Queueing models for urban traffic networks

With a growing population, traffic congestion puts a strain on individual travellers, economy and the environment and forms a major problem for cities all over the world. To decrease congestion, it is crucial to utilise the existing infrastructure more efficiently by using optimal traffic-light control. This requires a thorough analysis of possible control policies and their influence on the performance of the traffic network. For the analysis, we develop discrete-time queueing models and use them to compare different traffic-light control settings. Moreover, we present a novel computational approach for such queueing models.

In our models, we take into account acceleration of the vehicles and the correlation between arrivals, which leads to accurate predictions of the delays. We focus on several topics concerning traffic control. First, we analyse and compare two types of control: fixed and semi-actuated control. We show the fundamental differences between these types in terms of the system performance and optimisation of control parameters. Second, we propose a measure of green-wave efficiency and study how the green waves affect the vehicles delay. We observe that a high green-wave efficiency does not necessarily mean short delays. Finally, we construct a transient model for large traffic networks with traffic-light and priority intersections. This model is designed to be used for model-based online traffic control.

Traffic models developed in this thesis as well as many other queueing systems can be analysed using the probability-generating-function (pgf) technique, which often leads to expressions in terms of the (complex) roots of a certain equation. For a class of pgfs with a rational form, we show that it is not necessary to compute the roots in order to evaluate these expressions. Instead, one can use contour integrals, which is computationally a more reliable approach than the root-finding method.