Titlebook: Queues and Lévy Fluctuation Theory; Krzysztof Dębicki,Michel Mandjes Textbook 2015 Springer International Publishing Switzerland 2015 Lévy

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Textbook 2015applications 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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Steady-State Workload,ion to Wiener–Hopf theory, leading to an expression for the transform of . albeit in a rather implicit form. We conclude this chapter by presenting (semi-) explicit results for two specific classes of spectrally two-sided processes, that is, the class in which the jumps have a phase-type distribution, and the class of meromorphic processes.

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Heavy Traffic, has a finite variance, the appropriately scaled workload process tends to a Brownian motion reflected at 0 (i.e. a Lévy-driven queue with Brownian input). If the variance is infinite, on the contrary, we establish convergence to a Lévy-driven queue fed by an .-stable Lévy motion.

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Stationary Workload Asymptotics,ese are so-called ‘exact asymptotics’). A variety of techniques are used, such as change-of-measure arguments, large deviations, and Tauberian inversion. These techniques also shed light on . high buffer levels are achieved.

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0172-5939 queues.Applicable for both an applied- and a theory-oriente.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 probabilisti

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Transient Workload,itional on the initial workload .. = . ≥ 0. Again we distinguish between the spectrally one-sided case and the two-sided case. Rather explicit expressions are presented for the transform of .. in the spectrally positive case, and for the density of .. (in terms of scale functions) in the spectrally

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Heavy Traffic,traffic’. Resorting to the steady-state and transient results that were derived in the previous chapters, it appears that we observe an interesting dichotomy, in that one should distinguish between two scenarios that show intrinsically different behavior. In the case that the underlying Lévy process