# Performance Analysis of Complex Networks and Systems

Cambridge University Press

Edition: 2nd ed., 4/24/2014

EAN 9781107058606, ISBN10: 1107058600

Hardcover, 688 pages, 25.3 x 17.8 x 4 cm

Language: English

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 Ã¢â‚¬â€œ such as the Internet, World Wide Web, metabolic and human brain networks, utility infrastructures, social networks Ã¢â‚¬â€œ 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.

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.