IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v54y2006i2p247-260.html
   My bibliography  Save this article

Sensitivity of Performance in the Erlang-A Queueing Model to Changes in the Model Parameters

Author

Listed:
  • Ward Whitt

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027-6699)

Abstract

This paper studies the M/M/s+M queue, i.e., the M/M/s queue with customer abandonment, also called the Erlang-A model, having independent and identically distributed customer abandon times with an exponential distribution (the + M ), focusing on the case in which the arrival rate and the number of servers are large. The goal is to better understand the sensitivity of performance to changes in the model parameters: the arrival rate, the service rate, the number of servers, and the abandonment rate. Elasticities are used to show the percentage change of a performance measure caused by a small percentage change in a parameter. Elasticities are calculated using an exact numerical algorithm and simple finite-difference approximations. Insight is gained by applying fluid and diffusion approximations. The analysis shows that performance is quite sensitive to small percentage changes in the arrival rate or the service rate, but relatively insensitive to small percentage changes in the abandonment rate.

Suggested Citation

  • Ward Whitt, 2006. "Sensitivity of Performance in the Erlang-A Queueing Model to Changes in the Model Parameters," Operations Research, INFORMS, vol. 54(2), pages 247-260, April.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:2:p:247-260
    DOI: 10.1287/opre.1050.0257
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1050.0257
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1050.0257?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. Arie Harel, 1990. "Convexity Properties of the Erlang Loss Formula," Operations Research, INFORMS, vol. 38(3), pages 499-505, June.
    2. Ward Whitt, 2004. "Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments," Management Science, INFORMS, vol. 50(10), pages 1449-1461, October.
    3. Jimmie L. Davis & William A. Massey & Ward Whitt, 1995. "Sensitivity to the Service-Time Distribution in the Nonstationary Erlang Loss Model," Management Science, INFORMS, vol. 41(6), pages 1107-1116, June.
    4. Ward Whitt, 2005. "Engineering Solution of a Basic Call-Center Model," Management Science, INFORMS, vol. 51(2), pages 221-235, February.
    5. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    6. Ward Whitt, 1980. "Continuity of Generalized Semi-Markov Processes," Mathematics of Operations Research, INFORMS, vol. 5(4), pages 494-501, November.
    7. Arie Harel & Paul H. Zipkin, 1987. "Strong Convexity Results for Queueing Systems," Operations Research, INFORMS, vol. 35(3), pages 405-418, June.
    8. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    9. Sem Borst & Avi Mandelbaum & Martin I. Reiman, 2004. "Dimensioning Large Call Centers," Operations Research, INFORMS, vol. 52(1), pages 17-34, 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. Isadora Antoniano‐Villalobos & Emanuele Borgonovo & Sumeda Siriwardena, 2018. "Which Parameters Are Important? Differential Importance Under Uncertainty," Risk Analysis, John Wiley & Sons, vol. 38(11), pages 2459-2477, November.
    2. Charles Knessl & Johan Leeuwaarden, 2015. "Transient analysis of the Erlang A model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(2), pages 143-173, October.
    3. Yunan Liu & Ward Whitt & Yao Yu, 2016. "Approximations for heavily loaded G/GI/n + GI queues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(3), pages 187-217, 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. Francis de Véricourt & Otis B. Jennings, 2008. "Dimensioning Large-Scale Membership Services," Operations Research, INFORMS, vol. 56(1), pages 173-187, February.
    2. Opher Baron & Joseph Milner, 2009. "Staffing to Maximize Profit for Call Centers with Alternate Service-Level Agreements," Operations Research, INFORMS, vol. 57(3), pages 685-700, June.
    3. Niyirora, Jerome & Zhuang, Jun, 2017. "Fluid approximations and control of queues in emergency departments," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1110-1124.
    4. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    5. R. Bekker & A. Bruin, 2010. "Time-dependent analysis for refused admissions in clinical wards," Annals of Operations Research, Springer, vol. 178(1), pages 45-65, July.
    6. Avishai Mandelbaum & Petar Momčilović, 2008. "Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 561-586, August.
    7. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    8. Guodong Pang & Ward Whitt, 2009. "Service Interruptions in Large-Scale Service Systems," Management Science, INFORMS, vol. 55(9), pages 1499-1512, September.
    9. Jouini, Oualid & Pot, Auke & Koole, Ger & Dallery, Yves, 2010. "Online scheduling policies for multiclass call centers with impatient customers," European Journal of Operational Research, Elsevier, vol. 207(1), pages 258-268, November.
    10. 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.
    11. Achal Bassamboo & Assaf Zeevi, 2009. "On a Data-Driven Method for Staffing Large Call Centers," Operations Research, INFORMS, vol. 57(3), pages 714-726, June.
    12. Itai Gurvich & Ohad Perry, 2012. "Overflow Networks: Approximations and Implications to Call Center Outsourcing," Operations Research, INFORMS, vol. 60(4), pages 996-1009, August.
    13. van Leeuwaarden, Johan S.H. & Knessl, Charles, 2011. "Transient behavior of the Halfin-Whitt diffusion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1524-1545, July.
    14. A. J. E. M. Janssen & J. S. H. van Leeuwaarden & Bert Zwart, 2011. "Refining Square-Root Safety Staffing by Expanding Erlang C," Operations Research, INFORMS, vol. 59(6), pages 1512-1522, December.
    15. Guodong Pang & Ohad Perry, 2015. "A Logarithmic Safety Staffing Rule for Contact Centers with Call Blending," Management Science, INFORMS, vol. 61(1), pages 73-91, January.
    16. J. Michael Harrison & Assaf Zeevi, 2005. "A Method for Staffing Large Call Centers Based on Stochastic Fluid Models," Manufacturing & Service Operations Management, INFORMS, vol. 7(1), pages 20-36, September.
    17. Shuangchi He, 2020. "Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient," Operations Research, INFORMS, vol. 68(4), pages 1265-1284, July.
    18. Sunil Kumar & Ramandeep S. Randhawa, 2010. "Exploiting Market Size in Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 511-526, September.
    19. Rouba Ibrahim, 2018. "Sharing delay information in service systems: a literature survey," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 49-79, June.
    20. Rouba Ibrahim & Ward Whitt, 2009. "Real-Time Delay Estimation in Overloaded Multiserver Queues with Abandonments," Management Science, INFORMS, vol. 55(10), pages 1729-1742, October.

    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:54:y:2006:i:2:p:247-260. 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.