Queueing Systems

, Volume 16, Issue 1–2, pp 51–65 | Cite as

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

  • G. Falin
  • Z. Khalil
  • D. A. Stanford


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.


Hybrid switching system randomly varying service rate structural matrices of M/G/1 type heavy traffic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [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. [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. [3]
    S. Ethier and T. Kurtz,Markov Processes: Characterization and Convergence (Wiley, New York, 1986).Google Scholar
  4. [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. [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. [6]
    I. Mitrani and P.J.B. King, Multiprocessor systems with preemptive priorities, Perf. Eval. 1(1981) 118–125.Google Scholar
  7. [7]
    M.F. Neuts,Matrix-Geometric Solutions in Stochastic Models (Johns Hopkins University Press, Baltimore, 1981).Google Scholar
  8. [8]
    M.F. Neuts,Structured Stochastic Matrices of M/G/1 Type and Their Applications (Marcel Dekker, New York, 1989).Google Scholar
  9. [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

Copyright information

© J.C. Baltzer AG, Science Publishers 1994

Authors and Affiliations

  • G. Falin
    • 1
  • Z. Khalil
    • 2
  • D. A. Stanford
    • 3
  1. 1.Department of Probability, Mechanics and Mathematics FacultyMoscow State UniversityMoscowRussia
  2. 2.Department of Mathematics and StatisticsConcordia UniversityMontrealCanada
  3. 3.Department of Statistical and Actuarial SciencesThe University of Western OntarioLondonCanada

Personalised recommendations