Perimeter flow control of mixed bi-modal urban road networks

In this work we deal with the perimeter flow control problem of bi-modal urban networks by use of a three-dimensional Macroscopic Fundamental Diagram (3D-MFD). The 3D-MFD relates the accumulation of cars and buses and the outflow (or circulating flow) in a bi-modal traffic network. We assume that the impact of each mode on the traffic flow in the network is different, i.e. each bus can not be considered as equivalent to some number of passenger cars. In particular, cars are usually faster than buses (because of the bus stops) but if the percentage of buses in the overall accumulation is high, then the average speed of vehicles certainly differs from the one sustainable without the interference of buses. Thus the maximum throughput (capacity flow) varies with the composition of traffic in the network. For this reason, we introduce the composition of traffic in the network as a parameter that affects the shape of the 3D-MFD. The 3D-MFD is used to describe the aggregated traffic dynamics in the bi-modal urban network. A linear parameter varying model with uncertain parameter the composition of traffic in the network is used as a basis for designing a proportional robust perimeter flow controller. The control gain of the proposed scheme is calculated off-line using convex optimisation and semidefinite programming. To evaluate the proposed scheme, a simulation-based comparison of the robust perimeter flow controller with a pre-timed control plan for an area of the Downtown San Francisco is carried out.