Fundamental Diagram and Validation of Crowd Models
In recent years, several approaches for crowd modeling have been proposed. However, so far not much attention has been paid to their quantitative validation. The fundamental diagram , i.e. the density-dependence of the flow or velocity, is probably the mo
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J¨ ulich Supercomputing Centre, Forschungszentrum J¨ ulich, 52425 J¨ ulich, Germany [email protected] 2 Institut f¨ ur Theoretische Physik, Universit¨ at zu K¨ oln, 50937 K¨ oln, Germany [email protected]
Abstract. In recent years, several approaches for crowd modeling have been proposed. However, so far not much attention has been paid to their quantitative validation. The fundamental diagram , i.e. the densitydependence of the flow or velocity, is probably the most important relation as it connects the basic parameter to describe the dynamic of crowds. But specifications in different handbooks as well as experimental measurements for the fundamental diagram differ considerably. We give a review of the experimental data base and the causes for the discrepancies discussed in the literature. Up to now it was neglected that the way of measurement can cause variations between the results of different studies. To shed some light on this problem we studied by means of experimental trajectories of the single file movement how different measurement methods influence the resulting fundamental diagram. Keywords: empirical data, model validation, fundamental diagram.
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Introduction
The number of models for pedestrian dynamics has grown in the past years, but the experimental data to test them and to discriminate between these models is still to a large extent uncertain and contradictory (see e.g. [1]). In most models, pedestrians are considered to be autonomous mobile agents, hopping particles in a cellular automaton or self-driven particles in a continuous space. However, if one wants to make quantitative predictions (e.g. evacuation or travel times) the model has to be calibrated with empirical data, independent from the model type. One of the most important characteristics of pedestrian dynamics is the fundamental diagram giving the relation between pedestrian flow and density. Beside its importance for the dimensioning of pedestrian facilities it is associated with every qualitative self-organization phenomenon, like the formation of lanes or the occurrence of jams. However, specifications of different experimental studies, guidelines and handbooks, display non negligible differences concerning maximal flow values, the assigned density and the density where the flow is expected to become zero due to overcrowding. Although a large variety of models for pedestrian dynamics has been proposed, so far there have been only limited attempts to calibrate and validate these approaches with the fundamental H. Umeo et al. (Eds): ACRI 2008, LNCS 5191, pp. 563–566, 2008. c Springer-Verlag Berlin Heidelberg 2008
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diagram. In part, one reason is the unclear situation of the empirical data, as described above. This situation is very unsatisfactory and poses serious limitations to the use of such models e.g. in the area of safety planning. To improve the current state of affairs it is necessary to have more reliable data that can be used as basis for validation and calibration which then would al
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