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Some Queuing Problems with Balking and Reneging. I

Author

Listed:
  • C. J. Ancker

    (System Development Corporation, Santa Monica, California)

  • A. V. Gafarian

    (System Development Corporation, Santa Monica, California)

Abstract

Balking (refusing to join the queue) and reneging (leaving the queue after entering) are considered. The model assumes (1) Customers arrive from a single infinite source in a Poisson stream (2) Arriving customers balk with probability n / N where n is the number in system and N is the maximum number allowed in the system (3) Joining customers renege if service does not begin by a certain time, which is a random variable with negative exponential distribution (4) A single-service facility operates on a first-come, first-served basis with negative exponential service time distribution. For the steady state, the following are obtained the state probabilities, mean number in queue and system, the probability of R or more in system, the probabilities of balking, waiting, reneging, and acquiring service, the customer loss rate, the distribution and mean value of time in queue for customers who acquire service, and the corresponding results for those who renege. All of these results are also obtained for a pure balking system (no reneging) by setting the reneging parameter equal to zero. This case may be interpreted as the simple machine interference problem for which some of our results appear to be new.

Suggested Citation

  • C. J. Ancker & A. V. Gafarian, 1963. "Some Queuing Problems with Balking and Reneging. I," Operations Research, INFORMS, vol. 11(1), pages 88-100, February.
    • Handle: RePEc:inm:oropre:v:11:y:1963:i:1:p:88-100
    DOI: 10.1287/opre.11.1.88
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    Cited by:

    1. Ramin Behzad & Mohammad Reza Salehi Rad & Nader Nematollahi, 2019. "Queues with Simultaneous Arrival of Customers and the Dependence Structure of the Waiting Times," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1045-1056, December.
    2. Amina Angelika Bouchentouf & Aicha Messabihi, 2018. "Heterogeneous two-server queueing system with reverse balking and reneging," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 251-267, June.
    3. Veeraruna Kavitha & Jayakrishnan Nair & Raman Kumar Sinha, 2019. "Pseudo conservation for partially fluid, partially lossy queueing systems," Annals of Operations Research, Springer, vol. 277(2), pages 255-292, June.
    4. 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.
    5. P. Vijaya Laxmi & V. Goswami & K. Jyothsna, 2013. "Optimization of Balking and Reneging Queue with Vacation Interruption under -Policy," Journal of Optimization, Hindawi, vol. 2013, pages 1-9, June.
    6. Cheng-Dar Liou, 2015. "Markovian queue optimisation analysis with an unreliable server subject to working breakdowns and impatient customers," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(12), pages 2165-2182, September.
    7. Hayriye Ayhan, 2022. "Server assignment policies in queues with customer abandonments," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 393-395, April.
    8. Mohammad Firouz & Linda Li & Burcu B. Keskin, 2022. "Managing equipment rentals: Unreliable fleet, impatient customers, and finite commitment capacity," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 3963-3981, November.
    9. Navid Ghaffarzadegan & Richard C. Larson, 2018. "SD meets OR: a new synergy to address policy problems," System Dynamics Review, System Dynamics Society, vol. 34(1-2), pages 327-353, January.
    10. Katsunobu Sasanuma, 2021. "Asymptotic Analysis for Systems with Deferred Abandonment," Mathematics, MDPI, vol. 9(18), pages 1-11, September.

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