Traffic dynamics at a merging junction can be numerically solved with discrete conservation equationsand so-called supply-demand methods. In this paper, we first introduce a continuous multi-commoditykinematic wave model of merging traffic and then develop a new framework for constructing the solutionsto its Riemann problem with jump initial conditions. In the supply-demand spac...

Frequent lane-changes in highway merging, diverging, and weaving areas could disrupt traffic flow and, even worse, lead to accidents. In this paper, we propose a simple model for studying bottleneck effects of lane-changing traffic and aggregate traffic dynamics of a roadway with lane-changing areas. Based on the observation that, when changing its lane, a vehicle affects traffic on both its cu...

Frequent lane-changes in highway merging, diverging, and weaving areas often can disrupt traffic flow and, even worse, lead to accidents. For balanced lane-changing areas, where different lanes share the same traffic conditions, based on the observation that a vehicle has to take two lanes during its lane-changing period, we consider its contribution to traffic density is doubled. That is, ther...

Channel flow routing provides information on the movement of flood wave as it travels downstream. From the flood forecast viewpoint, it is desirable to have some knowledge about the expected arrival time of peak flow. However, many parameters involved in the flow routing model, in reality, can not be quantified with certainty. In this paper, a probabilistic analysis using the Mellin transform i...

A systematic understanding of traffic dynamics on road networks is crucial for many transportation studies and can help to develop more efficient ramp metering, evacuation, signal control, and other management and control strategies. In this study, we present a theory of multi-commodity network traffic flow based on the Lighthill–Whitham–Richards (LWR) model. In particular, we attempt to analyz...

Geometrical Shock Dynamics (GSD) is a simplified model for nonlinear shock wave propagation. It is based on the decomposition of the shock front into elementary ray tubes with a simple relation linking its local curvature and velocity. This relation is obtained under the assumption of strong shock in order to neglect the effect of the post-shock flow on the front. More recently, a new simplifie...