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The Lagged PSA for Estimating Peak Congestion in Multiserver Markovian Queues with Periodic Arrival Rates

Author

Listed:
  • Linda V. Green

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • Peter J. Kolesar

    (Graduate School of Business, Columbia University, New York, New York 10027)

Abstract

We propose using a modification of the simple peak hour approximation (SPHA) for estimating peak congestion in multiserver queueing systems with exponential service times and time-varying periodic Poisson arrivals. This lagged pointwise stationary approximation (lagged PSA) is obtained by first estimating the time of the actual peak congestion by the time of peak congestion in an infinite server model and then substituting the arrival rate at this time in the corresponding stationary finite server model. We show that the lagged PSA is always more accurate than the SPHA and results in dramatically smaller errors when average service times are greater than a half an hour (based on a 24 hour period). More importantly, the lagged PSA reliably identifies proper staffing levels to meet targeted performance levels to keep congestion low.

Suggested Citation

  • Linda V. Green & Peter J. Kolesar, 1997. "The Lagged PSA for Estimating Peak Congestion in Multiserver Markovian Queues with Periodic Arrival Rates," Management Science, INFORMS, vol. 43(1), pages 80-87, January.
    • Handle: RePEc:inm:ormnsc:v:43:y:1997:i:1:p:80-87
    DOI: 10.1287/mnsc.43.1.80
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    Citations

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    Cited by:

    1. Izady, Navid & Worthington, Dave, 2012. "Setting staffing requirements for time dependent queueing networks: The case of accident and emergency departments," European Journal of Operational Research, Elsevier, vol. 219(3), pages 531-540.
    2. 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.
    3. 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.
    4. Wall, A.D. & Worthington, D.J., 2007. "Time-dependent analysis of virtual waiting time behaviour in discrete time queues," European Journal of Operational Research, Elsevier, vol. 178(2), pages 482-499, April.
    5. 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.
    6. Samantha L. Zimmerman & Alexander R. Rutherford & Alexa Waall & Monica Norena & Peter Dodek, 2023. "A queuing model for ventilator capacity management during the COVID-19 pandemic," Health Care Management Science, Springer, vol. 26(2), pages 200-216, June.
    7. J. G. Dai & Pengyi Shi, 2017. "A Two-Time-Scale Approach to Time-Varying Queues in Hospital Inpatient Flow Management," Operations Research, INFORMS, vol. 65(2), pages 514-536, April.
    8. 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.
    9. Gabriel Zayas-Cabán & Mark E. Lewis, 2020. "Admission control in a two-class loss system with periodically varying parameters and abandonments," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 175-210, February.
    10. Wang, Haiyan & Olsen, Tava Lennon & Liu, Guiqing, 2018. "Service capacity competition with peak arrivals and delay sensitive customers," Omega, Elsevier, vol. 77(C), pages 80-95.
    11. Alnowibet, Khalid Abdulaziz & Perros, Harry, 2009. "Nonstationary analysis of the loss queue and of queueing networks of loss queues," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1015-1030, August.

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