IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v20y1972i6p1089-1114.html
   My bibliography  Save this article

Air-Terminal Queues under Time-Dependent Conditions

Author

Listed:
  • Bernard O. Koopman

    (Arthur D. Little, Inc., Cambridge, Massachusetts)

Abstract

The queues formed by aircraft in stacks awaiting landing clearance have usually been treated either by machine simulation, or analytically as stochastic processes with time-independent transition probabilities (possessing stationary solutions). In contrast to such methods, the present paper regards the queue-developing process in question as strongly time-dependent, often with a diurnal (24-hour) periodicity. The formulation and treatment are entirely analytic and make use of machines only to solve the equations for the probabilities, by economical deterministic steps, using the coefficients as given in tabular form. Time-varying Poisson arrivals are assumed, and also an upper limit to queue length. Two laws of servicing are used: Poisson and fixed service time; these extremes are found to lead to numerically close results in the realistic case. This situation contrasts with the much cruder approximation of deterministic flow models. The stochastic equations belong to well studied types of differential or difference equations. When the coefficients have a 24-hour period, so does just one solution, all others approaching it. Actual airport statistics are made the basis of certain revealing computations. A perturbation method for treating multiple queues is outlined. The concrete results are exhibited as graphs.

Suggested Citation

  • Bernard O. Koopman, 1972. "Air-Terminal Queues under Time-Dependent Conditions," Operations Research, INFORMS, vol. 20(6), pages 1089-1114, December.
    • Handle: RePEc:inm:oropre:v:20:y:1972:i:6:p:1089-1114
    DOI: 10.1287/opre.20.6.1089
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.20.6.1089
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.20.6.1089?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
    ---><---

    Citations

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


    Cited by:

    1. Woong-Gi Kim & Namhyuk Ham & Jae-Jun Kim, 2021. "Enhanced Subcontractors Allocation for Apartment Construction Project Applying Conceptual 4D Digital Twin Framework," Sustainability, MDPI, vol. 13(21), pages 1-21, October.
    2. Daniel, Joseph I, 1995. "Congestion Pricing and Capacity of Large Hub Airports: A Bottleneck Model with Stochastic Queues," Econometrica, Econometric Society, vol. 63(2), pages 327-370, March.
    3. Daniel, Joseph I. & Harback, Katherine Thomas, 2009. "Pricing the major US hub airports," Journal of Urban Economics, Elsevier, vol. 66(1), pages 33-56, July.
    4. Daniel, Joseph I. & Pahwa, Munish, 2000. "Comparison of Three Empirical Models of Airport Congestion Pricing," Journal of Urban Economics, Elsevier, vol. 47(1), pages 1-38, January.
    5. 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.
    6. 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.
    7. 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.
    8. Ioannis Simaiakis & Hamsa Balakrishnan, 2016. "A Queuing Model of the Airport Departure Process," Transportation Science, INFORMS, vol. 50(1), pages 94-109, February.
    9. 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.
    10. 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.
    11. Cynthia Barnhart & Peter Belobaba & Amedeo R. Odoni, 2003. "Applications of Operations Research in the Air Transport Industry," Transportation Science, INFORMS, vol. 37(4), pages 368-391, November.
    12. 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.
    13. Coy, Steven, 2006. "A global model for estimating the block time of commercial passenger aircraft," Journal of Air Transport Management, Elsevier, vol. 12(6), pages 300-305.
    14. Daniel, Joseph I., 2001. "Distributional Consequences of Airport Congestion Pricing," Journal of Urban Economics, Elsevier, vol. 50(2), pages 230-258, September.
    15. 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.
    16. 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.
    17. Walid W. Nasr & Michael R. Taaffe, 2013. "Fitting the Ph t / M t / s / c Time-Dependent Departure Process for Use in Tandem Queueing Networks," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 758-773, November.
    18. Tasos Nikoleris & Mark Hansen, 2016. "Effect of Trajectory Prediction and Stochastic Runway Occupancy Times on Aircraft Delays," Transportation Science, INFORMS, vol. 50(1), pages 110-119, February.
    19. Armann Ingolfsson & Elvira Akhmetshina & Susan Budge & Yongyue Li & Xudong Wu, 2007. "A Survey and Experimental Comparison of Service-Level-Approximation Methods for Nonstationary M(t)/M/s(t) Queueing Systems with Exhaustive Discipline," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 201-214, May.
    20. Ward Whitt & Wei You, 2019. "Time-Varying Robust Queueing," Operations Research, INFORMS, vol. 67(6), pages 1766-1782, November.
    21. Tasos Nikoleris & Mark Hansen, 2012. "Queueing Models for Trajectory-Based Aircraft Operations," Transportation Science, INFORMS, vol. 46(4), pages 501-511, November.

    More about this item

    Statistics

    Access and download statistics

    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:inm:oropre:v:20:y:1972:i:6:p:1089-1114. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.