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Full Description
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.
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.
