The Fundamental Diagram:
Basis of congestion assessment
Whenever we talk about assessing congestion situations, the term Fundamental Diagram comes up. But what exactly is a Fundamental Diagram? Why is it always referred to, and what does it mean in terms of simulations? This article answers these questions and more.
The origins of the Fundamental Diagram
Q = D * V
Q is the traffic flow, D is the traffic density, and V is the speed. It therefore describes the state of a traffic system. This state can range from free-flowing traffic to congested traffic to traffic jams.
This state equation was derived from empirical data and therefore every traffic system is subject to this relationship. Today it serves as an important basis for the design of traffic facilities or traffic management systems.
What significance does the Fundamental Diagram have
The diagram can therefore be used to describe the traffic situation as a function of the number of road users and the available capacity. For example, if a new highway feeder road is planned, this correlation is useful: this information can be used, for example, to check the flow between each traffic light phase to the feeder road to ensure that there is no congestion.
How does the Fundamental Diagram work for crowd simulation?
When looking at pedestrian traffic, there are also three phases: free flow, restricted flow, and congestion. Especially in evacuation situations, you want to avoid congestion, so regulations such as the MBO in its implementation or the MVstättVO specify permissible numbers of people for exit widths.
Very different experiments and empirical data have been used to derive the Fundamental Diagram for pedestrians. This resulted in very different basic diagrams: Depending on the type of population (young, old, mixed), culture (e.g. European, Asian, etc.), occasion (event, leisure traffic, commuter traffic), type of traffic system (unidirectional, bidirectional), very different diagrams result, as visualized in the figure below by [Meunders]:
What is the significance of the Fundamental Diagrams in a simulation?
The situation is completely different for microscopic models: There, the Fundamental Diagram is used not as an input variable, but as an output variable. Microscopic models are first calibrated using these diagrams to determine the values for modeling each person. Once a model has been calibrated to a graph, the Fundamental Diagram is generally used to validate the model. In German-speaking countries, the Weidmann Fundamental Diagram has become established and is used for validation.
The RiMEA test 4 [RiMEA] also aims at this validation. The microscopic model is simulated in a long straight corridor and a Fundamental Diagram is derived. The simulation results should show the fundamental diagram as a function of the input variables.
How are the microscopic models calibrated to produce accurate results?
This is not possible otherwise: because the Fundamental Diagram considers aggregated values such as people flow and density, these values cannot be used as input for microscopic models. Instead, these values can be displayed as aggregated results of the simulation. This makes sense: people flow simulations are used in complex projects where such an answer is needed to assess the safety situation.
Holl, Stefan: Methoden für die Bemessung der Leistungsfähigkeit multidirektional genutzter Fußverkehrsanlagen, Dissertation 2016
Meunders, Andreas: "Kalibrierung eines mikroskopischen Modells für Personenströme zur Anwendung im Projekt Hermes", Master Thesis 2011.
RiMEA Richtlinie für Mikroskopische Entfluchtungsanalysen, Version 3.0, 10. März 2016,
Weidmann, U. (1993): Transporttechnik der Fussgänger: Transporttechnische Eigenschaften des Fussgängerverkehrs (Literaturauswertung)