Revisiting shock wave theory

According to Lighthill and Whitham's shock wave model, there exists a shock wave even in a homogeneous speed condition. They referred to this wave as unobservable, that is analogous to a radio wave that cannot be seen. Other researchers described this wave as an imaginary but useful analytical tool. This paper initially attempted to identify how such a counterintuitive conclusion resulted in Lighthill and Whitham's shock wave model. It is shown that the existing shock wave model significantly relaxed the speed-space relationship change in accordance with the flow condition during the formulation of the model. A new model is derived in later parts of the paper by deploying stringent speed-space relationships between two consecutive vehicles in traffic. In the new model, the shock wave in a homogeneous speed traffic stream is identical to the ambient vehicle speed, and thus no radio-wave-like shock wave existed.