of Battery Charging and Purchasing at Electric Vehicle Battery Swap Stations," Transportation Science, INFORMS, vol. 52(5), pages 1211-1234, October.
    7. Ioannis Ch. Paschalidis & Yong Liu, 2003. "Large Deviations-Based Asymptotics for Inventory Control in Supply Chains," Operations Research, INFORMS, vol. 51(3), pages 437-460, June.
    8. Berling, Peter & Eng-Larsson, Fredrik, 2017. "Environmental implications of transport contract choice - capacity investment and pricing under volume and capacity contracts," European Journal of Operational Research, Elsevier, vol. 261(1), pages 129-142.
    9. Bradley, James R., 2005. "Optimal control of a dual service rate M/M/1 production-inventory model," European Journal of Operational Research, Elsevier, vol. 161(3), pages 812-837, March.
    10. Buddana Amrutha & Kozubowski Tomasz J., 2014. "Discrete Pareto Distributions," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 143-156, December.
    11. Wang, Xun & Disney, Stephen M. & Ponte, Borja, 2023. "On the stationary stochastic response of an order-constrained inventory system," European Journal of Operational Research, Elsevier, vol. 304(2), pages 543-557.
    12. Gunasekaran, Angappa & Ngai, Eric W.T., 2009. "Modeling and analysis of build-to-order supply chains," European Journal of Operational Research, Elsevier, vol. 195(2), pages 319-334, June.
    13. Erica L. Plambeck & Amy R. Ward, 2007. "Note: A Separation Principle for a Class of Assemble-to-Order Systems with Expediting," Operations Research, INFORMS, vol. 55(3), pages 603-609, June.
    14. Josh Reed & Bo Zhang, 2017. "Managing capacity and inventory jointly for multi-server make-to-stock queues," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 61-94, June.
    15. Daniel, J. Sudhir Ryan & Rajendran, Chandrasekharan, 2006. "Heuristic approaches to determine base-stock levels in a serial supply chain with a single objective and with multiple objectives," European Journal of Operational Research, Elsevier, vol. 175(1), pages 566-592, November.
    16. Hossein Abouee‐Mehrizi & Oded Berman & Hassan Shavandi & Ata G. Zare, 2011. "An exact analysis of a joint production‐inventory problem in two‐echelon inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(8), pages 713-730, December.
    17. Soroush Saghafian & Mark P. Van Oyen, 2016. "Compensating for Dynamic Supply Disruptions: Backup Flexibility Design," Operations Research, INFORMS, vol. 64(2), pages 390-405, April.
    18. Matt Bassett & Leslie Gardner, 2013. "Designing optimal global supply chains at Dow AgroSciences," Annals of Operations Research, Springer, vol. 203(1), pages 187-216, March.
    19. Yingdong Lu, 2007. "Estimation of average backorders for an assemble‐to‐order system with random batch demands through extreme statistics," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 33-45, February.
    20. Zoubida Benmamoun & Widad Fethallah & Mustapha Ahlaqqach & Ikhlef Jebbor & Mouad Benmamoun & Mariam Elkhechafi, 2023. "Butterfly Algorithm for Sustainable Lot Size Optimization," Sustainability, MDPI, vol. 15(15), pages 1-21, July.

    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:51:y:2003:i:5:p:748-758. 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.