Urban two-lane highway with quasi-dense traffic: analysis, finite element modelling, perturbation method and optimal control†

Study partially supported by the National Research Council of Canada

Abstract

For an urban highway with quasi-dense traffic, neither modelling via continuum equations nor modelling via stochastic counting processes are fully satisfactory. A model is suggested which consists of adding white noise to the deterministic equations, and which is supported by a physical analysis of the phenomenon. The theoretical stochastic distributed system so obtained is considered and a distributed diffusion equation is derived. For the practical purpose of implementing the traffic control, another modelling via the finite element technique is designed. In this way the initial distributed system is converted into a finite set of lumped parameter systems in a cascaded combination. The study is performed on this combination. Despite this paper being of an ‘ applied ’ nature, it gives rise to some new problems to which possible solutions are suggested. Notable, the catastrophe theory is utilized to check the validity of the finite element technique, and the study of the limiting probability density by using the diffusion equation. The content of the paper applies to a broad class of stochastic distributed systems

Notes

Study partially supported by the National Research Council of Canada