Steady-state analysis of second-order traffic models and application to traffic flow control

We investigate the problem of controller design after linearization around the steady-state solutions of second-order traffic models. At steady-state the traffic variables follow space-dependent autonomous ODEs. The steady-state solutions can be used to account for the heterogeneity of the road in space, which can be caused by different environmental factors. Proceeding by analogy with open-channel flow studies, where such states are relevant for operating a network with efficient control strategies, we analyse and compare steady-state solutions for different second-order traffic models. We show that the steady-state density profile remains in three different regions. The behaviour of the considered models is discussed, leading to proposed corrections of the models. We select one corrected model, which we use for the design and implementation of a boundary controller to illustrate the effectiveness of our approach.