Real-data modelling of transportation networks

In this thesis, after introducing the basics of Markov chains and mathematically analysing and proving the clustering properties of the eigenvector corresponding to a complex eigenvalue close to 1+0i , we develop several applications of Markov chains in transportation networks. We model bike sharing systems, bus networks, and multi-modal public transportation networks using Markov chains. The validation of the models is done by using real data from Boston and London for the bike sharing systems and the multi-modal public transportation networks respectively. We validate the Markov chain models that we developed for the bus network by using some data that we extracted from SUMO [69] (Simulator of Urban MObility). After successfully validating the models, we extract some important quantities of the Markov chains. These quantities provide useful information about the networks that help to improve the network for different purposes. Since some real data is used to validate our models, we need to know how trustworthy our result is. Therefore, we then define a set of indicators to extract the quality of data. The output of each indicator is a value between zero and one. If the value is close to one, it means that the quality of the data is high and we can trust the data and the result. The indicators are tested on some data from London highways. At the end a framework for the real time trading of budgeted emission rights between a fleet of participating vehicles is presented. The trading problem is formulated as an optimization problem and is solved by different algorithms. The results of some simulations are represented to compare the speed of convergence of the algorithms