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Pré-Publication, Document De Travail Année : 2021

Asymptotics for infinite server queues with fast/slow Markov switching and fat tailed service times

Résumé

We study a general $k$ dimensional infinite server queues process with Markov switching, Poisson arrivals and where the service times are fat tailed with index $\alpha\in (0,1)$. When the arrival rate is sped up by a factor $n^\gamma$, the transition probabilities of the underlying Markov chain are divided by $n^\gamma$ and the service times are divided by $n$, we identify two regimes ("fast arrivals", when $\gamma>\alpha$, and "equilibrium", when $\gamma=\alpha$) in which we prove that a properly rescaled process converges pointwise in distribution to some limiting process. In a third "slow arrivals" regime, $\gamma<\alpha$, we show the convergence of the two first joint moments of the rescaled process.
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Dates et versions

hal-01894007 , version 1 (12-10-2018)
hal-01894007 , version 2 (19-03-2020)
hal-01894007 , version 3 (18-06-2021)

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Citer

Landy Rabehasaina. Asymptotics for infinite server queues with fast/slow Markov switching and fat tailed service times. 2021. ⟨hal-01894007v3⟩
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