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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.

Mostra/Nascondi contenuto.
Introduction On November 1st 1772, Mr Antoine Lavoisier, chemist, physicist, natu- ralist, economist, tax collector and future politician (a very intense life broken by guillotine in 1794), deposited at the Academy of Sciences in Paris a package containing the announcement of a revolutionary dis- covery. From a series of experiments on sulfur combustion he came to a conclusion that the course of chemistry would have changed and maybe given rise to a new way of doing chemistry. Chemical trans- formations, or chemical reactions, said Mr. Lavoisier, changing the properties of matter without altering the overall mass. This statement is now known as the conservation law of mass or Lavoisier’s Principle. Someone even likes to use the suggestive aphorism: “Nothing is created, nothing is destroyed, but everything turns!” That of Lavoisier was the first conservation law in everyone’s memory. Since then conservation laws have come a long way. Today, in fact, we talk about the energy, moment, charge conservation law . . . It speaks a lot, but with greater care, because in 1913 a former employee of the Patent Office in Berne put forward a hypothesis (and thesis, too) that the conservation law of mass is not always true. But that’s another story. We will speak a lot, in this thesis, about conservation laws. Over the century, in fact, (but especially in the second half of the century) re- searchers from all over the world were keen on them. Physicists, math- ematicians and engineers, in recent times, took an interest in them, in order to develop models able to describe car traffic, data flows on telecommunication network, goods on supply chain, gas flows, pipeline networks, book flows, etc. Scientific community’s interest in studying traffic flows is justified by the emergence of congestion phenomenon due to the rapid vehicles number increase and transport one. The congestion occurs when a large number of vehicles try to use a common transport infrastructure with

Tesi di Dottorato

Dipartimento: Dipartimento di Matematica e Informatica

Autore: Annunziata Cascone Contatta »

Composta da 162 pagine.

 

Questa tesi ha raggiunto 373 click dal 17/04/2008.

Disponibile in PDF, la consultazione è esclusivamente in formato digitale.