Mathematical Modeling and Simulations of Traffic Flow

Abstract

This dissertation concerns modeling and computation of macroscopic fluid-like traffic flow on a single lane road as well as on multilane, coupled with lane changes. We start with single lane models and consider the scalar model, expressing car mass conservation, proposed in the 1950s (Lighthill-Whitham 1955, Richards 1956). This requires a velocity-density closure relation, called Fundamental Diagram. We propose a more realistic closure relation, based on field data fitting. Using a relationship between car headway and flow density, we develop and extend to a new 2x2 system that includes an intra-lane acceleration equation reflecting microscopic flow characteristics. The models are then generalized to multilane traffic flow and incorporate mass exchange terms, as well as inter-lane acceleration terms. We present two types of multilane models that are nonlinear hyperbolic equations: (i) scalar models and (ii) 2x2 systems. Both types are formulated by establishing lane changing conditions from drivers' perspectives and incorporating them into source terms. Consideration for lane changing includes the potential for velocity gain and available space. Using Roe-type upwind scheme, we reproduce realistic flow patterns such as stop-and-go flow and study the influence of lane changing and lane reduction on flow capacity.