Modelling and Optimization of Traffic Flows on Networks

Plan of the Thesis
The Thesis is organized as follows. Chapter 1 deals with hyperbolic systems of conservation laws. We introduce the basic definitions and give the basic tool to prove existence and uniqueness of solutions. Then we pass to consider, in Chapter 2, an optimization of the parameters that describe a fluid-dynamic model for traffic flow on road networks. The analogy with fluids comes from considering cars as particles. The idea is to look at the network at an intermediate time scale so that cars travelling happens at a faster level but the equilibria of the whole network are reached only as asymptotic. This permits to construct a model relying on a macroscopic description. A routing algorithm has been analyzed in order to solve Riemann problems at junctions. Particularly, some cost functionals, that measure average velocity, average travelling time and total flux of cars along the network, are defined for the optimization. Such cost functionals provide an estimate about some phenomena, such as traffic congestion, accidents and pollution.
The Chapter 3 is devoted to problems of car traffic flows in congested roads of an urban network. Particularly, one wants to consider how cars can be redirected in the case of high car densities on some roads, with an opportune choice of some traffic coefficients. An optimization technique of the traffic distribution parameters, that describe a fluid - dynamic model for road networks, is considered. In this case, with the term optimization, we refer to the possibility to improve traffic conditions in presence of some factors due to congestion phenomena.
In the Chapter 4, we deal with the optimization techniques applied to a fluid-dynamic model that describes data flows on telecommunications networks. The aim of this chapter is to present some results about the optimal choice of the parameters, that describe a fluid-dynamic model for data flow on telecommunication networks. In particular, some cost functionals, that measure average velocity, average travelling time and total flux of packets along the network, are defined. Such cost functionals are useful to measure the performances of the network, and to understand complex typical phenomena of telecommunication networks, such as packets congestion.
For all examined cases study, some simulation results are provided with accurate analysis and physical interpretation.