Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Approximate mean value performance analysis of cyclic queueing networks with production blocking

  • Articles
  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

A simple approximation method is developed for performance analysis of exponential cyclic queues with production blocking. With a modified Arrival Instant Theorem to cater for finite queue capacity, a set of equations involving the mean values of performance measures are established and an efficient algorithm is proposed. Numerical experiments show that the approximation method is very efficient in providing results with good accuracy.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. I.F. Akyildiz, On the exact and approximate throughput analysis of closed queueing networks with blocking, IEEE Trans. Software Eng. SE-14 (1988) 62–70.

    Google Scholar 

  2. I.F. Akyildiz, Mean value analysis for blocking queueing networks, IEEE Trans. Software Eng. SE-14 (1988) 418–429.

    Google Scholar 

  3. J. Buchan and E. Koenigsberg,Scientific Inventory Management (Prentice-Hall, Englewood Cliffs, NJ, 1963).

    Google Scholar 

  4. J.A. Buzacott and J.G. Shanthikumar,Stochastic Models of Manufacturing Systems (Prentice-Hall, Englewood Cliffs, NJ, 1993).

    Google Scholar 

  5. Y. Dallery and Y. Frein, A decomposition method for the approximate analysis of closed queueing networks with blocking, in:Queueing Networks with Blocking, eds. H.G. Perros and T. Altiok (Elsevier Science/North-Holland, Amsterdam, 1989).

    Google Scholar 

  6. Y. Dallery, Z. Liu and D. Towsley, Equivalence, reversibility and symmetry properties in fork/join queueing networks with blocking, Technical Report MASI No. 90–32 (1990).

  7. Y. Dallery and D. Towsley, Symmetry property of the throughput in closed tandem queueing networks with finite buffers, Oper. Res. Lett. 10 (1991) 541–547.

    Google Scholar 

  8. Y. Frein and Y. Dallery, Analysis of cyclic queueing networks with finite buffers and blocking before service, Perf. Eval. 10 (1989) 197–210.

    Google Scholar 

  9. S.S. Lavenberg and M. Reiser, Stationary state probabilities at arrival instants for closed queueing networks with multiple types of customers. J. Appl. Prob. 17 (1980) 1048–1061.

    Google Scholar 

  10. J.D.C. Little, A proof of the queueing formulaL=λW, Oper. Res. 9 (1961) 383–387.

    Google Scholar 

  11. X-G. Liu, Toward modelling assembly systems: applications of queueing networks with blocking, Ph.D. Thesis, University of Waterloo, Waterloo, Ontario, Canada (May 1990).

    Google Scholar 

  12. X-G. Liu, L. Zhuang and J.A. Buzacott, A decomposition method for throughput analysis of cyclic queues with production blocking, presented at2nd Int. Workshop on Queueing Networks with Blocking, Raleigh, North Carolina USA (1992).

  13. R.O. Onvural, Survey of closed queueing networks with blocking, ACM Comp. Surveys 22 (1990) 83–121.

    Google Scholar 

  14. R.O. Onvural and H.G. Perros, Approximate throughput analysis of cyclic queueing networks with finite buffers, IEEE Trans. Software Eng. SE-15 (1989) 800–808.

    Google Scholar 

  15. R.O. Onvural and H.G. Perros, Some equivalencies between closed queueing networks with blocking, Perf. Eval. 9 (1989) 111–118.

    Google Scholar 

  16. H.G. Perros, Open queueing networks with blocking, in:Stochastic Analysis of Computer and Communication Systems, ed. H. Takagi (North-Holland, Amsterdam, 1990).

    Google Scholar 

  17. M. Reiser and S.S. Lavenberg, Mean value analysis of closed multichain queueing networks, J. ACM 27 (1980) 313–322.

    Google Scholar 

  18. P.J. Schweitzer, Approximate analysis of multiclass closed networks of queues,Proc. Int. Conf. on Stochastic Control and Optimization, Free University, Amsterdam (1977).

    Google Scholar 

  19. P.J. Schweitzer, A. Seidmann and S. Shalev-oren, The correction term in approximate mean value analysis, Oper. Res. 4 (1986) 197–200.

    Google Scholar 

  20. K.C. Sevcik and I. Mitrani, The distribution of queueing network states at input and output instants, J. ACM28 (1981) 358–371.

    Google Scholar 

  21. J.G. Shanthikumar and D.D. Yao, Monotonicity and concavity properties in cyclic queueing networks with finite buffers, in:Queueing Networks with Blocking, eds. H.G. Perros and T. Altiok (Elsevier Science/North-Holland, Amsterdam, 1989).

    Google Scholar 

  22. R. Suri and G.W. Diehl, A variable buffer-size model and its use in analyzing closed queueing networks with blocking, Manag. Sci. 32 (1986) 206–224.

    Google Scholar 

  23. R. Suri and R. Hildebrant, Modelling flexible manufacturing systems using mean value analysis, J. Manufac. Sys. 3 (1984) 27–38.

    Google Scholar 

  24. D.D. Yao and J.A. Buzacott, Modelling a class of flexible manufacturing systems with reversible routing, Oper. Res. 35 (1987) 87–93.

    Google Scholar 

  25. L. Zhuang and K.S. Hindi, Mean value analysis for multiclass closed queueing network models of flexible manufacturing systems with limited buffers, Eur. J. Oper. Res. 46 (1990) 366–379.

    Google Scholar 

  26. L. Zhuang and K.S. Hindi, Approximate MVA for closed queueing network models of flexible manufacturing systems with a block-and-wait mechanism, Comp. Ind. Eng. 20 (1991) 35–44.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Management Sciences, University of Waterloo, N2L 3G1, Ontario, Waterloo, Canada

    Li Zhuang

  2. Faculty of Administrative Studies, York University, M3J 1PS, North York, Ontario, Canada

    John A. Buzacott

  3. Department of Management Sciences, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Xiao -Gao Liu

Authors
  1. Li Zhuang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John A. Buzacott
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiao -Gao Liu
    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

Zhuang, L., Buzacott, J.A. & Liu, X.G. Approximate mean value performance analysis of cyclic queueing networks with production blocking. Queueing Syst 16, 139–165 (1994). https://doi.org/10.1007/BF01158953

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158953

Keywords

Search

Navigation