IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v123y2013i6p2175-2227.html
   My bibliography  Save this article

On finite capacity queues with time dependent arrival rates

Author

Listed:
  • Tan, Xiaoqian
  • Knessl, Charles
  • Yang, Yongzhi (Peter)

Abstract

We consider the finite capacity M/M/1−K queue with a time dependent arrival rate λ(t). Assuming that the capacity K is large and that the arrival rate varies slowly with time (as t/K), we construct asymptotic approximations to the probability of finding n customers in the system at time t, as well as the mean number. We consider various time ranges, where the system is nearly empty, nearly full, or is filled to a fraction of its capacity. Extensive numerical studies are used to back up the asymptotic analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:6:p:2175-2227
    DOI: 10.1016/j.spa.2013.02.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414913000409
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2013.02.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bernard O. Koopman, 1972. "Air-Terminal Queues under Time-Dependent Conditions," Operations Research, INFORMS, vol. 20(6), pages 1089-1114, December.
    2. Basawa, I.V. & Bhat, U.N. & Zhou, J., 2008. "Parameter estimation using partial information with applications to queueing and related models," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1375-1383, September.
    3. Peter Kolesar, 1984. "Stalking the Endangered CAT: A Queueing Analysis of Congestion at Automatic Teller Machines," Interfaces, INFORMS, vol. 14(6), pages 16-26, December.
    4. T. Collings & C. Stoneman, 1976. "The M / M /∞ Queue with Varying Arrival and Departure Rates," Operations Research, INFORMS, vol. 24(4), pages 760-773, August.
    5. Avi Mandelbaum & William A. Massey, 1995. "Strong Approximations for Time-Dependent Queues," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 33-64, February.
    6. Linda Green & Peter Kolesar, 1989. "Testing the Validity of a Queueing Model of Police Patrol," Management Science, INFORMS, vol. 35(2), pages 127-148, February.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Ward Whitt & Wei You, 2019. "Time-Varying Robust Queueing," Operations Research, INFORMS, vol. 67(6), pages 1766-1782, November.
    3. 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.
    4. 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.
    5. Ali Yousefi & Reza Pourtaheri, 2024. "The Mt/M/1 queueing system with impatient customers and multiple vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 61(4), pages 2002-2022, December.
    6. Ali Yousefi & Reza Pourtaheri & Mohammad Reza Salehi Rad, 2024. "Analysis of the Mt/M/1 Queueing System with Impatient Customers and Single Vacation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 690-712, November.
    7. 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.
    8. Linda V. Green & Peter J. Kolesar, 1998. "A Note on Approximating Peak Congestion in Mt/G/\infty Queues with Sinusoidal Arrivals," Management Science, INFORMS, vol. 44(11-Part-2), pages 137-144, November.
    9. 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.
    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. Elvin Coban & Aliza Heching & Alan Scheller‐Wolf, 2019. "Service Center Staffing with Cross‐Trained Agents and Heterogeneous Customers," Production and Operations Management, Production and Operations Management Society, vol. 28(4), pages 788-809, April.
    12. Marcos Singer & Patricio Donoso & Natalia Jadue, 2004. "Evaluacion De Las Oportunidades De Mejoramiento De La Logistica Directa De Emergencia," Abante, Escuela de Administracion. Pontificia Universidad Católica de Chile., vol. 7(2), pages 179-209.
    13. Kerry Fendick & Ward Whitt, 2022. "Heavy traffic limits for queues with non-stationary path-dependent arrival processes," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 113-135, June.
    14. Sukanya Samanta & Goutam Sen & Soumya Kanti Ghosh, 2022. "A literature review on police patrolling problems," Annals of Operations Research, Springer, vol. 316(2), pages 1063-1106, September.
    15. Shone, Rob & Glazebrook, Kevin & Zografos, Konstantinos G., 2019. "Resource allocation in congested queueing systems with time-varying demand: An application to airport operations," European Journal of Operational Research, Elsevier, vol. 276(2), pages 566-581.
    16. P. Daniel Wright & Matthew J. Liberatore & Robert L. Nydick, 2006. "A Survey of Operations Research Models and Applications in Homeland Security," Interfaces, INFORMS, vol. 36(6), pages 514-529, December.
    17. 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.
    18. Velazco, Enio E., 1995. "Air traffic management: High-low traffic intensity analysis," European Journal of Operational Research, Elsevier, vol. 80(1), pages 45-58, January.
    19. Gianmarco Bet & Remco van der Hofstad & Johan S. H. van Leeuwaarden, 2019. "Heavy-Traffic Analysis Through Uniform Acceleration of Queues with Diminishing Populations," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 821-864, August.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:123:y:2013:i:6:p:2175-2227. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.