The exact asymptotic for the stationary distribution of some unreliable systems

2011/02/23 by Paweł Lorek, Pawel Lorek, Lorek, Pawel
Business, Management and Accounting · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1102.4707

arxiv created 2011/02/23 · openalex publication_date 2011/02/23 · arxiv updated 2011/02/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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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