Vlasov-Fokker-Planck type kinetic models for multilane traffic flow and large time behavior of kinetic density by entropy methods
Institution: | University of Victoria |
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Department: | |
Year: | 2010 |
Keywords: | traffic flow; mathematical models; UVic Subject Index::Sciences and Engineering::Mathematics |
Record ID: | 1867598 |
Full text PDF: | http://hdl.handle.net/1828/2098 |
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.