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

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  • 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
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    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.
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    Cited by:

    1. 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.
    2. 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.
    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.

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