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Sensitivity to the Service-Time Distribution in the Nonstationary Erlang Loss Model

Author

Listed:
  • Jimmie L. Davis

    (School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • William A. Massey

    (AT&T Bell Laboratories, Room 2C-120, Murray Hill, New Jersey 07974-0636)

  • Ward Whitt

    (AT&T Bell Laboratories, Room 2C-178, Murray Hill, New Jersey 07974-0636)

Abstract

The stationary Erlang loss model is a classic example of an insensitive queueing system: the steady-state distribution of the number of busy servers depends on the service-time distribution only through its mean. However, when the arrival process is a nonstationary Poisson process, the insensitivity property is lost. We develop a simple, effective numerical algorithm for the M t /PH/s/0 model with two service phases and a nonhomogeneous Poisson arrival process, and apply it to show that the time-dependent blocking probability with nonstationary input can be strongly influenced by the service-time distribution beyond the mean. With sinusoidal arrival rates, the peak blocking probability typically increases as the service-time distribution gets less variable. The influence of the service-time distribution, including this seemingly anomalous behavior, can be understood and predicted from the modified-offered-load and stationary-peakedness approximations, which exploit exact results for related infinite-server models.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:6:p:1107-1116
    DOI: 10.1287/mnsc.41.6.1107
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    Cited by:

    1. Lu, Jing & Osorio, Carolina, 2024. "Link transmission model: A formulation with enhanced compute time for large-scale network optimization," Transportation Research Part B: Methodological, Elsevier, vol. 185(C).
    2. Andrew M. Ross, 2009. "Distribution sensitivity in a highway flow model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 769-786, November.
    3. A. Bruin & R. Bekker & L. Zanten & G. Koole, 2010. "Dimensioning hospital wards using the Erlang loss model," Annals of Operations Research, Springer, vol. 178(1), pages 23-43, July.
    4. Ward Whitt, 1999. "Partitioning Customers into Service Groups," Management Science, INFORMS, vol. 45(11), pages 1579-1592, November.
    5. 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.
    6. Ward Whitt, 1999. "Improving Service by Informing Customers About Anticipated Delays," Management Science, INFORMS, vol. 45(2), pages 192-207, February.
    7. 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.
    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. 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.
    10. Md Asaduzzaman & Thierry Chaussalet & Nicola Robertson, 2010. "A loss network model with overflow for capacity planning of a neonatal unit," Annals of Operations Research, Springer, vol. 178(1), pages 67-76, July.
    11. Izady, N. & Worthington, D., 2011. "Approximate analysis of non-stationary loss queues and networks of loss queues with general service time distributions," European Journal of Operational Research, Elsevier, vol. 213(3), pages 498-508, September.
    12. Arnoud Bruin & A. Rossum & M. Visser & G. Koole, 2007. "Modeling the emergency cardiac in-patient flow: an application of queuing theory," Health Care Management Science, Springer, vol. 10(2), pages 125-137, June.
    13. R. Bekker & A. Bruin, 2010. "Time-dependent analysis for refused admissions in clinical wards," Annals of Operations Research, Springer, vol. 178(1), pages 45-65, July.
    14. René Bekker & Paulien Koeleman, 2011. "Scheduling admissions and reducing variability in bed demand," Health Care Management Science, Springer, vol. 14(3), pages 237-249, September.
    15. Vyacheslav Abramov, 2006. "Analysis of multiserver retrial queueing system: A martingale approach and an algorithm of solution," Annals of Operations Research, Springer, vol. 141(1), pages 19-50, January.

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