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Queuing with Impatient Customers and Ordered Service

Author

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  • D. Y. Barrer

    (Weapons Systems Evaluation Group, Institute for Defense Analyses, Washington 25, D.C.)

Abstract

Two types of customer behavior are considered: (1) if a customer is acquired for service before he has waited a time (tau) 0 , he remains in the queue until served irrespective of whether or not his total waiting time exceeds (tau) 0 . Only those customers who wait for a time (tau) 0 without being acquired for service become “lost” customers, and (2) a customer whose total waiting time is (tau) 0 becomes a lost customer irrespective of whether he is acquired for service or not.

Suggested Citation

  • D. Y. Barrer, 1957. "Queuing with Impatient Customers and Ordered Service," Operations Research, INFORMS, vol. 5(5), pages 650-656, October.
    • Handle: RePEc:inm:oropre:v:5:y:1957:i:5:p:650-656
    DOI: 10.1287/opre.5.5.650
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    Citations

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    Cited by:

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Bolandifar, Ehsan & DeHoratius, Nicole & Olsen, Tava, 2023. "Modeling abandonment behavior among patients," European Journal of Operational Research, Elsevier, vol. 306(1), pages 243-254.
    8. 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.
    9. 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.
    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. 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.
    12. David Perry, 1999. "Analysis of a Sampling Control Scheme for a Perishable Inventory System," Operations Research, INFORMS, vol. 47(6), pages 966-973, December.
    13. 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.
    14. 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.
    15. Hayriye Ayhan, 2022. "Server assignment policies in queues with customer abandonments," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 393-395, April.
    16. 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.
    17. 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.

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