Discontinuities in the Lagrangian formulation of the kinematic wave model

Abstract

In this article we demonstrate how network components can be modeled using the kinematic wave model in the Lagrangian formulation. This includes modeling nodes (or discontinuities) such as inflow and outflow boundaries, merges and bifurcations (e.g. ramps) and nonhomogeneous roads. Nodes are usually fixed in space. This makes their implementation in Lagrangian coordinates where the coordinates move with the vehicle more complex than in Eulerian coordinates where the coordinates are fixed in space. To this end we derive an analytical node model. The article then discusses how to implement such sink and source terms in a discretized version of the kinematic wave model in Lagrangian coordinates. In this implementation several choices have to be made. Test results show that even with the most simple choices (discretization based on full vehicle groups and discrete time steps) accurate and plausible results are obtained. We conclude that the Lagrangian formulation can successfully be applied for simulation of networks of nonhomogeneous roads.