An Equivalent Second Order Model with Application to Traffic Control

The most popular second order traffic model used for traffic control is the Payne-Papageorgiou model which is essentially density-speed dynamics. 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 Payne-Papageorgiou model. Such model plus a modified onramp queue model are used to formulate a traffic control problem to maximize recurrent bottleneck flow, which can be modeled as lane reduction. The problem formulated with Model Predictive Control turns out to be a quadratic programming.