Performance Modeling and Analysis of Communication Networks. A Lecture Note [article]

Phuoc Tran-Gia, Tobias Hoßfeld
2021
Queueing theory is a fundamental methodology which plays an important role in the analysis of communication networks and systems, but also in other domains like manufacturing systems. P. Tran-Gia published a first edition of this text book "Analytical performance evaluation of distributed systems" [108] in German language in 1996 as part of his lecture "Performance Evaluation of Distributed Systems" at the University of Würzburg. A second edition "Introduction to performance evaluation and
more » ... ic theory" [110] was published in German language in 2009 taking into account suggestions received from students and employees at the University of Würzburg. Some methods that have been used frequently in research collaborations were added. The present text book is published in English language in 2021 as open access book by the Würzburg University Press. The book focuses on the fundamental models of queueing theory as well as advanced models for recent communication systems and networks. It gives an introduction in common methods of performance modeling and analysis of communication systems. These methods form the basis of traffic engineering, teletraffic theory, and system analytical dimensioning tools. 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 practice, especially discrete-time analysis algorithms, or which go beyond classical performance like quality of experience or energy efficiency. Recent examples of modern communication networks include Software Defined Networking or the Internet of Things. Throughout the book, illustrative examples are used to provide practical experience in performance modeling and analysis. The book is intended for students and scientists in computer science and technical computer science, applied mathematics, operations research, electrical engineering and economics. For the listeners of the lecture "Performance Evaluation of Distributed Systems" at the University of Würzburg, we would like to point out that Chapter 1 up to and including Chapter 5 are used in the course, as well as the analysis algorithm in time domain for the discrete-time GI/GI/1 system in Chapter 6 and selected examples in Chapter 7. The lecture was originally developed by Phuoc Tran-Gia and is given by Tobias Hoßfeld since 2018. v An implementation of the models in the book is available as interactive notebooks online. The scripts will help students to better understand the impact of parameters on performance characteristics, will avoid common pitfalls in the implementation, and provide means for numerical robust and efficient implementations for researchers in the domain. Besides the computational scripts, we provide exercises and solutions. There are some major changes compared to the second edition [110] . The book was reorganized and includes the following new models and sections per chapter: • Chapter 1 "Introduction in Performance Modeling": some recent examples on software defined networking, video streaming, resource sharing in cloud computing, internet of things (IoT) and smart city applications, overload control -they will be analyzed throughout the book. • Chapter 2 "Fundamentals and Prerequisites": more examples on Little's theorem, general results for GI/GI/n delay systems, loss formula for GI/GI/n-S queues, important inequalities (Jensen, Markov, Chebyshev), notion of mixture distribution, concrete substitute distributions. • Chapter 3 "Elementary Random Processes": strong law of renewal theory, definition of continuous-time Markov chains and their transition behavior, properties of Poisson processes, superposition of renewal processes, Palm-Khintchine theorem. • Chapter 4 "Analysis of Markovian Systems": arrival theorem introduced in Engset model, processor sharing model M/M/1-PS and its application for data center power consumption as well as virtualized network functions. • Chapter 5 "Analysis of Non-Markovian Systems": formal definition of discretetime Markov chains, power method implementation, Kleinrock's result, results for continuous-time GI/GI/1 delay systems, Kingman's approximations of mean waiting times. • Chapter 6 "Discrete-time Models and Analysis": analysis of idle times, busy times, interdeparture times of discrete-time GI/GI/1 systems, distributional Little's law for queue size derivation of GI/GI/1. • Chapter 7 "Advanced Models and Applications": video streaming QoS and QoE (M/M/1 with N-policy, GI/M/1 with N-policy), traffic modeling in the IoT (nD/D/1 and M/D/1), order and gap statistics, renewal approximation, random access schemes of IoT sensors (M/D/∞, M/D/1-S), Kleinrock's approach for deriving the operational point, overload control for non-stationary discrete-time models. vi This textbook is available as open access document and intended for digital use. Therefore, we took care of including hyperlinks to Chapters, Equations, Figures, etc. as well as clickable literature references which guide the reader to the original documents. The latest computational scripts implementing the models as well as exercises and solutions are available online. https://modeling.systems The authors would like to thank especially Stefan Geißler for proofreading and correcting many things, Katharina Dietz, Fabian Poignée, Frank Loh, Florian Wamser for their helpful comments, Claudia Schober, Manuel Beck for their support in the publishing process, and Hermann Gold for his help in implementing the model with batch service and threshold control. We thank you for the many hours and the enormous effort that you have put into improving the book.
doi:10.25972/wup-978-3-95826-153-2 fatcat:uioyzlzfzzfj7pmyjyexfeijou