Subexponential asymptotics of the stationary distributions of \(\mathrm{GI}/\mathrm{G}/1\)-type Markov chains. (English) Zbl 1271.60099
Stoch. Models 29, No. 2, 190-239 (2013); corrigendum ibid. 31, No. 4, 673-677 (2015).
Summary: This article considers the subexponential asymptotics of the stationary distributions of \(\mathrm{GI}/\mathrm{G}/1\)-type Markov chains in two cases: (i) the phase transition matrix in non-boundary levels is stochastic; and (ii) it is strictly substochastic. For case (i), we present a weaker sufficient condition for the subexponential asymptotics than those given in the literature. As for case (ii), the subexponential asymptotics has not been studied, as far as we know. We show that the subexponential asymptotics in case (ii) is different from that in case (i). We also study the locally subexponential asymptotics of the stationary distributions in both cases (i) and (ii).
MSC:
| 60K25 | Queueing theory (aspects of probability theory) |
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
Keywords:
\(\mathrm{GI}/\mathrm{G}/1\)-type Markov chain; (Locally) subexponential; Markov additive process (MAdP); stationary distributionReferences:
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