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.
- 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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Product details
- Date Published: April 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
1. Introduction
Part I. Probability Theory:
2. Random variables
3. Basic distributions
4. Correlation
5. Inequalities
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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Author
Piet Van Mieghem, Technische Universiteit Delft, The Netherlands
Piet Van Mieghem is a Professor at the Delft University of Technology with a chair in telecommunication networks, and chairman of the Network Architectures and Services (NAS) section. His main research interests lie in the modeling and analysis of complex networks (such as biological, brain, social, infrastructural, and so on) and in new Internet-like architectures and algorithms for future communications networks.

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Performance Analysis of Complex Networks and Systems

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