The concept of the macroscopic fundamental diagram (MFD) is elegant and attractive because it provides a global view of traffic behavior and performance at a network level. However, recent research shows that the MFD shape can be influenced by local traffic heterogeneities. Notably, route choices and heterogeneous local capacities may drive uneven (in space) or inconsistent (in time) distributions of congestion and then affect the shape and the scatter of the MFD. We are far from having a global understanding of the connections between local phenomena and the resulting MFD. This paper first aims to improve existing MFD estimation method for a succession of links with traffic signals. The new method overcomes previous limitations, notably regarding to the topology and signal settings regularities, by fully utilizing the receipts of the variational theory. Then, a single network with several parallel routes is investigated. MFDs on different routes are estimated with the variational method and then aggregated in a unified MFD for stationary and dynamic conditions and different sorts of equilibria (user and system optimum). It appears that the flow distribution among routes smoothly varies with respect to the total flow either in free-flow or congestion situations. Such a distribution is much more rough for system optimum, where it presents some discontinuities and is far from equity. This means that a control strategy able to lead such a network to the perfect system optimum would be hard to tune, especially in the congested regime. However, being able to determine the MFD corresponding to the system optimum provides a valuable reference to estimate the current efficiency of the considered network. Case studies for different simple networks and insights for generalization at the city level are proposed
