TY - BOOK A1 - Tran-Gia, Phuoc A1 - Hoßfeld, Tobias T1 - Performance Modeling and Analysis of Communication Networks BT - A Lecture Note N2 - This textbook provides an introduction to common methods of performance modeling and analysis of communication systems. These methods form the basis of traffic engineering, teletraffic theory, and analytical system dimensioning. The fundamentals of probability theory, stochastic processes, Markov processes, and embedded Markov chains are presented. Basic queueing models are described with applications in communication networks. Advanced methods are presented that have been frequently used in recent practice, especially discrete-time analysis algorithms, or which go beyond classical performance measures such as Quality of Experience or energy efficiency. Recent examples of modern communication networks include Software Defined Networking and the Internet of Things. Throughout the book, illustrative examples are used to provide practical experience in performance modeling and analysis. Target group: The book is aimed at students and scientists in computer science and technical computer science, operations research, electrical engineering and economics. N2 - Dieses Lehrbuch bietet eine Einführung in gängige Methoden zur Modellbildung und analytische Leistungsbewertung von Kommunikationssystemen. Diese Methoden bilden die Grundlage für Verkehrstheorie und Systemdimensionierung. Die Grundlagen der Wahrscheinlichkeitstheorie, stochastische Prozesse, Markov-Prozesse und eingebettete Markov-Ketten werden vorgestellt. Grundlegende Warteschlangenmodelle werden mit Anwendungen aus Kommunikationsnetzwerken beschrieben. Es werden auch weiterführende Methoden vorgestellt, die in der jüngeren Praxis häufig verwendet wurden, insbesondere zeitdiskrete Analysealgorithmen, oder QoE und Energieeffizienz. Aktuelle Beispiele für moderne Kommunikationsnetze sind Software Defined Networking oder das Internet der Dinge. Im gesamten Buch werden anschauliche Beispiele verwendet, um praktische Erfahrungen in der Leistungsmodellierung und -analyse zu vermitteln. Zielgruppe: Das Buch richtet sich an Studierende und WissenschaftlerInnen aus den Bereichen Informatik und technische Informatik, Operations Research, Elektrotechnik und Wirtschaftswissenschaft. KW - performance modeling KW - Markovian and Non-Markovian systems KW - discrete-time models and analysis KW - communication networks KW - communication network KW - performance evaluation KW - Markov model KW - stochastic processes KW - queueing theory Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-241920 SN - 978-3-95826-152-5 SN - 978-3-95826-153-2 N1 - Parallel erschienen als Druckausgabe in Würzburg University Press, 978-3-95826-152-5, 65,00 Euro. PB - Würzburg University Press CY - Würzburg ET - 1st edition ER - TY - JOUR A1 - Breitenbach, Tim A1 - Borzì, Alfio T1 - The Pontryagin maximum principle for solving Fokker–Planck optimal control problems JF - Computational Optimization and Applications N2 - The characterization and numerical solution of two non-smooth optimal control problems governed by a Fokker–Planck (FP) equation are investigated in the framework of the Pontryagin maximum principle (PMP). The two FP control problems are related to the problem of determining open- and closed-loop controls for a stochastic process whose probability density function is modelled by the FP equation. In both cases, existence and PMP characterisation of optimal controls are proved, and PMP-based numerical optimization schemes are implemented that solve the PMP optimality conditions to determine the controls sought. Results of experiments are presented that successfully validate the proposed computational framework and allow to compare the two control strategies. KW - Fokker–Planck equation KW - Pontryagin maximum principle KW - non-smooth optimal control problems KW - stochastic processes Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-232665 SN - 0926-6003 VL - 76 ER - TY - THES A1 - Hofmann, Martin T1 - Contributions to Extreme Value Theory in the Space C[0,1] T1 - Beiträge zur Extremwerttheorie im Raum C[0,1] N2 - We introduce some mathematical framework for extreme value theory in the space of continuous functions on compact intervals and provide basic definitions and tools. Continuous max-stable processes on [0,1] are characterized by their “distribution functions” G which can be represented via a norm on function space, called D-norm. The high conformity of this setup with the multivariate case leads to the introduction of a functional domain of attraction approach for stochastic processes, which is more general than the usual one based on weak convergence. We also introduce the concept of “sojourn time transformation” and compare several types of convergence on function space. Again in complete accordance with the uni- or multivariate case it is now possible to get functional generalized Pareto distributions (GPD) W via W = 1 + log(G) in the upper tail. In particular, this enables us to derive characterizations of the functional domain of attraction condition for copula processes. Moreover, we investigate the sojourn time above a high threshold of a continuous stochastic process. It turns out that the limit, as the threshold increases, of the expected sojourn time given that it is positive, exists if the copula process corresponding to Y is in the functional domain of attraction of a max-stable process. If the process is in a certain neighborhood of a generalized Pareto process, then we can replace the constant threshold by a general threshold function and we can compute the asymptotic sojourn time distribution. N2 - Es wird ein Zugang zur Extremwerttheorie auf dem Raum C[0,1] gegeben. Nach Charakterisierung und Analyse standard max-stabiler Prozesse, wird ein "funktionaler Anziehungsbereich" für standard max-stabile Prozesse vorgeschlagen, der allgemeiner ist als der übliche, der mittels schwacher Konvergenz definiert wird. Schließlich werden Verweildauern stetiger Prozesse über hohen Schwellenwerten betrachtet. KW - Extremwertstatistik KW - stochastischer Prozess KW - Extremwerttheorie KW - extreme value theory KW - stochastic processes KW - functional D-norm Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-74405 ER -