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In this chapter, we consider asymptotic behavior for the stationary probability vector of any ergodic Markov chain of GI/G/1 type, and provide conditions under which the stationary probability vector is either light-tailed or heavy-tailed by means of the RG-factorization. At the same time, we provide expressions for both the light tail and the heavy tail. Note that the conditions and expressions can...
In this paper, we consider a MAP/G/1 queue with MAP arrivals of negative customers, where there are two types of service times and two classes of removal rules: the RCA and RCH, as introduced in section 2. We provide an approach for analyzing the system. This approach is based on the classical supplementary variable method, combined with the matrix-analytic method and the censoring technique. By using...
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