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Queuing with Impatient Customers and Indifferent Clerks

Author

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  • D. Y. Barrer

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

Abstract

A waiting-line problem in which the arrival and service rates are of Poisson type is considered subject to the additional conditions that (a) each customer is limited to a fixed time during which he is available for service and after which he automatically leaves the system and (b) customers are selected at random from among those in the system rather than on a first-come-first-served basis. The equilibrium distribution of the length of the queue and the expected rate at which customers escape service are obtained. The expected escape rate is plotted as a function of the limited time of customer availability for selected arrival and service rates and compared with the result of Monte Carlo trials of the model.

Suggested Citation

  • D. Y. Barrer, 1957. "Queuing with Impatient Customers and Indifferent Clerks," Operations Research, INFORMS, vol. 5(5), pages 644-649, October.
    • Handle: RePEc:inm:oropre:v:5:y:1957:i:5:p:644-649
    DOI: 10.1287/opre.5.5.644
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    Cited by:

    1. Veena Goswami & Gopinath Panda, 2024. "Analysis of Renewal Batch Arrival Queues with Multiple Vacations and Geometric Abandonment," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-27, June.
    2. 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.
    3. 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.
    4. Bolandifar, Ehsan & DeHoratius, Nicole & Olsen, Tava, 2023. "Modeling abandonment behavior among patients," European Journal of Operational Research, Elsevier, vol. 306(1), pages 243-254.
    5. 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.
    6. 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.
    7. 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.
    8. Hayriye Ayhan, 2022. "Server assignment policies in queues with customer abandonments," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 393-395, April.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.

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