Rather than a mathematical model of traffic flow, Kerner's three-phase theory is a qualitative traffic flow theory that consists of several hypotheses.
The first mathematical model of traffic flow in the framework of Kerner's three-phase theory that mathematical simulations can show and explain traffic breakdown by an F → S phase transition in the metastable free flow at the bottleneck was the Kerner-Klenov model introduced in 2002 [REF].