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.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/2098 |
| Date | 25 January 2010 |
| Creators | Zhou, Ting |
| Contributors | Illner, Reinhard |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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