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Pré-Publication, Document De Travail Année : 2018

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. When the service times are fat tailed, we prove that the properly rescaled process converges to some limiting process: in particular we identify three regimes including slow arrivals, fast arrivals, and equilibrium, which lead to different limits in distribution. AMS 2000 subject classifications: Primary 60G50, 60K30, 62P05, 60K25.
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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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Landy Rabehasaina. Asymptotics for infinite server queues with fast/slow Markov switching and fat tailed service times. 2018. ⟨hal-01894007v1⟩
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