@book{TranGiaHossfeld2021,
  author    = {Tran-Gia, Phuoc and Hoßfeld, Tobias},
  title     = {Performance Modeling and Analysis of Communication Networks},
  edition   = {1st edition},
  publisher = {W{\"u}rzburg University Press},
  address   = {W{\"u}rzburg},
  isbn      = {978-3-95826-152-5},
  doi       = {10.25972/WUP-978-3-95826-153-2},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-241920},
  publisher      = {W{\"u}rzburg University Press},
  pages     = {xiii, 353},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@article{BreitenbachBorzi2020,
  author    = {Breitenbach, Tim and Borz{\`i}, Alfio},
  title     = {The Pontryagin maximum principle for solving Fokker-Planck optimal control problems},
  series = {Computational Optimization and Applications},
  volume    = {76},
  journal   = {Computational Optimization and Applications},
  issn      = {0926-6003},
  doi       = {10.1007/s10589-020-00187-x},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-232665},
  pages     = {499-533},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@phdthesis{Hofmann2012,
  author    = {Hofmann, Martin},
  title     = {Contributions to Extreme Value Theory in the Space C[0,1]},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-74405},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {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.},
  subject      = {Extremwertstatistik},
  language  = {en}
}