The macroscopic fundamental diagram explained by a walking experiment in class

Abstract

In traffic flow theory, there is a relationship between the number of vehicles in a certain area and their average speed, the so-called macroscopic fundamental diagram (MFD). Related control concepts involve limiting the inflow into an area, so-called perimeter control. This may increase both the flow inside the controlled area and the outflow rate, reducing overall delays. This control concept is taught in classes on traffic flow theory around the globe. This paper presents an experiment that can be run in class to create the MFD with a group of students. The basic idea is that we have a confined area where participating students have to walk a predefined route. We repeat this experiment several times (runs of 2–4 minutes each), each time with a different, pre-defined number of students being simultaneously in the area (the accumulation). The number of students is controlled by metering the inflow of participants. Exit flow rates are determined for each run by dividing the number of exiting participants by the run time. One run will hence yield one observed combination of number of participants and run time. From this, an accumulation and exit flow rate can be computed. The Macroscopic Fundamental Diagram (MFD) is then created by plotting the exit flow rates and accumulation of all runs. Students can this way derive this MFD from data. Moreover, they also experience during the walking how delays change with accumulation, and thereby the experiment intuitively teaches them the concepts of the MFD and perimeter control. The paper describes the experiment, and provides tools (software, routes) for repeating the experiment with other groups.