Vlasov-Fokker-Planck type kinetic models for multilane traffic flow and large time behavior of kinetic density by entropy methods
| dc.contributor.author | Zhou, Ting | |
| dc.contributor.supervisor | Illner, Reinhard | |
| dc.date.accessioned | 2010-01-25T16:50:09Z | |
| dc.date.available | 2010-01-25T16:50:09Z | |
| dc.date.copyright | 2006 | en |
| dc.date.issued | 2010-01-25T16:50:09Z | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science M.Sc. | en |
| dc.description.abstract | We present a class of multi-lane traffic models of Vlasov-Fokker-Planck type incorporating non-local and time-delayed braking/acceleration, diffu¬sion and lane changing terms whose dependencies are based on empirical guidelines. By investigating the spatially homogeneous case with non-zero passing probability incorporated in the braking term. we are left with the drift diffusion equation. which leads to a multi-valued fundamental diagram. As a novelty of this thesis. we find out that the monotonicity of the quotient between the braking/acceleration and the diffusion term in average speed guarantees the single-valued fundamental diagram. We study the large time behavior of the time-dependent kinetic density by convex entropy methods based on [3]. With a positive "residual" diffusion, convergence results remain with fewer assumptions. Two simplified examples are studied to illustrate the application of entropy methods. | en |
| dc.identifier.uri | http://hdl.handle.net/1828/2098 | |
| dc.language | English | eng |
| dc.language.iso | en | en |
| dc.rights | Available to the World Wide Web | en |
| dc.subject | traffic flow | en |
| dc.subject | mathematical models | en |
| dc.subject.lcsh | UVic Subject Index::Sciences and Engineering::Mathematics | en |
| dc.title | Vlasov-Fokker-Planck type kinetic models for multilane traffic flow and large time behavior of kinetic density by entropy methods | en |
| dc.type | Thesis | en |