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.
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Dębicki, K., Mandjes, M. (2015). Stationary Workload Asymptotics. In: Queues and Lévy Fluctuation Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-20693-6_8
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DOI: https://doi.org/10.1007/978-3-319-20693-6_8
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