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A Closure Approximation for the Nonstationary M/M/s Queue

Author

Listed:
  • Michael H. Rothkopf

    (Xerox Palo Alto Research Center)

  • Shmuel S. Oren

    (Xerox Palo Alto Research Center)

Abstract

Typical queues do not have constant arrival rates. This paper discusses effective computational methods for dealing with queues having nonstationary arrival processes. It presents a computationally undemanding approximate method for finding the time dependent mean and standard deviation of the number of customers in an s server queueing system with time-varying arrival and service rates. Results are exhibited for various 1 and 3 server queues with constant service rates and sinusoidal components in the arrival rate.

Suggested Citation

  • Michael H. Rothkopf & Shmuel S. Oren, 1979. "A Closure Approximation for the Nonstationary M/M/s Queue," Management Science, INFORMS, vol. 25(6), pages 522-534, June.
    • Handle: RePEc:inm:ormnsc:v:25:y:1979:i:6:p:522-534
    DOI: 10.1287/mnsc.25.6.522
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    Cited by:

    1. Chen Li & Junjun Zheng & Hiroyuki Okamura & Tadashi Dohi, 2023. "Performance Evaluation of a Cloud Datacenter Using CPU Utilization Data," Mathematics, MDPI, vol. 11(3), pages 1-16, January.
    2. Michael R. Taaffe & Gordon M. Clark, 1988. "Approximating nonstationary two‐priority non‐preemptive queueing systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 125-145, February.
    3. Tan, Xiaoqian & Knessl, Charles & Yang, Yongzhi (Peter), 2013. "On finite capacity queues with time dependent arrival rates," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2175-2227.
    4. 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.
    5. Stolletz, Raik, 2008. "Approximation of the non-stationary M(t)/M(t)/c(t)-queue using stationary queueing models: The stationary backlog-carryover approach," European Journal of Operational Research, Elsevier, vol. 190(2), pages 478-493, October.
    6. Chaithanya Bandi & Nikolaos Trichakis & Phebe Vayanos, 2019. "Robust Multiclass Queuing Theory for Wait Time Estimation in Resource Allocation Systems," Management Science, INFORMS, vol. 65(1), pages 152-187, January.
    7. 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.
    8. Sriram Somanchi & Idris Adjerid & Ralph Gross, 2022. "To Predict or Not to Predict: The Case of the Emergency Department," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 799-818, February.
    9. Ward Whitt & Wei You, 2019. "Time-Varying Robust Queueing," Operations Research, INFORMS, vol. 67(6), pages 1766-1782, November.
    10. 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.
    11. Yang, Feng & Liu, Jingang, 2012. "Simulation-based transfer function modeling for transient analysis of general queueing systems," European Journal of Operational Research, Elsevier, vol. 223(1), pages 150-166.
    12. 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.
    13. Jamol Pender, 2017. "Sampling the Functional Kolmogorov Forward Equations for Nonstationary Queueing Networks," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 1-17, February.
    14. Vladimir Vishnevsky & Konstantin Vytovtov & Elizaveta Barabanova & Olga Semenova, 2022. "Analysis of a MAP / M /1/ N Queue with Periodic and Non-Periodic Piecewise Constant Input Rate," Mathematics, MDPI, vol. 10(10), pages 1-16, May.
    15. Heemskerk, M. & Mandjes, M. & Mathijsen, B., 2022. "Staffing for many-server systems facing non-standard arrival processes," European Journal of Operational Research, Elsevier, vol. 296(3), pages 900-913.
    16. Huh, Woonghee Tim & Lee, Jaywon & Park, Heesang & Park, Kun Soo, 2019. "The potty parity problem: Towards gender equality at restrooms in business facilities," Socio-Economic Planning Sciences, Elsevier, vol. 68(C).

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