Abstract
This first introductory chapter gives an overview of the material contained in this textbook. On a chapter-by-chapter basis it is pointed out what topics are included, and in addition how they relate to each other. At a high level, the book subsequently addresses a transform-based analysis of various workload-related metrics in Lévy-driven queues, asymptotics in various limiting regimes, simulation techniques, non-standard queues and networks, applications in communication networks and finance, and numerical inversion techniques.
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References
Applebaum, D.: Lévy Processes and Stochastic Calculus. Cambridge University Press, Cambridge (2004)
Applebaum, D.: Lévy processes—from probability to finance and quantum groups. Not. Am. Math. Soc. 51, 1336–1347 (2004)
Asmussen, S.: Applied Probability and Queues, 2nd edn. Springer, New York (2003)
Asmussen, S., Albrecher, H.: Ruin Probabilities, 2nd edn. World Scientific, Singapore (2010)
Bertoin, J.: Lévy Processes. Cambridge University Press, Cambridge (1998)
Cont, R., Tankov, P.: Financial Modelling with Jump Processes. Chapman & Hall/CRC, Boca Raton (2003)
Kella, O.: Reflecting thoughts. Stat. Probab. Lett. 76, 1808–1811 (2006)
Kyprianou, A.: Introductory Lectures on Fluctuations of Lévy Processes with Applications. Springer, Berlin (2006)
Mikosch, T., Resnick, S., Rootzé, H., Stegeman, A.: Is network traffic approximated by stable Lévy motion or fractional Brownian motion? Ann. Appl. Probab. 12, 23–68 (2002)
Prabhu, N.: Stochastic Storage Processes, 2nd edn. Springer, New York (1998)
Sato, K.: Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1999)
Taqqu, M., Willinge, W., Sherman, R.: Proof of a fundamental result in self-similar traffic modeling. Comput. Commun. Rev. 27, 5–23 (1997)
Whitt, W.: Stochastic-Process Limits. Springer, New York (2002)
Zolotarev, V.: The first passage time of a level and the behaviour at infinity for a class of processes with independent increments. Theor. Probab. Appl. 9, 653–661 (1964)
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Dębicki, K., Mandjes, M. (2015). Introduction. In: Queues and Lévy Fluctuation Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-20693-6_1
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DOI: https://doi.org/10.1007/978-3-319-20693-6_1
Publisher Name: Springer, Cham
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