The Statistics of Dynamic Networks

This thesis describes describes a small number of problems arising from the applied study of networks in various contexts. The work can be split into two main areas: telecommunications networks (particularly the Internet) and road networks. In the area of telecom networks, this research focuses on current mathematical developments concerning long-range dependence (LRD). LRD is a statistical phenomenon describing correlations in time series. A large body of research has found LRD is present in measurements of data traffic on the Internet. A novel model for generating LRD is developed based upon Markov Modulated Processes. This technique has considerable advantages over a number of other methods currently used in the area. In the area of road traffic, this work concerns the phenomenon known as driver route choice (how drivers pick their routes through a road network as day-follows-day). A survey is made of the current research in this area focussing on on-street studies and how theory (mainly equilibrium modelling) translates into practice. In analysing data related to driver route choice it became necessary to develop a technique for matching data across multiple survey sites. This novel mathematical technique uses set theory to investigate the “false match” problem in survey data. Finally, a large on-street survey is analysed statistically for insights into driver behaviour in response to a change in a network.