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.