This rigorous and self-contained book shows how the tools of stochastic analysis and probability theory can be used to assess the performance of networked systems. It consists of three parts. The first contains a review of probability theory. Part two treats the classical theory of stochastic processes (Poisson, renewal, Markov and queuing theory) which forms the basic building blocks of performance evaluation studies. Part three focuses on the relatively new field of the physics of networks, and deals with the recently obtained insight that many very different and complex networks - such as the World Wide Web, proteins, utility infrastructures and social networks - evolve and behave according to very similar 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.
Table of Contents
1. Introduction; 2. Random variables; 3. Basic distributions; 4. Correlation; 5. Inequalities; 6. Limit laws; 7. The Poisson process; 8. Renewal theory; 9. Discrete time Markov chains; 10. Continuous time Markov chains; 11. Applications of Markov chains; 12. Branching processes; 13. General queuing theory; 14. Queuing models; 15. General characteristics of graphs; 16. The shortest path problem; 17. The efficiency of multicast; 18. The hop count to an any cast group; Appendix A. Stochastic matrices; Appendix B. Algebraic graph theory; Appendix C. Solutions of problems; Bibliography; Index.
Piet F. A. Van Mieghem is a professor at the Delft University of Technology with a chair in telecommunication networks and is chairman of the Network Architectures and Services (NAS) group. His main research interests lie in new Internet-like architectures for future, broadband and QoS-aware networks and in the modelling and performance analysis of network behavior and complex infrastructures.