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Stabilizing Customer Abandonment in Many-Server Queues with Time-Varying Arrivals

Author

Listed:
  • Yunan Liu

    (Department of Industrial Engineering, North Carolina State University, Raleigh, North Carolina 27695)

  • Ward Whitt

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

Abstract

An algorithm is developed to determine time-dependent staffing levels to stabilize the time-dependent abandonment probabilities and expected delays at positive target values in the M t / GI / s t + GI many-server queueing model, which has a nonhomogeneous Poisson arrival process (the M t ), has general service times (the first GI ), and allows customer abandonment according to a general patience distribution (the + GI ). New offered-load and modified-offered-load approximations involving infinite-server models are developed for that purpose. Simulations show that the approximations are effective. A many-server heavy-traffic limit in the efficiency-driven regime shows that (i) the proposed approximations achieve the goal asymptotically as the scale increases, and (ii) it is not possible to simultaneously stabilize the mean queue length in the same asymptotic regime.

Suggested Citation

  • Yunan Liu & Ward Whitt, 2012. "Stabilizing Customer Abandonment in Many-Server Queues with Time-Varying Arrivals," Operations Research, INFORMS, vol. 60(6), pages 1551-1564, December.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:6:p:1551-1564
    DOI: 10.1287/opre.1120.1104
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    References listed on IDEAS

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    1. 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.
    2. Ward Whitt, 2005. "Engineering Solution of a Basic Call-Center Model," Management Science, INFORMS, vol. 51(2), pages 221-235, February.
    3. Zohar Feldman & Avishai Mandelbaum & William A. Massey & Ward Whitt, 2008. "Staffing of Time-Varying Queues to Achieve Time-Stable Performance," Management Science, INFORMS, vol. 54(2), pages 324-338, February.
    4. Ward Whitt, 2006. "Fluid Models for Multiserver Queues with Abandonments," Operations Research, INFORMS, vol. 54(1), pages 37-54, February.
    5. Otis B. Jennings & Avishai Mandelbaum & William A. Massey & Ward Whitt, 1996. "Server Staffing to Meet Time-Varying Demand," Management Science, INFORMS, vol. 42(10), pages 1383-1394, October.
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    Cited by:

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