Overview
- Combines Lévy-based fluctuation theory and queueing theory
- Studies the possibilities of fluctuation-theoretic elements and the connection to queues
- Applicable for both an applied- and a theory-oriented audience
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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About this book
The book provides an extensive introduction to queueing models driven by Lévy-processes as well as a systematic account of the literature on Lévy-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 Lévy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance.
Queues and Lévy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.
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Keywords
Table of contents (17 chapters)
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Front Matter
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Back Matter
Reviews
“The book presents, often in summary fashion, virtually all of the known results on Lévy-driven queues, quite a few of them obtained by the authors of this book, and thus it is ideal for a researcher who would like to enter this area. … I found the sketchy treatment of many results extremely useful and motivating. The list of references is complete, and a small number of useful exercises are included at the end of each chapter.” (Michael A. Zazanis, Mathematical Reviews, May, 2017)
Authors and Affiliations
About the authors
Krzysztof Dębicki is a professor at the University of Wrocław, 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 Lévy processes, limit theorems and stochastic networks. He serves as an associate editor of Queueing 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 book Large 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.
Bibliographic Information
Book Title: Queues and Lévy Fluctuation Theory
Authors: Krzysztof Dębicki, Michel Mandjes
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-20693-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-20692-9Published: 14 August 2015
eBook ISBN: 978-3-319-20693-6Published: 06 August 2015
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XI, 255
Number of Illustrations: 12 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Applications of Mathematics