Defining the Pedestrian Fundamental Diagram

First introduced in vehicular traffic, the fundamental diagram is now also used widely in pedestrian transport to describe the relationship between speed, flow, and density. Various equations have been proposed, which often exhibit strong differences. So far, several parameters that influence the pedestrian fundamental diagram have been identified. These parameters do not, however, explain the differences in proposed representations of the fundamental diagrams. Examining the literature, it becomes obvious that even though the concept is applied widely, a detailed and commonly accepted definition of the fundamental diagram for pedestrians is missing. Thus, the term “fundamental diagram” is used to describe different speed–density or flow–density relations. Without a proper definition, also the measurement and data evaluation methods differ strongly, which is then reflected in the resulting fundamental diagram curves. This contribution aims at providing a definition for the pedestrian fundamental diagram. Starting from its origin as a model for pedestrian flow, its background and area of application are discussed. Based on these fundamental insights, a definition for the pedestrian fundamental diagram is proposed. An important aspect of the fundamental diagram concept is its stochastic nature. As the flow at a specific density is not constant, but shows certain variations over time, the fundamental diagram can either be described by its mean value or by using a probabilistic approach. In this contribution, an extension of the fundamental diagram to include its stochastic nature is discussed.