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Research Article

An M/G/1 queueing model with k sequential heterogeneous service steps and vacations in the transient state

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Pages 633-647 | Accepted 11 Sep 2021, Published online: 26 Apr 2022

References

  • Ayyappan, G., & Shyamala, S. (2013). Time dependent solution of M[x]/G/1 queueing model with Bernoulli vacation and balking. International Journal of Computer Applications, 61(21), 8875–8887.
  • Badamchizadeh, A., & Shahkar, G. H. (2006). ON M/G1,G2,G3, …,Gk/V/1/(BS). Far East J. Theo. Stat, (20), 151–162.
  • Baek, J. W., Lee, H. W., Lee, S. W., & Ahn, S. (2013). A MAP-modulated fluid flow model with multiple vacations. Annals of Operations Research, 202(1), 19–34. https://doi.org/10.1007/s10479-012-1100-y
  • Baek, J. W., Lee, H. W., Lee, S. W., & Ahn, S. (2014). A workload factorization for BMAP/G/1 vacation queues under variable service speed. Operations Research Letters, 42(1), 58–63. https://doi.org/10.1016/j.orl.2013.11.009
  • Barron, Y. (2018). A threshold policy in a Markov-modulated production system with server vacation: The case of continuous and batch supplies. Advances in Applied Probability, 50(4), 1246–1274. https://doi.org/10.1017/apr.2018.59
  • Boxma, O. J., Schlegel, S., & Yechiali, U. (2002). A note on an M/G/1 queue with a waiting server, timer, and vacations. American Mathematical Society Translations Series, 2(207), 25–35.
  • Chang, S. H., Takine, T., Chae, K. C., & Lee, H. W. (2002). A unified queue length formula for BMAP/G/1 queue with generalized vacations. Stochastic Models, 18(3), 369–386. https://doi.org/10.1081/STM-120014218
  • Choudhury, G. (2002). Analysis of the M[x]/G/1 queueing system with vacation times. Sankhya – Series B, 64(1), 37–49.
  • Choudhury, G. (2003). Some aspects of M/G/1 queueing system with optional second service. TOP, 11(1), 141–150. https://doi.org/10.1007/BF02578955
  • Choudhury, G., & Deka, M. (2018). A batch arrival unreliable server delaying repair queue with two phases of service and Bernoulli vacation under multiple vacation policy. Quality Technology & Quantitative Management, 15(2), 157–176. https://doi.org/10.1080/16843703.2016.1208934
  • Doshi, B. T. (1986). Queueing system with vacation- a survey. Queueing Systems, 1(1), 29–66. https://doi.org/10.1007/BF01149327
  • Indra, A., & Bancal, S. (2010). The transient solution of an unreliable M/G/1 queue with vacation. International Journal of Information and Management Sciences, 21, 391–406.
  • Jehad, A.-J. K., & Madan, C. (2003). An M/G/1 queue with second optional service with general service time distribution. Information and Management Sciences, 14(2), 47–56.
  • Jeyakumar, S., & Senthilnathan, B. (2017). Modelling and analysis of a bulk service queueing model with multiple working vacations and server breakdown. RAIRO-Oper. Res, 51(2), 485–508. https://doi.org/10.1051/ro/2016037
  • Ke, J. C., Wu, C. H., & Zhang, Z. G. (2010). Recent developments in vacation queueing models: A short survey. International Journal of Operations Research, 7, 3–8.
  • Kuo, C. C., Ke, J. C., & Choudhury, G. (2015). Optimal NT policies for a two-phase service M/G/1 system with Bernoulli vacation schedule. Quality Technology & Quantitative Management, 12(3), 343–353. https://doi.org/10.1080/16843703.2015.11673385
  • Rao, S. H., Kumar, V. V., Kumar, V. V., & Rao, T. S. (2017). Analysis of two phase queueing system with impatient customers and server breakdowns and delayed repair. International Journal of Pure and Applied Mathematics, 115(4), 651–663. https://doi.org/10.12732/ijpam.v115i4.1
  • Saffer, Z. S., & Yue, W. (2015). M/G/1 multiple vacation model with balking for a class of disciplines. Quality Technology & Quantitative Management, 20(3), 383–407. https://doi.org/10.1080/16843703.2015.11673388
  • Shyamala, S., & Vijayaraj, R. (2020). Time dependent solution of two stages M[x]/G/1 queue model server vacation random setup time and balking with Bernoulli schedule. AIP Conference Proceedings, 2261(1). doi:10.1063/5.0017027.
  • Singh Bura, G. (2019). Transient solution of an M/M/∞ queue with catastrophes. Commun. Stat. Theory Methods, 48(14), 3439–3450. https://doi.org/10.1080/03610926.2018.1477960
  • Sundari, M., & Srinivasan, S. (2012). Analysis of transient behavior of M/G/1 queue with single vacation. International Journal of Pure and Applied Mathematics, 76(1), 149–156.
  • Suranga Sampath, M. I. G., & Jicheng, L. (2020). Impact of customers impatience on an M/M/1 queueing system subject to differentiated vacation with a waiting server. Quality Technology & Quantitative Management, 17(2), 125–148. https://doi.org/10.1080/16843703.2018.1555877
  • Tian, N., & Zhang, Z. G. (2006). Vacation queueing models: Theory and applications. Springer.
  • Vijayashree, K. V., & Janani, B. (2018). Impact of customers impatience on an M/M/1 queueing system subject to differentiated vacation with a waiting server. Quality Technology & Quantitative Management, 15(6), 730–748. https://doi.org/10.1080/16843703.2017.1335492

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