The exact asymptotic for the stationary distribution of some unreliable systems

Pawel Lorek

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arXiv · 1102.4707

The exact asymptotic for the stationary distribution of some unreliable systems

Pawel Lorek

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Abstract

In this paper we find asymptotic distribution for some unreliable networks. Using Markov Additive Structure and Adan, Foley, McDonald method, we find the exact asymptotic for the stationary distribution. With the help of MA structure and matrix geometric approach, we also investigate the asymptotic when breakdown intensity is small. In particular, two different asymptotic regimes for small breakdown intensity suggest two different patterns of large deviations, which is confirmed by simulation study.

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Pawel Lorek. 2011-02-23. The exact asymptotic for the stationary distribution of some unreliable systems. https://arxiv.org/abs/1102.4707

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