Skip to main content
SpringerLink
Log in

An Arrival Time Approach to M/G/1-type Queues with Generalized Vacations

  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

We propose a simple way, called the arrival time approach, of finding the queue length distributions for M/G/1-type queues with generalized server vacations. The proposed approach serves as a useful alternative to understanding complicated queueing processes such as priority queues with server vacations and MAP/G/1 queues with server vacations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R.B. Cooper, Introduction to Queueing Theory, 2nd ed. (North-Holland, Amsterdam, 1981).

    Google Scholar 

  2. L. Green, A limit theorem on subintervals of interrenewal times, Oper. Res. 30 (1982) 210-216.

    Google Scholar 

  3. H.W. Lee, B.Y. Ahn and N.I. Park, Decompositions of the queue length distributions in the MAP/G/1 queue under multiple and single vacations with N-policy, Stochastic Models (2001), to appear.

  4. D.M. Lucantoni, K.S. Meier-Hellstern and M.F. Neuts, A single-server queue with server vacations and a class of non-renewal arrival processes, Adv. Appl. Probab. 22 (1990) 676-705.

    Google Scholar 

  5. M.F. Neuts, Structured Stochastic Matrices of M/G/1 Type and their Applications (Marcel Dekker, New York, 1989).

    Google Scholar 

  6. J.G. Shanthikumar, On stochastic decomposition in M/G/1 type queues with generalized server vacations, Oper. Res. 36 (1988) 566-569.

    Google Scholar 

  7. H. Takagi, Queueing Analysis, Vol. 1 (North-Holland, Amsterdam, 1991).

    Google Scholar 

  8. T. Takine and T. Hasegawa, A generalization of the decomposition property in the M/G/1 queue with server vacations, Oper. Res. Lett. 12 (1988) 97-99.

    Google Scholar 

  9. T. Takine and Y. Takahashi, On the relationship between queue lengths at a random instant and a departure in the stationary queue with BMAP arrivals, Stochastic Models 14 (1998) 601-610.

    Google Scholar 

  10. R.W. Wolff, Poisson arrivals see time averages, Oper. Res. 30 (1982) 223-231.

    Google Scholar 

  11. B.K. Yoon and K.C. Chae, An invariance in the priority M/G/1 queue with generalized vacations, Working Paper, Department of Industrial Engineering, KAIST, Taejonshi, Korea (1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. KAIST, Taejon, Korea

    K.C. Chae

  2. Sung Kyun Kwan University, Su Won, Korea

    H.W. Lee

  3. ETRI, Taejon, Korea

    C.W. Ahn

Authors
  1. K.C. Chae
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H.W. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C.W. Ahn
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chae, K., Lee, H. & Ahn, C. An Arrival Time Approach to M/G/1-type Queues with Generalized Vacations. Queueing Systems 38, 91–100 (2001). https://doi.org/10.1023/A:1010876229827

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010876229827

Search

Navigation