Queues and Lévy Fluctuation Theory

• Κύριοι συγγραφείς: Dębicki, Krzysztof (Συγγραφέας), Mandjes, Michel (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Έκδοση: 1st ed. 2015.
• Σειρά: Universitext,
• Θέματα: Mathematics.; Applied mathematics.; Engineering mathematics.; Probabilities.; Probability Theory and Stochastic Processes.; Applications of Mathematics.

 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 graduate/postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes. 

 Introduction -- Lévy processes and Lévy-driven queues -- Steady-state workload -- Transient workload -- Heavy traffic -- Busy period -- Workload correlation function -- Stationary workload asymptotics -- Transient asymptotics -- Simulation of Lévy-driven queues -- Variants of the standard queue -- Lévy-driven tandem queues -- Lévy-driven queueing networks -- Applications in communication networks -- Applications in mathematical finance -- Computational aspects: inversion techniques -- Concluding remarks -- Bibliography.