Anzeige
Erschienen in:
2015 | OriginalPaper | Buchkapitel
8. Stationary Workload Asymptotics
verfasst von : Krzysztof Dębicki, Michel Mandjes
Erschienen in: Queues and Lévy Fluctuation Theory
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
Where the full distribution of Q was uniquely characterized in Chapter 3, Chapter 8 considers the tail asymptotics of the stationary workload; interestingly, where the full distribution of Q was expressed in terms of a Laplace transform, the tail asymptotics allow explicit expressions. Distinguishing between Lévy processes with light and heavy upper tails (as well as an intermediate regime), functions f(⋅ ) are identified such that \(\mathbb{P}(Q > u)/f(u) \rightarrow 1\) as u → ∞ (these are so-called ‘exact asymptotics’). A variety of techniques are used, such as change-of-measure arguments, large deviations, and Tauberian inversion. These techniques also shed light on how high buffer levels are achieved.