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Fluid Queue Driven by an M/M/1 Queue Subject to Working Vacation and Impatience

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Computational Intelligence, Cyber Security and Computational Models. Models and Techniques for Intelligent Systems and Automation (ICC3 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 844))

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Abstract

In recent years, fluid queueing modelling proves to be very effective in the analysis of computer and communication systems, production inventory systems and many other scenarios. This paper studies a fluid queueing model driven by an M/M/1 queue subject to working vacation and customer impatience. The fluid in the infinite capacity buffer is assumed to decrease when the background queueing model is empty and increase otherwise. The underlying system of differential difference equations that governs the process are solved using continued fraction and generating function methodologies. Explicit expressions for the joint steady state probabilities of the state of the background queueing model and the content of the fluid buffer are obtained in terms of modified Bessel function of the first kind.

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References

  1. Gao, S., Wang, J.: Discrete time \(Geo^X/G/1\) retrial queue with general retrial times, working vacations and vacation interruption. Qual. Technol. Quant. Manage. 10(4), 495–512 (2013)

    Article  Google Scholar 

  2. Gao, S., Yin, C.: Discrete-time \(Geo^X/G/1\) queue with geometrically working vacations and vacation interruption. Qual. Technol. Quant. Manage. 10(4), 423–442 (2013)

    Article  Google Scholar 

  3. Huo, Z., Jin, S., Tian, N.: Performance analysis and evaluation for connection-oriented networks based on discrete time vacation queueing model. Qual. Technol. Quant. Manage. 5(1), 51–62 (2008)

    Article  MathSciNet  Google Scholar 

  4. Latouche, G., Taylor, P.G.: A stochastic fluid model for an ad hoc mobile network. Queueing Syst. 63, 109–129 (2009)

    Article  MathSciNet  Google Scholar 

  5. Mao, B., Wang, F., Tian, N.: Fluid model driven by an \(M/M/1\) queue with multiple exponential vacations and N-policy. J. Appl. Math. Comput. 38, 119–131 (2012)

    Article  MathSciNet  Google Scholar 

  6. Mitra, D.: Stochastic theory of a fluid model of producers and consumers couple by a buffer. Adv. Appl. Probab. 20, 646–676 (1988)

    Article  MathSciNet  Google Scholar 

  7. Narayanan, C.V., Deepak, T.G., Krishnamoorthy, A., Krishnakumar., B.: On an (s, S) inventory policy with service time, vacation to server and correlated lead time. Qual. Technol. Quant. Manage. 5(2), 129–143 (2008)

    Google Scholar 

  8. Jain, M., Upadhyaya, S.: Threshold N-policy for degraded machining system with multiple type spares and multiple vacations. Qual. Technol. Quant. Manage. 6(2), 185–203 (2009)

    Article  MathSciNet  Google Scholar 

  9. Parthasarathy, P.R., Vijayashree, K.V., Lenin, R.B.: An M/M/1 driven fluid queue-continued fraction approach. Queueing Syst. 42, 189–199 (2002)

    Article  MathSciNet  Google Scholar 

  10. Ammar, S.I.: Analysis of an \(M/M/1\) driven fluid queue with multiple exponential vacations. Appl. Math. Comput. 227, 329–334 (2014)

    MathSciNet  MATH  Google Scholar 

  11. Vijayashree, K.V., Anjuka, A.: Stationary analysis of an \(M/M/1\) driven fluid queue subject to catastrophes and subsequent repair. IAENG Int. J. Appl. Math. 43(4), 238–241 (2013)

    MathSciNet  Google Scholar 

  12. Vijaya Lakxmi, P., Goswami, V., Jyothsna, K.: Analysis of discrete-time single server queue with balking and multiple working vacations. Qual. Technol. Quant. Manage. 10(4), 443–456 (2013)

    Article  Google Scholar 

  13. Xu, X., Geng, J., Liu, M., Guo, H.: Stationary analysis for the fluid model driven by the \(M/M/c\) working vacation queue. J. Math. Anal. Appl. 403(2), 423–433 (2013)

    Article  MathSciNet  Google Scholar 

  14. Xu, X., Zhao, Y., Geng, J., Jin, S.: Analysis for the fluid model driven by an \(M/PH/1\) queue. J. Inf. Comput. Sci. 10(11), 3489–3496 (2013)

    Article  Google Scholar 

  15. Yue, D., Yue, W., Xu, G.: Analysis of customers impatience in an \(M/M/1\) queue with working vacation. J. Industr. Manage. Optim. 8(4), 895–908 (2012)

    Article  MathSciNet  Google Scholar 

  16. Wang, F., Mao, B., Tian, N.: Fluid model driven by an \(M/M/1\) queue with multiple exponential vacation. In: The 2nd International Conference on Advanced Computer Control, vol. 3, pp. 112–115 (2010)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Anna University, Chennai, India

    K. V. Vijayashree

  2. Department of Mathematics, SRM Institute of Science and Technology, Kancheepuram, India

    A. Anjuka

Authors
  1. K. V. Vijayashree
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  2. A. Anjuka
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Corresponding author

Correspondence to K. V. Vijayashree .

Editor information

Editors and Affiliations

  1. PSG College of Technology, Coimbatore, India

    Geetha Ganapathi

  2. BITS Pilani, KK Birla, Goa, India

    Arumugam Subramaniam

  3. University of the Basque Country, San Sebastian, Spain

    Manuel Graña

  4. PSG College of Technology, Coimbatore, India

    Suresh Balusamy

  5. PSG College of Technology, Coimbatore, India

    Rajamanickam Natarajan

  6. PSG College of Technology, Coimbatore, India

    Periakaruppan Ramanathan

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Vijayashree, K.V., Anjuka, A. (2018). Fluid Queue Driven by an M/M/1 Queue Subject to Working Vacation and Impatience. In: Ganapathi, G., Subramaniam, A., Graña, M., Balusamy, S., Natarajan, R., Ramanathan, P. (eds) Computational Intelligence, Cyber Security and Computational Models. Models and Techniques for Intelligent Systems and Automation. ICC3 2017. Communications in Computer and Information Science, vol 844. Springer, Singapore. https://doi.org/10.1007/978-981-13-0716-4_14

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  • DOI: https://doi.org/10.1007/978-981-13-0716-4_14

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-0715-7

  • Online ISBN: 978-981-13-0716-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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