Skip to main content
SpringerLink
Log in

On product form approximations for communication networks with losses: Error bounds

  • Loss Networks
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

This paper studies communication networks with packet or message losses due to collisions, transmission errors or finite buffer constraints. Analytic error bounds are derived for simple product form approximations. The approximations are based on ignoring and bounding loss probabilities. The error bounds can be computed easily. Two extreme situations are considered: (1) Networks with infinite capacities but state-dependent loss probabilities; (2) Networks with finite capacities (buffers) and losses due to saturated buffers. The error bounds are of the order β when: (1) the loss probabilities are uniformly bounded by β, or when (2) the steady-state probability of capacity excess is of order β. The results provide formal justification for practical engineering approximations. Extensions to more complex communication networks seem possible.

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. I.J.B.F. Adan and J. Van der Wal, Monotonicity of a closed queueing network in the number of jobs, Oper. Res., to appear.

  2. I.J.B.F. Adan and J. Van der Wal, Monotonicity of the throughput in single server production and assembly networks with respect to the buffer sizes,Proc. 1st Int. Workshop on Queueing Systems with Blocking (North-Holland, 1989), pp. 345–356.

  3. D. Bertsekas and R. Gallager,Data Networks (Prentice-Hall, 1987).

  4. A. Hordijk and N.M. Van Dijk, Networks of queues: Part I and Part II.Lecture Notes in Control and Informational Services (Springer, 1983), pp. 156–205.

  5. F.P. Kelly,Stochastic Networks and Reversibility (Wiley, New York, 1979).

    Google Scholar 

  6. I. Mitrani,Modelling of Computer and Communication Networks (Cambridge Press, 1987).

  7. G. Pujolle and S. Fdida,Modèles de Systèmes et de Réseaux, Vol. 2: Files d'Attente (Eyrolles, 1989).

  8. M.L. Puterman, Markov decision processes, in:Handbook in Operations Research and Management Science: Stochastic Models II, ed. D.P. Heymand and M.J. Sobel (North-Holland, 1990), pp. 331–434. Is the second author's name correctly spelled?

  9. R.M. Ross,Applied Probability Models with Optimization Application (Holden-Day, 1970).

  10. Schwartz (1984),Telecommunication Networks (Addison-Wesley, 1984).

  11. J.G. Shanthikumar and D.D. Yao, Monotonicity properties in cyclic queueing networks with finite buffers,Proc. 1st Int. Workshop on Queueing Networks with Blocking (North-Holland, 1989), pp. 325–344.

  12. H.C. Tijms,Stochastic Modelling and Analysis: A Computational Approach (Wiley, New York, 1986).

    Google Scholar 

  13. N.M. Van Dijk, Simple bounds for queueing systems with breakdowns, Perform. Eval. 8(1988) 117–128.

    Article  Google Scholar 

  14. N.M. Van Dijk, A formal proof for the insensitivity of simple bounds for finite multi-server non-exponential tandem queues based on monotonicity results, Stoch. Proc. Appl. 27(1988)261–277.

    Google Scholar 

  15. N.M. Van Dijk, On the effect of loss probabilities in a two-stage circuit switch delay system. Research Report, Free University, Amsterdam (1990).

    Google Scholar 

  16. N.M. Van Dijk, The importance of bias-terms for error bounds and comparison results, in:Numerical Solution of Markov Chains, ed. W.J. Stewart (Marcel Dekker, 1991), pp. 617–642.

  17. N.M. Van Dijk, Approximate uniformization for continuous-time Markov chains with an application to performability analysis, Stoch. Proc. Appl. (1990), to appear.

  18. N.M. Van Dijk, A simple throughput bound for large closed queueing networks with finite capacities, Perform. Eval. 10(1989)153–167.

    Article  Google Scholar 

  19. N.M. Van Dijk and J. Van der Wal, Simple bounds and monotonicity results for multi-server exponential tandern queues, Queueing Systems 4(1989)1–19.

    Article  Google Scholar 

  20. N.M. Van Dijk, P. Tsoucas and J. Walrand, Simple bounds and monotonicity of the call congestion of finite multiserver delay systems, Prob. Eng. Info. Sci. 2(1988)129–138.

    Article  Google Scholar 

  21. P.K. Verma,Performance Estimation of Computer Communication Networks (Computer Science Press, 1989).

Download references

Author information

Authors and Affiliations

  1. Free University, Amsterdam, The Netherlands

    Nico M. van Dijk

  2. Ecole Nationale Supérieure des Télécommunications, Paris, France

    Hayri Korezlioglu

Authors
  1. Nico M. van Dijk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hayri Korezlioglu
    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

van Dijk, N.M., Korezlioglu, H. On product form approximations for communication networks with losses: Error bounds. Ann Oper Res 35, 69–94 (1992). https://doi.org/10.1007/BF02023091

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02023091

Keywords

Search

Navigation