Stochastic Networks (Institute of Mathematical Statistics Textbooks)

EAN: 9781107691704
Published 27/02/2014
Language: English

Communication networks underpin our modern world, and provide fascinating and challenging examples of large-scale stochastic systems. Randomness arises in communication systems at many levels: for example, the initiation and termination times of calls in a telephone network, or the statistical structure of the arrival streams of packets at routers in the Internet. How can routing, flow control and connection acceptance algorithms be designed to work well in uncertain and random environments? This compact introduction illustrates how stochastic models can be used to shed light on important issues in the design and control of communication networks. It will appeal to readers with a mathematical background wishing to understand this important area of application, and to those with an engineering background who want to grasp the underlying mathematical theory. Each chapter ends with exercises and suggestions for further reading.

Overview
Part I
1. Markov chains
2. Queueing networks
3. Loss networks
Part II
4. Decentralized optimization
5. Random access networks
6. Effective bandwidth
Part III
7. Internet congestion control
8. Flow level internet models
Appendix A. Continuous time Markov processes
Appendix B. Little's law
Appendix C. Lagrange multipliers
Appendix D. Foster-Lyapunov criteria
References
Index.