Piet Van Mieghem – författare

The Mittag-Leffler function is a basic function in fractional calculus and is an entire function in the complex plane. Entire functions are generalization of polynomials to infinite degree, do not have singularities in the complex plane, and possess a wealth of beautiful properties. Entire functions are defined by a Taylor series that converges for any finite complex number. In addition to the summation formulation and as a consequence of Weierstrass's factorization theorem, entire functions possess a product form in which all zeros appear.The study of properties of entire functions has led Mittag-Leffler, around 1900, to the study of his function. The Mittag-Leffler function is a primary example of an entire function, tunable in its order, and is represented by the simple eyeing Taylor series, in which another basic complex function, the Gamma function pops up. The Mittag-Leffler and Gamma Function mainly targets the mathematical properties of the Mittag-Leffler function in easy-to-understand language, not its applications to fractional analysis nor its numerical evaluation. Since the Gamma function plays a crucial role in the properties of the Mittag-Leffler function, a comprehensive treatment of the Mittag-Leffler function requires the knowledge of the Gamma function. The second part of the book attempts to present a complete study, enriched with historical references.

This rigourous and self-contained book describes mathematical and, in particular, stochastic methods to assess the performance of networked systems. It consists of three parts. The first part is a review on probability theory. Part two covers the classical theory of stochastic processes (Poisson, renewal, Markov and queuing theory), which are considered to be the basic building blocks for performance evaluation studies. Part three focuses on the relatively new field of the physics of networks. This part deals with the recently obtained insights that many very different large complex networks - such as the Internet, World Wide Web, proteins, utility infrastructures, social networks - evolve and behave according to more general common scaling laws. This understanding is useful when assessing the end-to-end quality of communications services, for example, in Internet telephony, real-time video and interacting games. Containing problems and solutions, this book is ideal for graduate students taking courses in performance analysis.

This concise and self-contained introduction builds up the spectral theory of graphs from scratch, with linear algebra and the theory of polynomials developed in the later parts. The book focuses on properties and bounds for the eigenvalues of the adjacency, Laplacian and effective resistance matrices of a graph. The goal of the book is to collect spectral properties that may help to understand the behavior or main characteristics of real-world networks. The chapter on spectra of complex networks illustrates how the theory may be applied to deduce insights into real-world networks. The second edition contains new chapters on topics in linear algebra and on the effective resistance matrix, and treats the pseudoinverse of the Laplacian. The latter two matrices and the Laplacian describe linear processes, such as the flow of current, on a graph. The concepts of spectral sparsification and graph neural networks are included.

This rigorous, self-contained book describes mathematical and, in particular, stochastic and graph theoretic methods to assess the performance of complex networks and systems. It comprises three parts: the first is a review of probability theory; Part II covers the classical theory of stochastic processes (Poisson, Markov and queueing theory), which are considered to be the basic building blocks for performance evaluation studies; Part III focuses on the rapidly expanding new field of network science. This part deals with the recently obtained insight that many very different large complex networks - such as the Internet, World Wide Web, metabolic and human brain networks, utility infrastructures, social networks - evolve and behave according to general common scaling laws. This understanding is useful when assessing the end-to-end quality of Internet services and when designing robust and secure networks. Containing problems and solved solutions, the book is ideal for graduate students taking courses in performance analysis.

This rigorous, self-contained book describes mathematical and, in particular, stochastic and graph theoretic methods to assess the performance of complex networks and systems. It comprises three parts: the first is a review of probability theory; Part II covers the classical theory of stochastic processes (Poisson, Markov and queueing theory), which are considered to be the basic building blocks for performance evaluation studies; Part III focuses on the rapidly expanding new field of network science. This part deals with the recently obtained insight that many very different large complex networks – such as the Internet, World Wide Web, metabolic and human brain networks, utility infrastructures, social networks – evolve and behave according to general common scaling laws. This understanding is useful when assessing the end-to-end quality of Internet services and when designing robust and secure networks. Containing problems and solved solutions, the book is ideal for graduate students taking courses in performance analysis.

This rigorous, self-contained book describes mathematical and, in particular, stochastic and graph theoretic methods to assess the performance of complex networks and systems. It comprises three parts: the first is a review of probability theory; Part II covers the classical theory of stochastic processes (Poisson, Markov and queueing theory), which are considered to be the basic building blocks for performance evaluation studies; Part III focuses on the rapidly expanding new field of network science. This part deals with the recently obtained insight that many very different large complex networks – such as the Internet, World Wide Web, metabolic and human brain networks, utility infrastructures, social networks – evolve and behave according to general common scaling laws. This understanding is useful when assessing the end-to-end quality of Internet services and when designing robust and secure networks. Containing problems and solved solutions, the book is ideal for graduate students taking courses in performance analysis.

Thisstate-of-the-artsurveyoftechnologies,algorithms,models,andexperiments in the area of Internet Quality of Service is the ?nal report of COST (European Cooperation in the ?eld of Scienti?c and Technical Research) Action 263,Qu- ity of future Internet Services, http://www. fokus. fraunhofer. de/cost263 (QofIS). COST 263 ran from January 1999 until October 2003 with the participation of some 70 researchers from 38 organizations from 14 European countries (France, Hungary, Italy, Sweden, UK, Belgium, Germany, the Netherlands, Portugal, Slovenia, Switzerland, Finland, Greece, Romania, and Spain). The Action - longed to the COST area "Multimedia and Internet Communication"; together with COST 264, Networked Group Communication, this Action continued the e?ort started in 1992 by COST 237, Multimedia Telecommunications Services. Both groups have combined their e?orts now in the Network of Excellence in Emerging Networking Experiments and Technologies, http://www. ist-e-next. net (E-NEXT) of the 6th European Framework program. The book consists of seven chapters that were written in 18 months by 67 individual authors.The main objective of this book is to report the state of the art in the area of QofIS, as percieved by the authors, including achievements that wereoriginatedby the authors. The book wasdesigned in a top-downm- ner: after three years of running the Action with close co-ordination of research e?orts, it was easy to achieve a consensus on the table of contents. To ensure the content quality the following roles were de?ned and assigned to COST 263 members: chapter editor, chapter author, chapter reader.

This volume of the Lecture Notes in Computer Science series contains the set of papers accepted for presentation at the 5th International Workshop on Quality of future Internet Services (QofIS 2004) and at the two one-day workshops - locatedwithQofIS2004,namelythe1stInternationalWorkshoponQoSRouting (WQoSR 2004) and the 4th International Workshop on Internet Charging and QoS Technology (ICQT 2004). QofIS 2004, the ?fth international event, was organized under the umbrella of the E-NEXT Network of Excellence on "Emerging Networking Experiments and Technologies", which started its activities in January 2004. QofIS 2004 took place on September 29-30, 2004 at the Telef' onica premises in Barcelona, and was arranged by the Universitat Polit' ecnica de Catalunya (UPC). QofIS 2004 in Barcelona followed the highly successful workshops in Stockholm in 2003, Zuric .. h in2002,Coimbrain2001,andBerlinin2000.ThepurposeofQofIS2004,asofall QofIS events, was to present and discuss design and implementation techniques for providing quality of service in the Internet. Theimpactofemergingterminals,mobilityandembeddedsystemsiscreating a new environment where networks are ambient.New challenges are opened by this new space where networks of interest ranging from personal networks to large-scale application networks need to be designed and often integrated. Protocol mechanisms for supporting quality of service at the di?erent layers of thenetworksneedtobeassessedandeventuallyredesignedinsuchenvironments. In this context, the focus of the QofIS 2004 workshop was on the provisioning of Quality of Service in the Emerging Networking Panorama, assessed by results of experiments carried out in simulation platforms and test-beds, and given the progressive irruption of optical technologies.