Asymptotics of Hybrid Fluid Queues with Lévy Input

Author:

Dębicki Krzysztof,Sierpińska Iwona,Zwart Bert

Abstract

Let {X(t):t∈ℝ} be the integrated on–off process with regularly varying on-periods, and let {Y(t):t∈ℝ} be a centered Lévy process with regularly varying positive jumps (independent of X(·)). We study the exact asymptotics of ℙ(supt≥0{X(t)+Y(t)-ct}>u) as u→∞, with special attention to the case r=c, where r is the increase rate of the on–off process during the on-periods.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

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