IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v193y2009i1p317-320.html
   My bibliography  Save this article

How pre-emptive priority affects completion rate in an M/M/1 queue with Poisson reneging

Author

Listed:
  • Nasrallah, Walid F.

Abstract

Queuing problems in which customers leave the queue without obtaining service (i.e. renege) have many applications. This paper looks at a queue where arrival, service and reneging events are all generated by independent Poisson processes, and customers are selected for service according to priority. A closed-form expression is derived for the probability of completing service for each priority class if high-priority customers always pre-empt low-priority ones. This result has applications in modeling the value of communications between members of an interacting population, such as a formal organization or an online community.

Suggested Citation

  • Nasrallah, Walid F., 2009. "How pre-emptive priority affects completion rate in an M/M/1 queue with Poisson reneging," European Journal of Operational Research, Elsevier, vol. 193(1), pages 317-320, February.
    • Handle: RePEc:eee:ejores:v:193:y:2009:i:1:p:317-320
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(07)01152-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Andreas Brandt & Manfred Brandt, 1999. "On a Two-Queue Priority System with Impatience and its Application to a Call Center," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 191-210, September.
    2. D. Y. Barrer, 1957. "Queuing with Impatient Customers and Indifferent Clerks," Operations Research, INFORMS, vol. 5(5), pages 644-649, October.
    3. Walid F. Nasrallah, 2006. "When does management matter in a dog-eat-dog world: An “Interaction Value Analysis” model of organizational climate," Computational and Mathematical Organization Theory, Springer, vol. 12(4), pages 339-359, December.
    4. D. Y. Barrer, 1957. "Queuing with Impatient Customers and Ordered Service," Operations Research, INFORMS, vol. 5(5), pages 650-656, October.
    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. Eliran Sherzer & Yoav Kerner, 2018. "Customers’ abandonment strategy in an M / G / 1 queue," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 65-87, October.
    2. W. Rogiest & K. Laevens & J. Walraevens & H. Bruneel, 2015. "Random-order-of-service for heterogeneous customers: waiting time analysis," Annals of Operations Research, Springer, vol. 226(1), pages 527-550, March.
    3. Walid Nasrallah & Raymond Levitt & Peter Glynn, 2003. "Interaction Value Analysis: When Structured Communication Benefits Organizations," Organization Science, INFORMS, vol. 14(5), pages 541-557, October.
    4. Chai, Xudong & Liu, Liwei & Chang, Baoxian & Jiang, Tao & Wang, Zhen, 2019. "On a batch matching system with impatient servers and boundedly rational customers," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 308-328.
    5. Shaul K. Bar-Lev & Hans Blanc & Onno Boxma & Guido Janssen & David Perry, 2013. "Tandem Queues with Impatient Customers for Blood Screening Procedures," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 423-451, June.
    6. Bolandifar, Ehsan & DeHoratius, Nicole & Olsen, Tava, 2023. "Modeling abandonment behavior among patients," European Journal of Operational Research, Elsevier, vol. 306(1), pages 243-254.
    7. Pala, Ali & Zhuang, Jun, 2018. "Security screening queues with impatient applicants: A new model with a case study," European Journal of Operational Research, Elsevier, vol. 265(3), pages 919-930.
    8. Yoshiaki Inoue & Onno Boxma & David Perry & Shelley Zacks, 2018. "Analysis of $$\hbox {M}^{\mathrm {x}}/\hbox {G}/1$$ M x / G / 1 queues with impatient customers," Queueing Systems: Theory and Applications, Springer, vol. 89(3), pages 303-350, August.
    9. Ken’ichi Kawanishi & Tetsuya Takine, 2016. "MAP/M/c and M/PH/c queues with constant impatience times," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 381-420, April.
    10. Pel, Adam J. & Chaniotakis, Emmanouil, 2017. "Stochastic user equilibrium traffic assignment with equilibrated parking search routes," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 123-139.
    11. Hayriye Ayhan, 2022. "Server assignment policies in queues with customer abandonments," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 393-395, April.
    12. Bong Dae Choi & Bara Kim & Dongbi Zhu, 2004. "MAP/M/c Queue with Constant Impatient Time," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 309-325, May.
    13. Dengpan Liu & Subodha Kumar & Vijay S. Mookerjee, 2012. "Advertising Strategies in Electronic Retailing: A Differential Games Approach," Information Systems Research, INFORMS, vol. 23(3-part-2), pages 903-917, September.
    14. Kouki, Chaaben & Legros, Benjamin & Zied Babai, M. & Jouini, Oualid, 2020. "Analysis of base-stock perishable inventory systems with general lifetime and lead-time," European Journal of Operational Research, Elsevier, vol. 287(3), pages 901-915.
    15. Legros, Benjamin & Jouini, Oualid & Akşin, O. Zeynep & Koole, Ger, 2020. "Front-office multitasking between service encounters and back-office tasks," European Journal of Operational Research, Elsevier, vol. 287(3), pages 946-963.
    16. Nasrallah, Walid F. & Qawasmeh, Suleiman J., 2009. "Comparing multi-dimensional contingency fit to financial performance of organizations," European Journal of Operational Research, Elsevier, vol. 194(3), pages 911-921, May.
    17. Xuan Li & Toshiyuki Yamamoto & Tao Yan & Lili Lu & Xiaofei Ye, 2020. "First Train Timetabling for Urban Rail Transit Networks with Maximum Passenger Transfer Satisfaction," Sustainability, MDPI, vol. 12(10), pages 1-22, May.
    18. H. Christian Gromoll & Philippe Robert & Bert Zwart, 2008. "Fluid Limits for Processor-Sharing Queues with Impatience," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 375-402, May.
    19. Wei Xiong & Tayfur Altiok, 2009. "An approximation for multi-server queues with deterministic reneging times," Annals of Operations Research, Springer, vol. 172(1), pages 143-151, November.
    20. David Perry, 1999. "Analysis of a Sampling Control Scheme for a Perishable Inventory System," Operations Research, INFORMS, vol. 47(6), pages 966-973, December.

    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:ejores:v:193:y:2009:i:1:p:317-320. 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/locate/eor .

    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.