Basics of modelling the pedestrian flow

Socio-Economic Planning Sciences, 1974

An entropy-maximizing model of a generalized pedestrian flow system is developed. This model is based on a fundamental conception of pedestrian traffic as being contained within a linear network. The model then maximizes the entropy of pedestrian flow within any given network, subject to a basic set of Kirchofl conditions. The resulting final equations are a special case of the gravity model. A general solution method is discussed and several numerical experiments with the model are described.

2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology, 2009

This paper introduces a space-continuous forcebased model for simulating pedestrian dynamics. The main interest of this work is the quantitative description of pedestrian movement through a bottleneck. Measurements of flow and density will be presented and compared with empirical data. The results of the proposed model show a good agreement with empirical data. Furthermore, we emphasize the importance of volume exclusion in force-based models.

This paper introduces a spatially continuous force-based model for simulating pedestrian dynamics. The main intention of this work is the quantitative description of pedestrian movement through bottlenecks and in corridors. Measurements of flow and density at bottlenecks will be presented and compared with empirical data. Furthermore the fundamental diagram for the movement in a corridor is reproduced. The results of the proposed model show a good agreement with empirical data.

Transportation Research Record, 2005

This paper discusses the validity of first-order traffic flow theory for the description of two-dimensional pedestrian flow operations in the case of an oversaturated bottleneck in front of which a large high-density region has formed. The paper shows how observations of density, speed, and flow that have been collected from laboratory walking experiments can be interpreted from the viewpoint of first-order theory. It is observed that pedestrians present at the same cross section inside of the congested region may encounter different flow conditions. This mainly depends on the lateral position of the pedestrian with respect to the center of the congested region. In the lateral center, high densities and low speeds are observed. However, on the boundary of the congested region, pedestrians may walk in nearly free-flow conditions and literally walk around this congested region. Visualization of these data in the flowdensity plane results in a large scatter of points that have similar flows (bottleneck capacity) but different densities. This can be explained by noticing that observations of congestion of pedestrian traffic over the total width of the cross section do not belong to a single fundamental diagram but belong to a set of different fundamental diagrams. This observation has consequences for estimation of the fundamental diagram describing pedestrian traffic.

Journal of Computers

This article proposes a new pedestrian model that precisely simulates the avoidance behavior so as to realize the pedestrians' walking action. For the design of the facility, the simulation is used as a means for predicting and analyzing the movement of pedestrians. However, most of the simulators focus on the flow of pedestrian but do not consider the movement of each pedestrian. As a result, conventional simulators are useful to simulate the phenomenon of macro level movement of pedestrian but are not useful to simulate the micro-level simulation. Therefore, we aim to implement the pedestrian flow simulator that enables us to observe each pedestrian behavior by using the Multi-Agent System. Research on pedestrian model began in the 1970s, but all models cannot simulate the behavior of the pedestrian individual well. Social Force Model, which is one of the typical pedestrian models, reproduces the behavior using the equation of motion by considering the mass point pedestrian. Accordingly, this model is effective in high-density state. By contrast, there is several problems in low-density state: the avoidance speed and trajectory. Hence, we propose a new model by introducing the concept of sub-goal and new force in order to solve this problem. Furthermore, the evaluation experiment shows that proposal model improves these problems.

Transportation Research Procedia, 2014

Consistent definitions of important variables in pedestrian flow dynamics are proposed. They are based on the definition of similar variables for road traffic flow from the 1960's by Edie. The definitions are extended to include multi-class flows where pedestrians move in different directions or have different characteristics. The new definitions provide a foundation of already existing crowd flow models and support their further development and the development of better observation methods. Nomenclature q flow in pedestrians per meter second, vector q absolute flow in pedestrians per meter second, scalar ρ density in pedestrians per square meter, scalar v velocity in meter per second, vector v speed in meter per second, scalar

arXiv: Physics and Society, 2018

The fundamental diagram of pedestrian dynamics gives the relation between the density and the flow within a specific enclosure. It is characterized by two distinctive behaviors: the free-flow regime (for low densities) and the congested regime (for high densities). In the former, the flow is an increasing function of the density, while in the latter, the flow remains on hold or decreases. In this work we perform numerical simulations of the pilgrimage at the entrance of the Jamaraat bridge (pedestrians walking along a straight corridor) and compare flow-density measurements with empirical measurements made by Helbing et al. We show that under high density conditions, the basic Social Force Model (SFM) does not completely handle the fundamental diagram reported in empirical measurements. We use analytical techniques and numerical simulations to prove that with an appropriate modification of the friction coefficient (but sustaining the SFM) it is possible to attain behaviors which are...

The relation between density and velocity of pedestrian movement has so far mainly been analysed using an empirical approach and fundamental relations found from the fitting of experimental measurements of the main quantities. The present study proposes a phenomenological model that is able to distinguish and take into account various factors that can affect the density-velocity relation by means of the induced microscopic walking phenomena. In particular, three factors are retained: the geographic area; the travel purpose; the effect of the lateral vibrations of the platform on which pedestrians walk, in view of the use of the fundamental diagrams within a crowd-structure interaction model applied to lively footbridges. The main features of the phenomenological model are then applied to a non-linear law found in literature and herein revisited in a more general form. The latter is finally used within a crowd-structure interaction model, which is applied to the T-bridge in Japan, in order to perform a sensitivity study of the deck response to different travel purposes.

Traffic and Granular Flow '13, 2014

It has been shown that a relation exists between the number of pedestrians in an area and the average flow in that area (production); this is called the Macroscopic Fundamental Diagram (MFD). Using this relation, we can express the average production of a network as a function of the average density (or accumulation) of the network. One of the assumptions under which a proper shape of the MFD is found, is that the congestion is spread homogeneously over the network. In vehicular traffic, it is shown that when this assumption is relaxed, the spatial variation of density within the network leads to a decreased production. This paper shows to which extent a function of accumulation and an aggregated variable of the spatial spread can predict the performance of a pedestrian traffic flow.

2004

Abstract In order to fully understand and analyze how the infrastructure in public facilities as well as in urban regions affects the overall characteristics of pedestrian crowds within these areas, computer simulations need to be performed. An implementation of the Social Force Model is discussed, which is suitable for both small-scale pedestrian simulations as well as computationally fast large-scale pedestrian simulations.