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Asymptotic Analysis of Reliability for Switching Systems in Light and Heavy Traffic Conditions

  • Vladimir V. Anisimov
Chapter
Part of the Statistics for Industry and Technology book series (SIT)

Abstract

An asymptotic analysis of flows of rare events switched by some random environment is provided. An approximation by nonhomogeneous Poisson flows in case of mixing environment is studied. Special notions of S-set and “monotone” structure for finite Markov environment are introduced. An approximation by Poisson flows with Markov switches in case of asymptotically consolidated environment is proved. An analysis of the 1st exit time from a subset is also given. In heavy traffic conditions an averaging principle for trajectories with Poisson approximation for flows of rare events in systems with fast switches is proved. The method of proof is based on limit theorems for processes with semi-Markov switches.

Applications to the reliability analysis of state-dependent Markov and semi-Markov queueing systems in light and heavy traffic conditions are considered

Keywords and phrases

asymptotic analysis reliability switching processes rare events Markov and semi-Markov processes consolidation queueing models light and heavy traffic 

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Vladimir V. Anisimov
    • 1
    • 2
  1. 1.Bilkent UniversityAnkaraTurkey
  2. 2.Turkey & Kiev UniversityKievUkraine

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