The Cliiord Paterson Lecture, 1995 Modelling Communication Networks, Present and Future

Modern communication networks are able to respond to randomly uctuating demands and failures by allowing buuers to ll, by rerouting traac and by real-locating resources. They are able to do this so well that, in many respects, large-scale networks appear as coherent, almost intelligent, organisms. The design and control of such networks present challenges of a mathematical, engineering and economic nature. In this lecture I describe some of the models that have proved useful in the analysis of stability, statistical sharing and pricing, in systems ranging from the telephone networks of today to the information superhighways of tomorrow. Contents page 1. Introduction 2 (a) Outline 3 2. Loss networks 4 (a) Erlang's formula 4 (b) A n e t work model 4 (c) Examples 6 3. Dynamic routing and stability 7 (a) Instability 8 (b) Dynamic Alternative Routing 10 (c) Extensions 12 4. Coalitions and global routing 14 (a) D o m i n a n t coalitions 15 (b) The core 16 (c) Transit payments 16 (d) Network evolution 18 5. Broadband traac and statistical sharing 19 (a) EEective bandwidths 19 (b) Multiplexing models 21 (c) Charging mechanisms 23 6. Conclusion 25 References 25