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Transient Analysis of an M/M/c Queue Subject to Multiple Exponential Vacation

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Computational Intelligence, Cyber Security and Computational Models

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 412))

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Abstract

In this paper, we consider an M/M/c queueing model subject to multiple exponential vacation wherein arrivals occur according to a Poisson distribution and the c servers provide service according to an exponential distribution. When the system is empty, all the c servers go on a vacation and the vacation times are assumed to follow exponential distribution. Further arrivals are allowed to join the queue when servers are in vacation. Explicit analytical expressions for the time dependent probabilities of the number in the system are presented using matrix geometric method.

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Author information

Authors and Affiliations

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

    K. V. Vijayashree

  2. Department of Mathematics, Central Institute of Plastics Engineering and Technology, Chennai, India

    B. Janani

Authors
  1. K. V. Vijayashree
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  2. B. Janani
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Corresponding author

Correspondence to K. V. Vijayashree .

Editor information

Editors and Affiliations

  1. Applied Mathematics and Computational Sc, PSG College of Technology, Coimbatore, Tamil Nadu, India

    Muthukrishnan Senthilkumar

  2. Applied Mathematics and Computational Sc, PSG College of Technology, Coimbatore, Tamil Nadu, India

    Vijayalakshmi Ramasamy

  3. Applied Mathematics and Computational Sc, PSG College of Technology, Coimbatore, Tamil Nadu, India

    Shina Sheen

  4. Applied Mathematics and Computational Sc, PSG College of Technology, Coimbatore, Tamil Nadu, India

    C. Veeramani

  5. Department of Mathematics, Ryerson University, TORONTO, Ontario, Canada

    Anthony Bonato

  6. Fac. Science&Technology, Deakin University, Burwood, Australia

    Lynn Batten

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© 2016 Springer Science+Business Media Singapore

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Vijayashree, K.V., Janani, B. (2016). Transient Analysis of an M/M/c Queue Subject to Multiple Exponential Vacation. In: Senthilkumar, M., Ramasamy, V., Sheen, S., Veeramani, C., Bonato, A., Batten, L. (eds) Computational Intelligence, Cyber Security and Computational Models. Advances in Intelligent Systems and Computing, vol 412. Springer, Singapore. https://doi.org/10.1007/978-981-10-0251-9_51

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  • DOI: https://doi.org/10.1007/978-981-10-0251-9_51

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-0250-2

  • Online ISBN: 978-981-10-0251-9

  • eBook Packages: EngineeringEngineering (R0)

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