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Journal of Systems Science and Complexity

, Volume 25, Issue 2, pp 293–302 | Cite as

The recursive solution of queue length for Geo/G/1 queue with N-policy

  • Chuanyi LuoEmail author
  • Yinghui Tang
  • Wei Li
  • Kaili Xiang
Article

Abstract

This paper considers a discrete-time queue with N-policy and LAS-DA (late arrival system with delayed access) discipline. By using renewal process theory and probability decomposition techniques, the authors derive the recursive expressions of the queue-length distributions at epochs n , n +, and n. Furthermore, the authors obtain the stochastic decomposition of the queue length and the relations between the equilibrium distributions of the queue length at different epochs (n , n +, n and departure epoch D n ).

Key words

Discrete-time queue N-policy recursive expression stochastic decomposition 

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References

  1. [1]
    Bharah-Kumar K, Discrete time queueing systems and their networks, IEEE Trans. Comm. Com., 1980, 28: 260–263.CrossRefGoogle Scholar
  2. [2]
    I. Rubin and L. F. Morness, Message delay analysis for polling and token multiple-access schemes for local communication networks, IEEE J. Selected Areas in Communications, 1983, SAC-1, 5: 935–947.CrossRefGoogle Scholar
  3. [3]
    H. Takagi and K. Leung, Analysis of a discrete time queueing system with time-limited service, Queueing Systems, 1994, 18: 183–197.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Z. Niu, T. Shu, and Y. Takahashi, A vacation queue with setup and close-down time and batch Markovian arrival processes, Performance Evaluation, 2003, 54: 225–248.CrossRefGoogle Scholar
  5. [5]
    R. B. Cooper, Introduction to Queueing Theory, Elsevier North Holland, New York, 1981.Google Scholar
  6. [6]
    N. Tian, Discrete Time Queue Theory, Science Press, Beijing, 2007: 87–108.Google Scholar
  7. [7]
    L. Tadj and G. Choudhury, Optimal design and control of queues, Top, 2005 13: 359–412.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    M. Yadin and P. Naor, Queueing systems with a removable service station, Operational Research Quarterly, 1963, 14: 393–405.CrossRefGoogle Scholar
  9. [9]
    J. Li and N. Tian, The discrete-time Geo/Geo/1 queue with single working vacation, Quality Technology and Quantitation Managgement, 2008, 5: 77–89.MathSciNetzbMATHGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Chuanyi Luo
    • 1
    Email author
  • Yinghui Tang
    • 2
  • Wei Li
    • 1
  • Kaili Xiang
    • 1
  1. 1.School of Economic MathematicsSouthwestern University of Finance and EconomicsChengduChina
  2. 2.School of Mathematics and Software ScienceSichuan Normal UniversityChengduChina

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