An Equivalent Second Order Model Based on Flow and Speed

Traffic models developed for control include first order LWR model and second order models. The first order model is essentially density dynamics which states the conservation of the number of vehicles in a section of highway. Most second order models are essentially a speed dynamics coupled with the first order density dynamics. There are several second order models but most are for explaining traffic flow. Only a couple of second order models were developed for traffic control purpose. The most popular one is the Payne-Papageorgiou model. Due to point sensor detection limit in highways such as inductive loops, flow estimation is easy and reasonably accurate while density estimation is very difficult. This is the motivation for us to have a look at flow dynamics in place of density. It turns out that flow dynamics of first order cannot be well-defined contrasted to the Cell Transmission Model. However, a flow-speed dynamics can be obtained which is equivalent to the density-speed dynamics of the PaynePapageorgiou model.