Macroscopic fundamental diagrams for train operations - are we there yet?

We discuss the concept and applicability of macroscopic descriptions of operations for railways systems. The concept of macroscopic or network fundamental diagram (MFD or NFD) for vehicular traffic in an urban network has been recently found empirically. The notion of MFD/NFD has been exploited to understand the real-time traffic state and the relevant control actions to keep traffic flow smooth. It has been used predominantly as a monitoring tool in traffic control strategies, which helps mitigate congestion. The railway mode has the same goals of maximizing speed and flow, though it has many substantial differences with vehicular traffic. We investigate the theoretical possibility to derive macroscopic representations of the traffic flow theory macroscopic variables; i.e. speed, density, flow, for railway traffic. We do this with closed formula expression when possible, or with simulation tools when the complex setup does not allow any analytical solution. The implications for applicability of macroscopic representations in railways or railway-like systems are discussed.