Skip to main content
SpringerLink
Log in

Performance analysis of a hybrid switching system where voice messages can be queued

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

Abstract

In the classical model of a hybrid switching system with movable boundary it is assumed that blocked voice messages are lost and do not affect the further functioning of the system. We describe a more realistic model where blocked voice messages are queued and then are served once a channel becomes free. The main mathematical difficulty in the analysis of such models lies in the fact that the underlying stochastic process has as state space the whole quadrant ℤ 2+ . We reduce the problem to a set of equations defined over the lattice semi-strip {1,...,N} × ℤ+. This in turn allows us to use available general mathematical theories.

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. D. Burman, An analytic approach to diffusion approximation in queuing, Ph.D. Dissertation, Courante Institute of Mathematics, New York University, New York (1979).

    Google Scholar 

  2. J.K. Choi, J.U. Seo and C.K. Un, Performance analysis of a packet-switched synchronous voice data transmission system, IEEE Trans. Commun. C-38 (1990) 1419–1429.

    Google Scholar 

  3. S. Ethier and T. Kurtz,Markov Processes: Characterization and Convergence (Wiley, New York, 1986).

    Google Scholar 

  4. H. Heffes and D.M. Lucantoni, A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance, IEEE J. Sel. Areas Commun. SAC-4 (1986) 856–868.

    Google Scholar 

  5. S. Li and J.W. Mark, Performance of voice/data integration on a TDM system, IEEE Trans. Commun. C 33 (1985) 1265–1273.

    Google Scholar 

  6. I. Mitrani and P.J.B. King, Multiprocessor systems with preemptive priorities, Perf. Eval. 1(1981) 118–125.

    Google Scholar 

  7. M.F. Neuts,Matrix-Geometric Solutions in Stochastic Models (Johns Hopkins University Press, Baltimore, 1981).

    Google Scholar 

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

    Google Scholar 

  9. M. Zuckerman, Applications of matrix-geometric solutions for queueing performance evaluation of a hybrid switching system, J. Austral. Math. Soc. Ser. B 31 (1989) 219–239.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Probability, Mechanics and Mathematics Faculty, Moscow State University, 119899, Moscow, Russia

    G. Falin

  2. Department of Mathematics and Statistics, Concordia University, H4B 1R6, Montreal, Quebec, Canada

    Z. Khalil

  3. Department of Statistical and Actuarial Sciences, The University of Western Ontario, N6A 5B7, London, Ontario, Canada

    D. A. Stanford

Authors
  1. G. Falin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. Khalil
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. A. Stanford
    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

Falin, G., Khalil, Z. & Stanford, D.A. Performance analysis of a hybrid switching system where voice messages can be queued. Queueing Syst 16, 51–65 (1994). https://doi.org/10.1007/BF01158948

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158948

Keywords

Search

Navigation