Queues and Lévy Fluctuation Theory electronic resource by Krzysztof Dębicki, Michel Mandjes.
Material type: TextSeries: UniversitextPublication details: Cham : Springer International Publishing : Imprint: Springer, 2015Edition: 1st ed. 2015Description: XI, 255 p. 12 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319206936Subject(s): mathematics | Applied mathematics | Engineering mathematics | Probabilities | Mathematics | Probability Theory and Stochastic Processes | Applications of MathematicsDDC classification: 519.2 LOC classification: QA273.A1-274.9QA274-274.9Online resources: Click here to access onlineIntroduction -- 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.
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.
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