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A sufficient condition for subexponential asymptotics of GI/G/1type Markov chains with queueing applications
, 2013
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Tail asymptotics for cumulative processes sampled at heavytailed random times with applications to queueing models in Markovian environments
 Journal of the Operations Research Society of Japan
, 2013
"... Abstract This paper considers the tail asymptotics for a cumulative process {B(t); t ≥ 0} sampled at a heavytailed random time T. The main contribution of this paper is to establish several sufficient conditions for the asymptotic equality P(B(T)> bx) ∼ P(M(T)> bx) ∼ P(T> x) as x → ∞, wh ..."
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Abstract This paper considers the tail asymptotics for a cumulative process {B(t); t ≥ 0} sampled at a heavytailed random time T. The main contribution of this paper is to establish several sufficient conditions for the asymptotic equality P(B(T)> bx) ∼ P(M(T)> bx) ∼ P(T> x) as x → ∞, where M(t) = sup0≤u≤tB(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 singleserver finitebuffer queue with an on/off arrival process in a Markovian environment.