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G/M/1 queues with delayed vacations

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Abstract

We considerG/M/1 queues with multiple vacation discipline, where at the end of every busy period the server stays idle in the system for a period of time called changeover time and then follows a vacation if there is no arrival during the changeover time. The vacation time has a hyperexponential distribution. By using the methods of the shift operator and supplementary variable, we explicitly obtain the queue length probabilities at arrival time points and arbitrary time points simultaneously.

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References

  1. B.D. Choi and D.H. Han,G/M a,b /1 queue with server vacations, J. of Oper. Res. in Japan37 (1994), 171–181.

    Google Scholar 

  2. B.T. Doshi,Queueing systems with vacation — a survey, Queueing Systems1 (1986), 29–66.

    Article  MathSciNet  Google Scholar 

  3. D. Gross and C.M. Harris,Fundamental of Queueing Theory, John Wiley & Sons, 1985.

  4. H. Li and Y. Zhu,Analysis of M/G/1 queues with delayed vacations and exhaustive service discipline, European J. of Oper. Res.92 (1996), 125–134.

    Article  Google Scholar 

  5. H. Takagi,Queueing Analysis: A Foundation of Performance Evaluation, Vol 1: Vacation and Priority Systems, Part 1, North-Holland, 1991.

  6. J.H. Wilkinson,The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Sunmoon University, Asan, 336 - 840, ChungNam, Korea

    Dong Hwan Han

  2. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, 60607-7045, Chicago, Illinois, USA

    Doo Il Choi

Authors
  1. Dong Hwan Han
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  2. Doo Il Choi
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Correspondence to Dong Hwan Han.

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Han, D.H., Choi, D.I. G/M/1 queues with delayed vacations. Korean J. Comput. & Appl. Math. 5, 1–11 (1998). https://doi.org/10.1007/BF03008931

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  • DOI: https://doi.org/10.1007/BF03008931

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