Skip to main content
SpringerLink
Log in

Steady-State Analysis of Bulk Queuing System with Renovation, Prolonged Vacation and Tune-Up/Shutdown Times

  • Conference paper
  • First Online:
Proceedings of 2nd International Conference on Mathematical Modeling and Computational Science

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1422))

  • 194 Accesses

Abstract

This paper investigates bulk arrival and batch service queueing system with server failure, prolonged vacation and tune-up time/shutdown times. On service completion epoch, if the queue length is less than ‘a’, then the server leaves for vacation (secondary job). When the server gets breakdown whilst serving customers service process will not be interrupted, it will be continued for present batch of customers by doing some precaution arrangements. The server will be repaired after the service process during renewal time of the server. In vacation queueing models, the server will be idle after the vacation due to insufficient number of customers, but in this model, if the server wishes to go another type of vacation, it will be allowed with probability α or the server will go to dormant period with probability 1 − α. For the proposed model, probability generating function of the queue size distribution at an arbitrary time epoch is obtained by using supplementary variable technique. Various performance measures are derived.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Takagi, H. 1991. Vacation and priority systems, vol. 1. North Holland.

    Google Scholar 

  2. Tian, N. and Z.G. Zhang. 2006. Vacation Queueing Models: Theory and Applications, vol. 93. Springer Science & Business Media.

    Google Scholar 

  3. Neuts, M.F. 1967. A general class of bulk queues with Poisson input. The Annals of Mathematical Statistics 38 (3): 759–770.

    Article  MathSciNet  Google Scholar 

  4. Arumuganathan, R., and S. Jeyakumar. 2005. Steady state analysis of a bulk queue with multiple vacations, setup times with N-policy and closedown times. Applied Mathematical Modelling 29 (10): 972–986.

    Article  Google Scholar 

  5. Lee, H.W., S.S. Lee, J.O. Park, and K.C. Chae. 1994. Analysis of the Mx/G/1 queue by N-policy and multiple vacations. Journal of Applied Probability 31 (2): 476–496.

    MathSciNet  MATH  Google Scholar 

  6. Jeyakumar, S., and B. Senthilnathan. 2016. Steady state analysis of bulk arrival and bulk service queueing model with multiple working vacations. International Journal of Mathematics in Operational Research 9 (3): 375–394.

    Article  MathSciNet  Google Scholar 

  7. Madan, K.C. 2018. On optional deterministic server vacations in a single server queue providing two types of first essential service followed by two types of additional optional service. Applied Mathematical Sciences 12 (4): 147–159.

    Article  MathSciNet  Google Scholar 

  8. Ayyappan, G., and T. Deepa. 2019. Analysis of batch arrival bulk service queue with additional optional service multiple vacation and setup time. International Journal of Mathematics in Operational Research 15 (1): 1–25.

    Article  MathSciNet  Google Scholar 

  9. Haridass, M., and R. Arumuganathan. 2012. Analysis of a MX/G (a, b)/1 queueing system with vacation interruption. RAIRO-Operations Research 46 (4): 305–334.

    Article  MathSciNet  Google Scholar 

  10. Agrawal, P.K., M. Jain, and A. Singh. 2017. Optimal N-policy for finite queue with server breakdown and state-dependent rate. International Journal Computer Engineering Research 7: 61–68.

    Google Scholar 

  11. Madan, K.C., W. Abu-Dayyeh, and M. Gharaibeh. 2003. Steady state analysis of two queue models with random breakdowns. Information and Management Science 14 (3): 37–51.

    MathSciNet  MATH  Google Scholar 

  12. Li, W., D. Shi, and X. Chao. 1997. Reliability analysis of M/G/1 queueing systems with server breakdowns and vacations. Journal of Applied probability 34 (2): 546–555.

    Article  MathSciNet  Google Scholar 

  13. Nishimura, S., and Y. Jiang. 1995. An M/G/l vacation model with two service modes. Probability in the Engineering and Informational Sciences 9 (3): 355–374.

    Article  MathSciNet  Google Scholar 

  14. Nobel, R.D., and H.C. Tijms. 1999. Optimal control for an MX/G/1 queue with two service modes. European Journal of Operational Research 113 (3): 610–619.

    Article  Google Scholar 

  15. Jeyakumar, S., and B. Senthilnathan. 2012. A study on the behaviour of the server breakdown without interruption in a MX/G (a, b)/1 queueing system with multiple vacations and closedown time. Applied Mathematics and Computation 219 (5): 2618–2633.

    Article  MathSciNet  Google Scholar 

  16. Wu, W., Y. Tang, and M. Yu. 2015. Analysis of an M/G/1 queue with N-policy, single vacation, unreliable service station and replaceable repair facility. Opsearch 52 (4): 670–691.

    Article  MathSciNet  Google Scholar 

  17. Choudhury, G., and M. Deka. 2016. A batch arrival unreliable server queue with two phases of service and Bernoulli vacation schedule under randomised vacation policy. International Journal of Services and Operations Management 24 (1): 33–72.

    Article  Google Scholar 

  18. Cox, D.R. 1955, July. The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Mathematical Proceedings of the Cambridge Philosophical Society 51(3): 433–441. Cambridge University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai, India

    S. P. Niranjan & B. Komala Durga

  2. Jain (Deemed-To-Be University), Bangalore, India

    M. Thangaraj

Authors
  1. S. P. Niranjan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Komala Durga
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Thangaraj
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. P. Niranjan .

Editor information

Editors and Affiliations

  1. Department of Creative Technologies and Product Design, National Taipei University of Business, Taoyuan, Taiwan

    Sheng-Lung Peng

  2. Department of Computer Science, National Yang Ming Chiao Tung University, Hsinchu, Taiwan

    Cheng-Kuan Lin

  3. Department of Computer Science and Engineering, Sister Nivedita University, Kolkata, West Bengal, India

    Souvik Pal

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Niranjan, S.P., Komala Durga, B., Thangaraj, M. (2022). Steady-State Analysis of Bulk Queuing System with Renovation, Prolonged Vacation and Tune-Up/Shutdown Times. In: Peng, SL., Lin, CK., Pal, S. (eds) Proceedings of 2nd International Conference on Mathematical Modeling and Computational Science. Advances in Intelligent Systems and Computing, vol 1422. Springer, Singapore. https://doi.org/10.1007/978-981-19-0182-9_4

Download citation

Publish with us

Policies and ethics

Search

Navigation