Modeling and control of congestion phenomena

As congestion plays a more prominent role in today's world than ever, this thesis is devoted to the development and study of models that capture the dynamics of systems that may experience congestion, and the construction of control measures that aim to mitigate congestion phenomena. An important aspect of this thesis is that the fluctuating dynamics of such systems are taken into account. That is, it is acknowledged that certain processes governing these systems may be time-dependent and/or suffering from randomness. Examples include rates of incoming calls in mobile phone networks and the occurrence of incidents in road networks.
The thesis is divided into two parts. The first part specifically considers the road traffic setting, and presents stochastic road models and corresponding control problems in the areas of routing, optimal departure-time advice, and input rate control. The second part of the thesis considers a classical congestion model for an element in a telecommunication network: a single-server queue. To guide control policies that aim to find a social optimum by levying tolls to arriving customers, this part studies the so-called externalities: the cost of additional arrivals to queues, in terms of the total extra waiting time.