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Computational Analysis of Stationary and Transient Distribution of Single Server Queue with Working Vacation

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Global Trends in Computing and Communication Systems (ObCom 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 269))

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Abstract

The classical M/M/1 queue is considered with vacations, in which the server works with different service rates rather than completely stops service during the vacation period. Service times during vacation period, service times during service period and vacation times are all exponentially distributed. An exact transient system size probability distributions and other system characteristics are derived in closed form and also obtained the time-dependent system size probability in the absence of working vacation. Further we deduce the stationary distributions from time-dependent system size probabilities. A numerical illustration is provided by considering various parameters.

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References

  1. Baba, Y.: Analysis of a GI/M/1 queue with multiple working vacations. Oper. Res. Letters 33, 201–209 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Banik, A.D., Gupta, U.C., Pathak, S.S.: On the GI/M/1/N queue with multiple working vacations-analytic analysis and computation. Appl. Math. Modelling 31, 1701–1710 (2007)

    Article  MATH  Google Scholar 

  3. Doshi, B.T.: Queueing system with vacations - a survey. Queueing Syst. 1, 29–66 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  4. Jain, M., Jain, A.: Working vacations queueing model with multiple types of server breakdowns. Appl. Math. Modelling 34, 1–13 (2010)

    Article  MATH  Google Scholar 

  5. Liu, W., Xu, X., Tian, N.: Stochastic decompositions in the M/M/1 queue with working vacations. Oper. Res. Letters 35, 595–600 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Parthasarathy, P.R., Sudhesh, R.: Exact transient solution of state-dependent birth-death processes. J. App. Math. and Stoc. Analysis 2006, 1–16 (2006)

    Article  Google Scholar 

  7. Parthasarathy, P.R., Sudhesh, R.: Exact Transient solution of a discrete time queue with state-dependent rates. American J. Math. and Mgt. Sci. 26, 253–276 (2006)

    MathSciNet  Google Scholar 

  8. Servi, L.D., Finn, S.G.: M/M/1 queues with working vacations (M/M/1/WV). Perform. Evaluation 50, 41–52 (2002)

    Article  Google Scholar 

  9. Sudhesh, R.: Transient analysis of a queue with system disasters and customer impatience. Queueing Syst. 66, 95–105 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Tian, N., Zhang, Z.G.: Vacation Queueing Models: Theory and Applications. Springer, New York (2006)

    MATH  Google Scholar 

  11. Xiu, C., Tian, N., Liu, Y.: The M/M/1 Queue with Single Working Vacation Serving at a Slower Rate during the Start-up Period. Jornal of Mathematics Research 2, 98–102 (2010)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. University College of Engineering, Villupuram, Villupuram, 605 103, T.N., India

    R. Sudhesh

  2. Anna University, Chennai, T.N., India

    R. Sudhesh

  3. School of Advanced Sciences, Mathematics Division, VIT University, Vellore, 632 014, India

    L. Francis Raj

Authors
  1. R. Sudhesh
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  2. L. Francis Raj
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Editor information

Editors and Affiliations

  1. School of Computing Science and Engineering, VIT University, 632014, Vellore, TN, India

    P. Venkata Krishna

  2. School of Computing and Engineering, VIT University, 632014, Vellore, TN, India

    M. Rajasekhara Babu

  3. London Metropolitan University, UK

    Ezendu Ariwa

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© 2012 Springer-Verlag Berlin Heidelberg

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Sudhesh, R., Raj, L.F. (2012). Computational Analysis of Stationary and Transient Distribution of Single Server Queue with Working Vacation. In: Krishna, P.V., Babu, M.R., Ariwa, E. (eds) Global Trends in Computing and Communication Systems. ObCom 2011. Communications in Computer and Information Science, vol 269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29219-4_55

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  • DOI: https://doi.org/10.1007/978-3-642-29219-4_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29218-7

  • Online ISBN: 978-3-642-29219-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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