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.
Author(s): Krzysztof Dębicki, Michel Mandjes (auth.)
Series: Universitext
Edition: 1
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: XI, 255
Tags: Probability Theory and Stochastic Processes; Applications of Mathematics
Front Matter....Pages i-xi
Introduction....Pages 1-6
Lévy Processes and Lévy-Driven Queues....Pages 7-22
Steady-State Workload....Pages 23-47
Transient Workload....Pages 49-66
Heavy Traffic....Pages 67-80
Busy Period....Pages 81-95
Workload Correlation Function....Pages 97-104
Stationary Workload Asymptotics....Pages 105-117
Transient Asymptotics....Pages 119-129
Simulation of Lévy-Driven Queues....Pages 131-141
Variants of the Standard Queue....Pages 143-159
Lévy-Driven Tandem Queues....Pages 161-179
Lévy-Driven Queueing Networks....Pages 181-196
Applications in Communication Networks....Pages 197-207
Applications in Mathematical Finance....Pages 209-233
Computational Aspects: Inversion Techniques....Pages 235-243
Concluding Remarks....Pages 245-245
Back Matter....Pages 247-255
