Macroscopic Fundamental Diagram for pedestrian networks: Theory and applications

The Network or Macroscopic Fundamental diagram (MFD) has been a topic receiving a lot of attention in the past decade. Both from a theoretical angle and from a more application-oriented perspective, the MFD has proven to be a powerful concept in understanding and managing vehicular network dynamics.In particular, the application in traffic management has inspired the research presented in this contribution, where we explore the existence and the characteristics of the pedestrian Macroscopic Fundamental Diagram (p-MFD). This is first of all done from a theoretical perspective, which results in the main contribution of this research showing how we can derive the p-MFD from assumed local fundamental diagrams (FDs). In doing so, we show that we can relate the average (out-)flow from a pedestrian network as a function of the average spatial density ρ- and the density spatial variation σ2. We show that the latter is essential to provide a reasonable description of the overall network conditions. For simple relations between density and speed (i.e. Greenshields and Underwood fundamental diagrams), we derive analytical results; for more commonly used FDs in pedestrian flow theory, such as the triangular FD of Newell or the FD of Weidmann, we show the resulting relation by proposing a straightforward simulation approach.As a secondary contribution of the paper, we show how the p-MFD can be constructed from pedestrian trajectory data stemming from either microsimulation or from experimental studies. We argue that the results found are in line with the theoretical results, providing further evidence for the validity of the p-MFD concept. We furthermore discuss concepts of hysteresis, also observed in vehicular network dynamics, due to the differences in the queue build up and recuperation phases.We finally present some applications of the presented concepts in crowd management, network level-of-service determination, and coarse-scale modelling.