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
Articles

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.

Keywords

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

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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

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