Queues and L? Fluctuation Theory

The book provides an extensive introduction to queueing models driven by Levy-processes as well as a systematic account of the literature on Levy-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 Levy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance.

Queues and Levy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.

Krzysztof Debicki is a professor at the University of Wroclaw, Poland. His research interests lie in extreme value analysis of stochastic processes and their applications in risk and queueing theory. His work is focused on extremes and boundary crossing probabilities of Gaussian and Levy processes, limit theorems and stochastic networks. He serves as an associate editor ofQueueing Systems and Probability and Mathematical Statistics.

Michel Mandjes is a professor at the University of Amsterdam, the Netherlands; he is also part-time with Eurandom and CWI; he previously worked at Bell Labs (Murray Hill), and had a sabbatical at Stanford. His research focuses on queueing theory and stochastic process analysis, with operations-research-type applications. He is author of the bookLarge Deviations for Gaussian Queues. He serves as an associate editor of Queueing Systems, Stochastic Systems, Stochastic Models, and Advances in Applied Probability / Journal of Applied Probability.