IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v100y2022i1d10.1007_s11134-021-09732-9.html
   My bibliography  Save this article

On a single server queue fed by scheduled traffic with Pareto perturbations

Author

Listed:
  • Victor F. Araman

    (American University of Beirut)

  • Hong Chen

    (Shanghai Jiaotong University)

  • Peter W. Glynn

    (Stanford University)

  • Li Xia

    (Sun Yat-Sen University)

Abstract

A“scheduled” arrival process is one in which the nth arrival is scheduled for time n, but instead occurs at $$n+\xi _n$$ n + ξ n , where the $$\xi _j$$ ξ j ’s are i.i.d. We describe here the behavior of a single server queue fed by such traffic in which the processing times are deterministic. A particular focus is on perturbations with Pareto-like tails but with finite mean. We obtain tail approximations for the steady-state workload in both cases where the queue is critically loaded and under a heavy-traffic regime. A key to our approach is our analysis of the tail behavior of a sum of independent Bernoulli random variables with parameters of the form $$p_n\sim c \,n^{-\alpha }$$ p n ∼ c n - α as $$n\rightarrow \infty $$ n → ∞ , for $$c>0$$ c > 0 and $$\alpha >1$$ α > 1 .

Suggested Citation

  • Victor F. Araman & Hong Chen & Peter W. Glynn & Li Xia, 2022. "On a single server queue fed by scheduled traffic with Pareto perturbations," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 61-91, February.
  • Handle: RePEc:spr:queues:v:100:y:2022:i:1:d:10.1007_s11134-021-09732-9
    DOI: 10.1007/s11134-021-09732-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-021-09732-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11134-021-09732-9?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. Kemper, Benjamin & Klaassen, Chris A.J. & Mandjes, Michel, 2014. "Optimized appointment scheduling," European Journal of Operational Research, Elsevier, vol. 239(1), pages 243-255.
    2. Christos Zacharias & Mor Armony, 2017. "Joint Panel Sizing and Appointment Scheduling in Outpatient Care," Management Science, INFORMS, vol. 63(11), pages 3978-3997, November.
    3. Refael Hassin & Sharon Mendel, 2008. "Scheduling Arrivals to Queues: A Single-Server Model with No-Shows," Management Science, INFORMS, vol. 54(3), pages 565-572, March.
    Full references (including those not matched with items on IDEAS)

    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. Dongyang Wang & Kumar Muthuraman & Douglas Morrice, 2019. "Coordinated Patient Appointment Scheduling for a Multistation Healthcare Network," Operations Research, INFORMS, vol. 67(3), pages 599-618, May.
    2. Kuiper, Alex & de Mast, Jeroen & Mandjes, Michel, 2021. "The problem of appointment scheduling in outpatient clinics: A multiple case study of clinical practice," Omega, Elsevier, vol. 98(C).
    3. Christos Zacharias & Tallys Yunes, 2020. "Multimodularity in the Stochastic Appointment Scheduling Problem with Discrete Arrival Epochs," Management Science, INFORMS, vol. 66(2), pages 744-763, February.
    4. Ahmadi-Javid, Amir & Jalali, Zahra & Klassen, Kenneth J, 2017. "Outpatient appointment systems in healthcare: A review of optimization studies," European Journal of Operational Research, Elsevier, vol. 258(1), pages 3-34.
    5. Oualid Jouini & Saif Benjaafar & Bingnan Lu & Siqiao Li & Benjamin Legros, 2022. "Appointment-driven queueing systems with non-punctual customers," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 1-56, June.
    6. Vink, Wouter & Kuiper, Alex & Kemper, Benjamin & Bhulai, Sandjai, 2015. "Optimal appointment scheduling in continuous time: The lag order approximation method," European Journal of Operational Research, Elsevier, vol. 240(1), pages 213-219.
    7. Kuiper, Alex & Mandjes, Michel, 2015. "Appointment scheduling in tandem-type service systems," Omega, Elsevier, vol. 57(PB), pages 145-156.
    8. Song-Hee Kim & Ward Whitt & Won Chul Cha, 2018. "A Data-Driven Model of an Appointment-Generated Arrival Process at an Outpatient Clinic," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 181-199, February.
    9. Jiang, Bowen & Tang, Jiafu & Yan, Chongjun, 2019. "A stochastic programming model for outpatient appointment scheduling considering unpunctuality," Omega, Elsevier, vol. 82(C), pages 70-82.
    10. Tugba Cayirli & Pinar Dursun & Evrim D. Gunes, 2019. "An integrated analysis of capacity allocation and patient scheduling in presence of seasonal walk-ins," Flexible Services and Manufacturing Journal, Springer, vol. 31(2), pages 524-561, June.
    11. 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.
    12. Haolin Feng & Yiwu Jia & Siyi Zhou & Hongyi Chen & Teng Huang, 2023. "A Dataset of Service Time and Related Patient Characteristics from an Outpatient Clinic," Data, MDPI, vol. 8(3), pages 1-15, February.
    13. Wen-Ya Wang & Diwakar Gupta, 2011. "Adaptive Appointment Systems with Patient Preferences," Manufacturing & Service Operations Management, INFORMS, vol. 13(3), pages 373-389, July.
    14. Katsumi Morikawa & Katsuhiko Takahashi & Daisuke Hirotani, 2018. "Performance evaluation of candidate appointment schedules using clearing functions," Journal of Intelligent Manufacturing, Springer, vol. 29(3), pages 509-518, March.
    15. Tito Homem-de-Mello & Qingxia Kong & Rodrigo Godoy-Barba, 2022. "A Simulation Optimization Approach for the Appointment Scheduling Problem with Decision-Dependent Uncertainties," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2845-2865, September.
    16. Jin Qi, 2017. "Mitigating Delays and Unfairness in Appointment Systems," Management Science, INFORMS, vol. 63(2), pages 566-583, February.
    17. Yu Zhang & Vidyadhar G. Kulkarni, 2017. "Two-day appointment scheduling with patient preferences and geometric arrivals," Queueing Systems: Theory and Applications, Springer, vol. 85(1), pages 173-209, February.
    18. Navid Izady, 2015. "Appointment Capacity Planning in Specialty Clinics: A Queueing Approach," Operations Research, INFORMS, vol. 63(4), pages 916-930, August.
    19. van Eekelen, Wouter, 2023. "Distributionally robust views on queues and related stochastic models," Other publications TiSEM 9b99fc05-9d68-48eb-ae8c-9, Tilburg University, School of Economics and Management.
    20. Tugba Cayirli & Kum Khiong Yang & Ser Aik Quek, 2012. "A Universal Appointment Rule in the Presence of No‐Shows and Walk‐Ins," Production and Operations Management, Production and Operations Management Society, vol. 21(4), pages 682-697, July.

    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:spr:queues:v:100:y:2022:i:1:d:10.1007_s11134-021-09732-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.