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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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VII.04 The Mathematics of Traffic in Networks

Frank Kelly

1 Introduction

We are all familiar with congested roads, and perhaps also with congestion in other networks such as the Internet, so it is obviously important to have a general understanding of how and why congestion occurs in networks. However, the pattern of the flow of traffic through a network is the consequence of a subtle and complex interaction between different users. For example, in a road network we would normally expect each driver to attempt to choose the most convenient route, and this choice will depend upon the delays the driver expects to encounter on different roads; but these delays will in turn depend upon the choices of routes made by others. This mutual interdependence ...

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