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 Publish in OALib Journal ISSN: 2333-9721 APC: Only $99  Views Downloads  Relative Articles Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment Max-Weight Scheduling in Queueing Networks with Heavy-Tailed Traffic A note on the stability of multiclass Markovian queueing networks Two-node queueing network with a heavy-tailed random input: the strong stability case A non-Markovian queueing system with a variable number of channels A queueing theory description of fat-tailed price returns in imperfect financial markets Sample path large deviations for multiclass feedforward queueing networks in critical loading Heavy-Tailed Distributions Generated by Randomly Sampled Gaussian, Exponential and Power-Law Functions Large deviations for tandem queueing systems More... Statistics 2012 # Tail asymptotics for cumulative processes sampled at heavy-tailed random times with applications to queueing models in Markovian environments  Full-Text Cite this paper Abstract: This paper considers the tail asymptotics for a cumulative process$\{B(t); t \ge 0\}$sampled at a heavy-tailed random time$T$. The main contribution of this paper is to establish several sufficient conditions for the asymptotic equality${\sf P}(B(T) > bx) \sim {\sf P}(M(T) > bx) \sim {\sf P}(T>x)$as$x \to \infty$, where$M(t) = \sup_{0 \le u \le t}B(u)$and$b\$ is a certain positive constant. The main results of this paper can be used to obtain the subexponential asymptotics for various queueing models in Markovian environments. As an example, using the main results, we derive subexponential asymptotic formulas for the loss probability of a single-server finite-buffer queue with an on/off arrival process in a Markovian environment.

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