• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2021, Volume: 14, Issue: 9, Pages: 801-809

Original Article

Some aspects of customers impatience with varying rates of Reneging

Received Date:22 December 2021, Accepted Date:05 March 2021, Published Date:22 March 2021


Objectives: Stochastic modeling of M/M/c/k queuing system in the presence of Position dependent reneging (PDR) and state dependent balking (SDB) along with closed form expression of various performance measures. Methods: Markov process and probability generating functions (pgf) are used. Findings: Closed form expression of a number of traditional as well as newly designed performance measures are derived along with explicit derivation of the steady state probabilities of the model. Novelty: Analysis of finite buffer multi server Markovian queuing model in the presence of balking and reneging.

Keywords: Queue; finite buffer; multiserver; reneging; balking; impatience


  1. Bouchentouf AA, Messabihi A. Heterogeneous two-server queueing system with reverse balking and reneging. OPSEARCH. 2018;55:251–267. Available from: https://dx.doi.org/10.1007/s12597-017-0319-4
  2. Som BK, Kumar R. A heterogeneous queuing system with reverse balking and reneging. Journal of Industrial and Production Engineering. 2018;35(1):1–5. Available from: https://dx.doi.org/10.1080/21681015.2017.1297739
  3. Haight FA. Queuing with Balking. Biometrika. 1957;44:360–369. Available from: https://doi.org/10.1093/biomet/44.3-4.360
  4. Pallabi M, Choudhury A. Aspects of Impatience in a Finite Buffer Queue. RAIRO - Operations Research. 2012;46:189–209. Available from: https://dx.doi.org/10.1051/ro/2012014
  5. Yue D, Yue W. A heterogeneous two-server network system with balking and a bernoulli vacation schedule. Journal of Industrial and Management Optimization. 2010;6(3):501–516. Available from: https://doi.org/10.3934/jimo.2010.6.501
  6. Al-Seedy RO, El-Sherbiny AA, El-Shehawy SA, Ammar SI. Transient solution of the M/M/c queue with balking and reneging. Computers & Mathematics with Applications. 2009;57(8):1280–1285. Available from: https://dx.doi.org/10.1016/j.camwa.2009.01.017
  7. Choudhury A, Medhi P. Some aspects of balking and reneging in finite buffer queues. RAIRO - Operations Research. 2011;45:223–240. Available from: https://dx.doi.org/10.1051/ro/2011113
  8. Choudhury A, Medhi P. Balking and reneging in multiserver Markovian queuing system. International Journal of Mathematics in Operational Research. 2011;3(4). Available from: https://dx.doi.org/10.1504/ijmor.2011.040874
  9. Kumar R, Som BK. An M/M/1/N Feedback Queuing System with Reverse Balking, Reverse Reneging and Retention of Reneged Customers. Indian Journal of Industrial and Applied Mathematics. 2015;6(2). Available from: https://dx.doi.org/10.5958/1945-919x.2015.00013.4
  10. Jain NK, Kumar R, Som BK. An M/M/1/N queuing system with reverse balking. American Journal of Operational Research. 2014;2(2):17–20. Available from: https://www.ripublication.com/gjpam17/gjpamv13n7_49.pdf
  11. Kumar R. A catastrophic-cum-restorative queueing problem with correlated input and impatient customers. International Journal of Agile Systems and Management. 2012;5:122–131. Available from: https://doi.org/10.1504/IJASM.2012.046893
  12. Kuila M. Balking and Reneging in the Queuing System. IOSR Journal of Mathematics. 2013;6(1):35–37. Available from: https://dx.doi.org/10.9790/5728-0613537
  13. Ammar SI, El-Sherbiny AA, El-Shehawy SA, Al-Seedy RO. A matrix approach for the transient solution of an M/M/1/N queue with discouraged arrivals and reneging. International Journal of Computer Mathematics. 2012;89(4):482–491. Available from: https://dx.doi.org/10.1080/00207160.2011.637553
  14. Saikia G, Medhi P, Choudhury A. Analyzing Impatience in Multiserver Markovian Queues. International Journal of Supply and Operations Management. 2020;7:310–321. Available from: https://doi.org/10.22034/IJSOM.2020.4.2
  15. Choudhury A, Medhi P. Modeling Customers’ Impatience in M/M/1 queue under General Distribution. Journal of Assam Science Society. 2016;57(1-2):90–107.
  16. Medhi J. Stochastic Processes (Second). New Age International (P) Ltd.. 1994.


© 2021 Medhi.This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)


Subscribe now for latest articles and news.