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Approximate Expressions for Queueing Systems with Scheduled Arrivals and Established Service Order

Author

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  • Federico Sabria

    (University of California, Berkeley, California)

  • Carlos F. Daganzo

    (University of California, Berkeley, California)

Abstract

This paper studies single server queueing systems where customers arrive according to a schedule, but not punctually, and where service might be provided in the scheduled order; thus, customers may leave the system in a sequence different to that of their arrivals. The situation arises in connection with maritime container terminals. The steady state solution to the problem follows an integral equation that may be solved numerically. When congestion is light (as is usual in well managed ports) approximate analytic solutions to the integral equation can be found. As an illustration, formulas are given that apply if the deviations from the schedule and the service times have some specific distributions. These expressions accurately predict the expected delay for systems with fairly unpunctual arrivals and occasional congestion. The paper also contains an exact analytical solution for the special case in which service times are constant and the deviations from the arrival schedule are independent Gumbel variables.

Suggested Citation

  • Federico Sabria & Carlos F. Daganzo, 1989. "Approximate Expressions for Queueing Systems with Scheduled Arrivals and Established Service Order," Transportation Science, INFORMS, vol. 23(3), pages 159-165, August.
    • Handle: RePEc:inm:ortrsc:v:23:y:1989:i:3:p:159-165
    DOI: 10.1287/trsc.23.3.159
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    Cited by:

    1. Carlo Lancia & Gianluca Guadagni & Sokol Ndreca & Benedetto Scoppola, 2018. "Asymptotics for the late arrivals problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 475-493, December.
    2. Ho-Yin Mak & Ying Rong & Jiawei Zhang, 2015. "Appointment Scheduling with Limited Distributional Information," Management Science, INFORMS, vol. 61(2), pages 316-334, February.
    3. Ho-Yin Mak & Ying Rong & Jiawei Zhang, 2014. "Sequencing Appointments for Service Systems Using Inventory Approximations," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 251-262, May.
    4. Illana Bendavid & Yariv N. Marmor & Boris Shnits, 2018. "Developing an optimal appointment scheduling for systems with rigid standby time under pre-determined quality of service," Flexible Services and Manufacturing Journal, Springer, vol. 30(1), pages 54-77, June.
    5. Shenghai Zhou & Yichuan Ding & Woonghee Tim Huh & Guohua Wan, 2021. "Constant Job‐Allowance Policies for Appointment Scheduling: Performance Bounds and Numerical Analysis," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 2211-2231, July.
    6. Arlen Dean & Amirhossein Meisami & Henry Lam & Mark P. Van Oyen & Christopher Stromblad & Nick Kastango, 2022. "Quantile regression forests for individualized surgery scheduling," Health Care Management Science, Springer, vol. 25(4), pages 682-709, December.
    7. Mehmet A. Begen & Retsef Levi & Maurice Queyranne, 2012. "Technical Note---A Sampling-Based Approach to Appointment Scheduling," Operations Research, INFORMS, vol. 60(3), pages 675-681, June.
    8. Haughton, Michael & Sapna Isotupa, K.P., 2012. "Scheduling commercial vehicle queues at a Canada–US border crossing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 190-201.
    9. Yifei Sun & Usha Nandini Raghavan & Vikrant Vaze & Christopher S Hall & Patricia Doyle & Stacey Sullivan Richard & Christoph Wald, 2021. "Stochastic programming for outpatient scheduling with flexible inpatient exam accommodation," Health Care Management Science, Springer, vol. 24(3), pages 460-481, September.
    10. Z Fu & Y Li & A Lim & B Rodrigues, 2007. "Port space allocation with a time dimension," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 797-807, June.
    11. Shehadeh, Karmel S. & Cohn, Amy E.M. & Epelman, Marina A., 2019. "Analysis of models for the Stochastic Outpatient Procedure Scheduling Problem," European Journal of Operational Research, Elsevier, vol. 279(3), pages 721-731.
    12. Mehmet A. Begen & Maurice Queyranne, 2011. "Appointment Scheduling with Discrete Random Durations," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 240-257, May.
    13. Andrew Lim & Brian Rodrigues & Fei Xiao & Yi Zhu, 2004. "Crane scheduling with spatial constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 386-406, April.
    14. 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.
    15. Shnits, Boris & Bendavid, Illana & Marmor, Yariv N., 2020. "An appointment scheduling policy for healthcare systems with parallel servers and pre-determined quality of service," Omega, Elsevier, vol. 97(C).
    16. Branislav Dragovic & Nenad Dj. Zrnic, 2011. "A Queuing Model Study of Port Performance Evolution," Analele Universitatii "Eftimie Murgu" Resita Fascicola de Inginerie, "Eftimie Murgu" University of Resita, vol. 2(XVIII), pages 65-76, December.
    17. Brian T. Denton & Andrew J. Miller & Hari J. Balasubramanian & Todd R. Huschka, 2010. "Optimal Allocation of Surgery Blocks to Operating Rooms Under Uncertainty," Operations Research, INFORMS, vol. 58(4-part-1), pages 802-816, August.
    18. Lawrence W. Robinson & Rachel R. Chen, 2011. "Estimating the Implied Value of the Customer's Waiting Time," Manufacturing & Service Operations Management, INFORMS, vol. 13(1), pages 53-57, February.
    19. Branislav Dragović & Nam Kyu Park & Zoran Radmilović, 2006. "Ship-berth link performance evaluation: simulation and analytical approaches," Maritime Policy & Management, Taylor & Francis Journals, vol. 33(3), pages 281-299, July.
    20. Tasos Nikoleris & Mark Hansen, 2012. "Queueing Models for Trajectory-Based Aircraft Operations," Transportation Science, INFORMS, vol. 46(4), pages 501-511, November.
    21. P. Patrick Wang, 1993. "Static and dynamic scheduling of customer arrivals to a single‐server system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(3), pages 345-360, April.
    22. Creemers, Stefan & Lambrecht, Marc R. & Beliën, Jeroen & Van den Broeke, Maud, 2021. "Evaluation of appointment scheduling rules: A multi-performance measurement approach," Omega, Elsevier, vol. 100(C).

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