Multi-class kinematic wave theory of traffic flow

Abstract

The kinematic wave theory of traffic flow was independently developed by Lighthill and Whitham [Lighthill, M.J., Whitham, G.B., 1955. On kinematic waves. II. A theory of traffic flow on long crowded roads. Procedings of Royal Society A 229, 281-345] and Richards [Richards, P.I., 1956. Shockwaves on the highway. Operations Research 4, 42-51]. The original LWR model was extended in different directions to incorporate more and realistic details. The distinction of classes in traffic flow has received considerable attention recently. This paper proposes a framework for the different existing multi-class extensions of the kinematic wave theory. It turns out that the difference between all models lies in the assumption on how several classes interact. A new model is proposed where classes interact on a non-cooperative way. Slow vehicles act as moving bottlenecks for the fast vehicles, while fast vehicles maximize their speed without influencing slower vehicles. This leads to anisotropic behaviour of the traffic stream. This means that vehicles only react on stimuli in front of them. The new multi-class model is presented and illustrated in the moving bottleneck example of Newell [Newell, G.F., 1998. A moving bottleneck. Transportation Research Part B 32(8), 531-537].