Ottimizzazione e simulazione di flussi di traffico stradale su network

The main scienti¯c objective of the proposed research plan is the e±cient and reliable numeri- cal treatment of simulation and optimal control problems in the context of tra±c °ow on road networks. In recent years there has been intense research in the ¯eld of modeling and analysis of network phenomena. The research started and focused on transportation problems and in particular tra±c °ow to its importance for society. The improved understanding in the theoretical aspects of the mathematical description then in°uenced other areas of application, for example, supply chain management, gas transport, internet tra±c, and so forth. Further, there has been improved understanding in the ¯eld of optimal control problems governed by partial di®erential equations in a general context as well as for particular applications like control tra±c lights. The long term goal of the research is now to also provide reliable and fast numerical meth- ods for such network phenomena. The obtained mathematical understanding of the processes will be embedded in the numerical treatment and then allow for practical improvements in simulation, prediction and control and yield applicable outcomes of the theoretical studies. The mid-range goal to be achieved within the duration of the project is the development of fast and reliable numerical methods in the context of tra±c °ow. In particular, we consider a reformulation of the network dynamics in kinetic variables used to derive a numerical scheme. Further, we are interested in extending the scheme to optimality systems for control problems. These derivations is accompanied by a mathematical analysis of the derived schemes where in particular the heritage of properties of the continuous models will be addressed.