Titlebook: Queues and Lévy Fluctuation Theory; Krzysztof Dębicki,Michel Mandjes Textbook 2015 Springer International Publishing Switzerland 2015 Lévy

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Workload Correlation Function,on function. A variety of techniques is used to analyze the correlation between .. and .., where it is assumed that the queue is in stationarity at time 0. Specifically, for the spectrally one-sided case the structural result is established that the workload correlation function is positive, decreas

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Stationary Workload Asymptotics,tingly, where the full distribution of . 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 .(⋅ ) are identified such that . as . → . (th

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Transient Asymptotics, light and heavy tails should be made. We also pay attention to the asymptotics of the joint distribution of the workloads at two different time epochs; these asymptotics allow an intuitive interpretation.

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,Simulation of Lévy-Driven Queues, of Lévy processes and their associated workload processes. In addition, we point out how importance-sampling-based simulation is of great help when estimating rare-event probabilities (and small covariances, associated to the workload at time 0 and ., for . large).

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,Lévy-Driven Tandem Queues,del the joint steady-state workload of both queues is determined, and various special cases are dealt with in more explicit terms (such as the Brownian tandem queue). Also, attention is paid to the joint workload asymptotics, that is, the (bivariate) asymptotics corresponding to the event that both

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Applications in Communication Networks,s argued under what conditions and scaling limits, Lévy processes form a natural candidate to model network traffic. These limits involve both aggregation over time (so-called horizontal aggregation) and over the number of network users (vertical aggregation). As a result, the performance of the net

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Applications in Mathematical Finance,rocesses (such as the evolution of an asset price); special attention is paid to the normal inverse Gaussian process, the variance gamma process, and the generalized tempered stable process (which also covers the CGMY process). Then we explain how Lévy processes can be estimated from data. A substan