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Staffing of Time-Varying Queues to Achieve Time-Stable Performance

Author

Listed:
  • Zohar Feldman

    (The William Davidson Faculty of Industrial Engineering and Management, Technion Institute of Technology, Haifa 32000, Israel)

  • Avishai Mandelbaum

    (The William Davidson Faculty of Industrial Engineering and Management, Technion Institute of Technology, Haifa 32000, Israel)

  • William A. Massey

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544)

  • Ward Whitt

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

Abstract

This paper develops methods to determine appropriate staffing levels in call centers and other many-server queueing systems with time-varying arrival rates. The goal is to achieve targeted time-stable performance, even in the presence of significant time variation in the arrival rates. The main contribution is a flexible simulation-based iterative-staffing algorithm (ISA) for the M t /G/s t + G model--with nonhomogeneous Poisson arrival process (the M t ) and customer abandonment (the + G). For Markovian M t /M/s t + M special cases, the ISA is shown to converge. For that M t /M/s t + M model, simulation experiments show that the ISA yields time-stable delay probabilities across a wide range of target delay probabilities. With ISA, other performance measures--such as agent utilizations, abandonment probabilities, and average waiting times--are stable as well. The ISA staffing and performance agree closely with the modified-offered-load approximation, which was previously shown to be an effective staffing algorithm without customer abandonment. Although the ISA algorithm so far has only been extensively tested for M t /M/s t + M models, it can be applied much more generally--to M t /G/s t + G models and beyond.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:2:p:324-338
    DOI: 10.1287/mnsc.1070.0821
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    References listed on IDEAS

    as
    1. Linda Green & Peter Kolesar, 1991. "The Pointwise Stationary Approximation for Queues with Nonstationary Arrivals," Management Science, INFORMS, vol. 37(1), pages 84-97, January.
    2. Linda V. Green & Peter J. Kolesar & João Soares, 2001. "Improving the Sipp Approach for Staffing Service Systems That Have Cyclic Demands," Operations Research, INFORMS, vol. 49(4), pages 549-564, August.
    3. Ward Whitt, 2005. "Engineering Solution of a Basic Call-Center Model," Management Science, INFORMS, vol. 51(2), pages 221-235, February.
    4. 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.
    5. Rodney B. Wallace & Ward Whitt, 2005. "A Staffing Algorithm for Call Centers with Skill-Based Routing," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 276-294, August.
    6. Ward Whitt, 1991. "The Pointwise Stationary Approximation for Mt/Mt/s Queues Is Asymptotically Correct As the Rates Increase," Management Science, INFORMS, vol. 37(3), pages 307-314, March.
    7. Stephen G. Eick & William A. Massey & Ward Whitt, 1993. "Mt/G/\infty Queues with Sinusoidal Arrival Rates," Management Science, INFORMS, vol. 39(2), pages 241-252, February.
    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. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
    10. Ward Whitt, 1992. "Understanding the Efficiency of Multi-Server Service Systems," Management Science, INFORMS, vol. 38(5), pages 708-723, May.
    11. 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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