IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v19y2017i1d10.1007_s11009-015-9476-1.html
   My bibliography  Save this article

Waiting Time Distributions in the Preemptive Accumulating Priority Queue

Author

Listed:
  • Val Andrei Fajardo

    (University of Waterloo)

  • Steve Drekic

    (University of Waterloo)

Abstract

We consider a queueing system in which a single server attends to N priority classes of customers. Upon arrival to the system, a customer begins to accumulate priority linearly at a rate which is distinct to the class to which it belongs. Customers with greater accumulated priority levels are given preferential treatment in the sense that at every service selection instant, the customer with the greatest accumulated priority level is selected next for servicing. Furthermore, the system is preemptive so that the servicing of a customer is interrupted for customers with greater accumulated priority levels. The main objective of the paper is to characterize the waiting time distributions of each class. Numerical examples are also provided which exemplify the true benefit of incorporating an accumulating prioritization structure, namely the ability to control waiting times.

Suggested Citation

  • Val Andrei Fajardo & Steve Drekic, 2017. "Waiting Time Distributions in the Preemptive Accumulating Priority Queue," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 255-284, March.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:1:d:10.1007_s11009-015-9476-1
    DOI: 10.1007/s11009-015-9476-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-015-9476-1
    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/s11009-015-9476-1?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. Fajardo, Val Andrei & Drekic, Steve, 2015. "Controlling the workload of M/G/1 queues via the q-policy," European Journal of Operational Research, Elsevier, vol. 243(2), pages 607-617.
    2. L. Kleinrock, 1964. "A delay dependent queue discipline," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 11(3‐4), pages 329-341, September.
    3. J. M. Holtzman, 1971. "Bounds for a Dynamic-Priority Queue," Operations Research, INFORMS, vol. 19(2), pages 461-468, April.
    4. A. Netterman & I. Adiri, 1979. "A Dynamic Priority Queue with General Concave Priority Functions," Operations Research, INFORMS, vol. 27(6), pages 1088-1100, December.
    5. Jiunn Hsu, 1970. "A Continuation of Delay-Dependent Queue Disciplines," Operations Research, INFORMS, vol. 18(4), pages 733-738, August.
    6. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
    7. Uttarayan Bagchi & Robert S. Sullivan, 1985. "Dynamic, Non-Preemptive Priority Queues with General, Linearly Increasing Priority Function," Operations Research, INFORMS, vol. 33(6), pages 1278-1298, December.
    8. Percy H. Brill, 2008. "Level Crossing Methods in Stochastic Models," International Series in Operations Research and Management Science, Springer, number 978-0-387-09421-2, September.
    9. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    10. James R. Jackson, 1961. "Queues with Dynamic Priority Discipline," Management Science, INFORMS, vol. 8(1), pages 18-34, October.
    11. James R. Jackson, 1962. "Waiting‐time distributions for queues with dynamic priorities," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(1), pages 31-36, March.
    12. Leonard Kleinrock & Roy P. Finkelstein, 1967. "Time Dependent Priority Queues," Operations Research, INFORMS, vol. 15(1), pages 104-116, February.
    13. John J. Kanet, 1982. "A Mixed Delay Dependent Queue Discipline," Operations Research, INFORMS, vol. 30(1), pages 93-96, February.
    14. James R. Jackson, 1960. "Some problems in queueing with dynamic priorities," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 7(3), pages 235-249, September.
    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. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Single-Server Multi-Class Queue with Unreliable Service, Batch Correlated Arrivals, Customers Impatience, and Dynamical Change of Priorities," Mathematics, MDPI, vol. 9(11), pages 1-17, May.
    2. Na Li & David A. Stanford & Peter Taylor & Ilze Ziedins, 2017. "Nonlinear Accumulating Priority Queues with Equivalent Linear Proxies," Operations Research, INFORMS, vol. 65(6), pages 1712-1721, December.
    3. Seokjun Lee & Sergei Dudin & Olga Dudina & Chesoong Kim & Valentina Klimenok, 2020. "A Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities," Mathematics, MDPI, vol. 8(8), pages 1-20, August.
    4. Valentina Klimenok & Alexander Dudin & Olga Dudina & Irina Kochetkova, 2020. "Queuing System with Two Types of Customers and Dynamic Change of a Priority," Mathematics, MDPI, vol. 8(5), pages 1-25, May.

    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. Phadhana Tosirisuk & Jeya Chandra, 1990. "Multiple finite source queueing model with dynamic priority scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(3), pages 365-381, June.
    2. Na Li & David A. Stanford & Peter Taylor & Ilze Ziedins, 2017. "Nonlinear Accumulating Priority Queues with Equivalent Linear Proxies," Operations Research, INFORMS, vol. 65(6), pages 1712-1721, December.
    3. Moshe Haviv & Liron Ravner, 2016. "Strategic bidding in an accumulating priority queue: equilibrium analysis," Annals of Operations Research, Springer, vol. 244(2), pages 505-523, September.
    4. Brian Fralix, 2020. "On classes of Bitcoin-inspired infinite-server queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 29-52, June.
    5. Öner-Közen, Miray & Minner, Stefan, 2017. "Impact of priority sequencing decisions on on-time probability and expected tardiness of orders in make-to-order production systems with external due-dates," European Journal of Operational Research, Elsevier, vol. 263(2), pages 524-539.
    6. Shu, Yin & Feng, Qianmei & Liu, Hao, 2019. "Using degradation-with-jump measures to estimate life characteristics of lithium-ion battery," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    7. David H Collins & Richard L Warr & Aparna V Huzurbazar, 2013. "An introduction to statistical flowgraph models for engineering systems," Journal of Risk and Reliability, , vol. 227(5), pages 461-470, October.
    8. C. E. Phelan & D. Marazzina & G. Germano, 2020. "Pricing methods for α-quantile and perpetual early exercise options based on Spitzer identities," Quantitative Finance, Taylor & Francis Journals, vol. 20(6), pages 899-918, June.
    9. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2018. "Optimal liquidation under stochastic liquidity," Finance and Stochastics, Springer, vol. 22(1), pages 39-68, January.
    10. Corsaro, Stefania & Kyriakou, Ioannis & Marazzina, Daniele & Marino, Zelda, 2019. "A general framework for pricing Asian options under stochastic volatility on parallel architectures," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1082-1095.
    11. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2021. "Random variate generation for exponential and gamma tilted stable distributions," LSE Research Online Documents on Economics 108593, London School of Economics and Political Science, LSE Library.
    12. Brill, Percy H., 2015. "Note on the service time in an M/G/1 queue with bounded workload," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 162-169.
    13. Phelan, Carolyn E. & Marazzina, Daniele & Fusai, Gianluca & Germano, Guido, 2018. "Fluctuation identities with continuous monitoring and their application to the pricing of barrier options," European Journal of Operational Research, Elsevier, vol. 271(1), pages 210-223.
    14. 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.
    15. Runhuan Feng & Pingping Jiang & Hans Volkmer, 2020. "Geometric Brownian motion with affine drift and its time-integral," Papers 2012.09661, arXiv.org.
    16. Peter Braunsteins & Sophie Hautphenne & Peter G. Taylor, 2016. "The roles of coupling and the deviation matrix in determining the value of capacity in M/M/1/C queues," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 157-179, June.
    17. Gökçe Kahveciog̃lu & Barış Balcıog̃lu, 2016. "Coping with production time variability via dynamic lead-time quotation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 877-898, October.
    18. Zeynep Akşin & Baris Ata & Seyed Morteza Emadi & Che-Lin Su, 2017. "Impact of Delay Announcements in Call Centers: An Empirical Approach," Operations Research, INFORMS, vol. 65(1), pages 242-265, February.
    19. Felix Lokin & Fenghui Yu, 2024. "Fill Probabilities in a Limit Order Book with State-Dependent Stochastic Order Flows," Papers 2403.02572, arXiv.org.
    20. Feng, Runhuan & Jiang, Pingping & Volkmer, Hans, 2021. "Geometric Brownian motion with affine drift and its time-integral," Applied Mathematics and Computation, Elsevier, vol. 395(C).

    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:metcap:v:19:y:2017:i:1:d:10.1007_s11009-015-9476-1. 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.