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The Impact of Dependent Service Times on Large-Scale Service Systems

Author

Listed:
  • Guodong Pang

    (Harold and Inge Marcus Department of Industrial and Manufacturing Engineering, Pennsylvania State University, University Park, Pennsylvania 16802)

  • Ward Whitt

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

Abstract

This paper investigates the impact of dependence among successive service times on the transient and steady-state performance of a large-scale service system. This is done by studying an infinite-server queueing model with time-varying arrival rate, exploiting a recently established heavy-traffic limit, allowing dependence among the service times. This limit shows that the number of customers in the system at any time is approximately Gaussian, where the time-varying mean is unaffected by the dependence, but the time-varying variance is affected by the dependence. As a consequence, required staffing to meet customary quality-of-service targets in a large-scale service system with finitely many servers based on a normal approximation is primarily affected by dependence among the service times through this time-varying variance. This paper develops formulas and algorithms to quantify the impact of the dependence among the service times on that variance. The approximation applies directly to infinite-server models but also indirectly to associated finite-server models, exploiting approximations based on the peakedness (the ratio of the variance to the mean in the infinite-server model). Comparisons with simulations confirm that the approximations can be useful to assess the impact of the dependence.

Suggested Citation

  • Guodong Pang & Ward Whitt, 2012. "The Impact of Dependent Service Times on Large-Scale Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 14(2), pages 262-278, April.
    • Handle: RePEc:inm:ormsom:v:14:y:2012:i:2:p:262-278
    DOI: 10.1287/msom.1110.0363
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    References listed on IDEAS

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    1. William A. Massey & Ward Whitt, 1996. "Stationary-Process Approximations for the Nonstationary Erlang Loss Model," Operations Research, INFORMS, vol. 44(6), pages 976-983, December.
    2. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    3. P. A. Jacobs & P. A. W. Lewis, 1983. "Stationary Discrete Autoregressive‐Moving Average Time Series Generated By Mixtures," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(1), pages 19-36, January.
    4. 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.
    5. Berkes, István & Hörmann, Siegfried & Schauer, Johannes, 2009. "Asymptotic results for the empirical process of stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1298-1324, April.
    6. 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.
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    Citations

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    Cited by:

    1. Song‐Hee Kim & Ward Whitt, 2014. "Choosing arrival process models for service systems: Tests of a nonhomogeneous Poisson process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(1), pages 66-90, February.
    2. Chenguang (Allen) Wu & Achal Bassamboo & Ohad Perry, 2019. "Service System with Dependent Service and Patience Times," Management Science, INFORMS, vol. 65(3), pages 1151-1172, March.
    3. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.
    4. Ibrahim, Rouba & L’Ecuyer, Pierre & Shen, Haipeng & Thiongane, Mamadou, 2016. "Inter-dependent, heterogeneous, and time-varying service-time distributions in call centers," European Journal of Operational Research, Elsevier, vol. 250(2), pages 480-492.
    5. Guodong Pang & Yuhang Zhou, 2018. "Two-parameter process limits for infinite-server queues with dependent service times via chaining bounds," Queueing Systems: Theory and Applications, Springer, vol. 88(1), pages 1-25, February.
    6. Song-Hee Kim & Ward Whitt, 2014. "Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 464-480, July.

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