From data processing to distributional modelling of traffic measurements: Dissertation

This thesis is motivated by the need to analyse measured traffic data from networks. It develops and applies statistical methods to characterize and to model such data. The application areas are related to teletraffic and telecommunication networks, vehicular traffic and road/street networks, and Internet of Things applications. The research is based on four scientific publications, augmented with the statistical framework and theoretical development included in this summary. From the applications' point of view, the addressed research problems diverge on the types of the engineering problems, while from the statistical point of view, they share common theoretical methods.

The application problems are: i) to study whether a Gaussian process is a feasible model for aggregated Internet traffic, ii) to obtain aggregated flow level models for flow sizes, flow durations and their bivariate joint distribution, iii) to deduce vehicular traffic routes from correlated counts of vehicles that are observed at different locations of a street network, and iv) to develop a data reduction algorithm that works with limited computational capacity and can be deployed by Internet of Things applications.

This summary provides the statistical framework that combines the developed and applied methodologies and emphasizes their common features. Rigorous mathematical proofs are given for certain less-known, possibly novel, results about mutual information of pairs of order statistics, and a convergence result related to simultaneous estimation of several quantiles. These were used in the publications or, alternatively, bring new statistical insight to the methods that were used in the publications.