Queues and Lvy Fluctuation Theory

The book provides an extensive introduction to queueing models driven by Lvy-processes as well as a systematic account of the literature on Lvy-driven queues. The objective is to make the reader familiar with the wide set of probabilistic techniques that have been developed over the past decades, including transform-based techniques, martingales, rate-conservation arguments, change-of-measure, importance sampling, and large deviations. On the application side, it demonstrates how Lvy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance. Queues and Lvy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.