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Some Queuing Problems with Balking and Reneging---II

Author

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  • C. J. Ancker

    (System Development Corporation, Santa Monica, California)

  • A. V. Gafarian

    (System Development Corporation, Santa Monica, California)

Abstract

This is the second of two papers in which balking (refusing to join the queue) and reneging (leaving the queue after joining) are considered. The new element here is that the balking behavior is drastically altered The model assumes (1) Customers arrive from a single infinite source in a Poisson stream (2) Arriving customers join the system if it is empty or balk with probability 1 - (beta)/ n , n = 1, 2, ... where n is the number in system. Thus (beta) is a measure of customer willingness to join the queue (3) Joining customers renege if service does not begin within a certain time. This time is a, random variable whose density function is negative exponential with parameter (alpha) (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 a equal to zero.

Suggested Citation

  • C. J. Ancker & A. V. Gafarian, 1963. "Some Queuing Problems with Balking and Reneging---II," Operations Research, INFORMS, vol. 11(6), pages 928-937, December.
    • Handle: RePEc:inm:oropre:v:11:y:1963:i:6:p:928-937
    DOI: 10.1287/opre.11.6.928
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    Cited by:

    1. Li Xiao & Susan H. Xu & David D. Yao & Hanqin Zhang, 2022. "Optimal staffing for ticket queues," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 309-351, October.
    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. Tkachenko Andrey, 2013. "Multichannel queuing systems with balking and regenerative input fl ow," HSE Working papers WP BRP 14/STI/2013, National Research University Higher School of Economics.
    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.

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