Networks: Optimisation and Evolution (Cambridge Series in Statistical and Probabilistic Mathematics)

Networks: Optimisation and Evolution (Cambridge Series in Statistical and Probabilistic Mathematics)

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Peter Whittle
Cambridge University Press, 4/12/2007
EAN 9780521871006, ISBN10: 052187100X

Hardcover, 282 pages, 22.8 x 15.2 x 1.8 cm
Language: English

Point-to-point vs hub-and-spoke. Questions of network design are real and involve many billions of dollars. Yet little is known about optimising design - nearly all work concerns optimising flow assuming a given design. This foundational book tackles optimisation of network structure itself, deriving comprehensible and realistic design principles. With fixed material cost rates, a natural class of models implies the optimality of direct source-destination connections, but considerations of variable load and environmental intrusion then enforce trunking in the optimal design, producing an arterial or hierarchical net. Its determination requires a continuum formulation, which can however be simplified once a discrete structure begins to emerge. Connections are made with the masterly work of Bendsøe and Sigmund on optimal mechanical structures and also with neural, processing and communication networks, including those of the Internet and the World Wide Web. Technical appendices are provided on random graphs and polymer models and on the Klimov index.

Tour d'horizon
Part I. Distribution Networks
1. Simple flows
2. Continuum formulations
3. Multi-class and destination-specific flows
4. Design optimality under variable loading
5. Concave costs and hierarchical structure
6. Road networks
7. Structural optimisation
Michell structures
8. Structures
computational experience of evolutionary algorithms
9. Structure design for variable loading
Part II. Artificial Neural Networks
10. Models and learning
11. Some particular nets
12. Oscillatory operation
Part III. Processing Networks
13. Queuing networks
14. Time-sharing networks
Part IV. Communication Networks
15. Loss networks
optimality and robustness
16. Loss networks
stochastics and self-regulation
17. Operation of the Internet
18. Evolving networks and the World-wide Web
Appendix 1. Spatial integrals for the telephone problem
Appendix 2. Bandit and tax processes
Appendix 3. Random graphs and polymer models

'... a remarkable book ... a pleasure to read ... plenty of interesting results, ideas and inspiration.' Hartmut Noltemeier, Zentralblatt MATH