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International Conference on Information Technologies and Mathematical Modelling

ITMM 2015: Information Technologies and Mathematical Modelling - Queueing Theory and Applications pp 250–262Cite as

On an M/G/1 Queue with Vacation in Random Environment

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 564))

Abstract

We study an M / G / 1 queue with multiple vacation and vacation interruption. Both normal vacation (type I) and working vacation (type II) are considered. The exhaustive service discipline is assumed in this paper. At the end of a busy period, depending on the environment, the server either opts for normal vacation or working vacation. On completion of type I vacation if the server finds the system empty he goes for type II vacation. On completion of type II vacation if the server finds the system empty goes for another type II vacation. On completion of service in type II vacation, if the server finds one or more customers in queue he returns to normal service, interrupting the vacation. An arriving customer, during type I vacation, joins the queue with probability q or leaves the system with probability \(\displaystyle 1-q\) and during type II vacation all the arriving customers join the queue. Using supplementary variable technique we derive the distributions for the queue length and service status under steady state condition. Laplace-Stieltjes transform of the stationary waiting time is also developed. Some numerical illustrations are also given.

A. Krishnamoorthy—Research supported by Kerala State Council for Science, Technology & Environment (No. 001/KESS/2013/CSTE))

Jaya S—Research supported by FDP of UGC, No.F.FIP/12th Plan/KLMG009 TF-12.

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Authors and Affiliations

  1. Cochin University of Science and Technology, Kochi, India

    Achyutha Krishnamoorthy & Balakrishnan Lakshmy

  2. Maharaja’s College, Kochi, India

    Jaya Sivadasan

Authors
  1. Achyutha Krishnamoorthy
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  2. Jaya Sivadasan
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  3. Balakrishnan Lakshmy
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Corresponding author

Correspondence to Achyutha Krishnamoorthy .

Editor information

Editors and Affiliations

  1. Applied Mathematics and Computer Science, Belarusian State University, Minsk, Russia

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Kemerovo State University, Anzhero-Sudzhensk, Russia

    Rafael Yakupov

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Krishnamoorthy, A., Sivadasan, J., Lakshmy, B. (2015). On an M/G/1 Queue with Vacation in Random Environment. In: Dudin, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2015. Communications in Computer and Information Science, vol 564. Springer, Cham. https://doi.org/10.1007/978-3-319-25861-4_22

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  • DOI: https://doi.org/10.1007/978-3-319-25861-4_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25860-7

  • Online ISBN: 978-3-319-25861-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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