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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.Read more
- Covers the basics of probability and includes problems and solved solutions, making the book self-contained and ideal for self-study
- Emphasises rigorous mathematical derivations, providing computational methods to solve realistic network problems analytically
- Dedicates a full chapter to a complete overview of SIS epidemics on networks
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- Date Published: June 2014
- format: Hardback
- isbn: 9781107058606
- length: 688 pages
- dimensions: 253 x 178 x 40 mm
- weight: 1.38kg
- contains: 103 b/w illus. 4 tables 104 exercises
- availability: Available
Table of Contents
Part I. Probability Theory:
2. Random variables
3. Basic distributions
6. Limit laws
Part II. Stochastic Processes:
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 queueing theory
14. Queueing models
Part III. Network Science:
15. General characteristics of graphs
16. The shortest path problem
17. Epidemics in networks
18. The efficiency of multicast
19. The hopcount and weight to an anycast group
Appendix A. A summary of matrix theory
Appendix B. Solutions to problems.
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