Analyzing Stop-and-Go Waves by Experiment and Modeling

The main topic of this paper is the analysis and modeling of stop-and-go waves, observable in experiments of single lane movement with pedestrians. The velocity density relation using measurements on a 'microscopic' scale shows the coexistence of two phases at one density. These data are used to calibrate and verify a spatially continuous model. Several criteria are chosen that a model has to satisfy: firstly we investigated the fundamental diagram (velocity versus density) using different measurement methods. Furthermore the trajectories are compared to the occurrence of stop-and-go waves qualitatively. Finally we checked the distribution of the velocities at fixed density against the experimental one. The adaptive velocity model introduced satisfies these criteria well.Comment: Fifth International Conference on Pedestrian and Evacuation Dynamics, March 8-10, 2010, National Institute of Standards and Technology, Gaithersburg, MD US

Methods for measuring pedestrian density, flow, speed and direction with minimal scatter

The progress of image processing during recent years allows the measurement of pedestrian characteristics on a "microscopic" scale with low costs. However, density and flow are concepts of fluid mechanics defined for the limit of infinitely many particles. Standard methods of measuring these quantities locally (e.g. counting heads within a rectangle) suffer from large data scatter. The remedy of averaging over large spaces or long times reduces the possible resolution and inhibits the gain obtained by the new technologies. In this contribution we introduce a concept for measuring microscopic characteristics on the basis of pedestrian trajectories. Assigning a personal space to every pedestrian via a Voronoi diagram reduces the density scatter. Similarly, calculating direction and speed from position differences between times with identical phases of movement gives low-scatter sequences for speed and direction. Closing we discuss the methods to obtain reliable values for derived quantities and new possibilities of in depth analysis of experiments. The resolution obtained indicates the limits of stationary state theory.Comment: 16 pages, 10 figs, submitted to Physica

Comparison of Pedestrian Fundamental Diagram Across Cultures

The relation between speed and density is connected with every self-organization phenomenon of pedestrian dynamics and offers the opportunity to analyze them quantitatively. But even for the simplest systems, like pedestrian streams in corridors, this fundamental relation isn't completely understood. Specifications of this characteristic in guidelines and text books differ considerably reflecting the contradictory database and the controversial discussion documented in the literature. In this contribution it is studied whether cultural influences and length of the corridor can be the causes for these deviations. To reduce as much as possible unintentioned effects, a system is chosen with reduced degrees of freedom and thus the most simple system, namely the movement of pedestrians along a line under closed boundary conditions. It is found that the speed of Indian test persons is less dependent on density than the speed of German test persons. Surprisingly the more unordered behaviour of the Indians is more effective than the ordered behaviour of the Germans. Without any statistical measure one cannot conclude about whether there are differences or not. By hypothesis test it is found quantitatively that these differences exist, suggesting cultural differences in the fundamental diagram of pedestrians.Comment: 12 pages, 7 figure

From traffic and pedestrian follow-the-leader models with reaction time to first order convection-diffusion flow models

In this work, we derive first order continuum traffic flow models from a microscopic delayed follow-the-leader model. Those are applicable in the context of vehicular traffic flow as well as pedestrian traffic flow. The microscopic model is based on an optimal velocity function and a reaction time parameter. The corresponding macroscopic formulations in Eulerian or Lagrangian coordinates result in first order convection-diffusion equations. More precisely, the convection is described by the optimal velocity while the diffusion term depends on the reaction time. A linear stability analysis for homogeneous solutions of both continuous and discrete models are provided. The conditions match the ones of the car-following model for specific values of the space discretization. The behavior of the novel model is illustrated thanks to numerical simulations. Transitions to collision-free self-sustained stop-and-go dynamics are obtained if the reaction time is sufficiently large. The results show that the dynamics of the microscopic model can be well captured by the macroscopic equations. For non--zero reaction times we observe a scattered fundamental diagram. The scattering width is compared to real pedestrian and road traffic data

Experimental study of pedestrian flow through a T-junction

In this study, series of experiments under laboratory conditions were carried out to investigate pedestrian flow through a T-junction, i.e., two branches merging into the main stream. The whole duration of the experiments was recorded by video cameras and the trajectories of each pedestrian were extracted using the software Petrack from these videos. The Voronoi method is used to resolve the fine structure of the fundamental diagram and spatial dependence of the measured quantities from trajectories. In our study, only the data in the stationary state are used by analyzing the time series of density and velocity. The density, velocity and specific flow profiles are obtained by refining the size of the measurement area (here 10 cm \times 10 cm are adopted). With such a high resolution, the spatial distribution of density, velocity and specific flow can be obtained separately and the regions with higher value can be observed intuitively. Finally, the fundamental diagrams of T-junction flow is compared in three different locations. It is shown that the fundamental diagrams of the two branches match well. However, the velocities in front of the merging are significantly lower than that in the main stream at the same densities. After the merging, the specific flow increases with the density \rho till 2.5 m-2. While in the branches, the specific flow is almost independent of the density between \rho = 1.5 m-2 and 3.5 m-2Comment: 9 pages, 4 figures, 2 tables, TGF'1

Influence of the number of predecessors in interaction within acceleration-based flow models

In this paper, the stability of the uniform solutions is analysed for microscopic flow models in interaction with $K\ge1$ predecessors. We calculate general conditions for the linear stability on the ring geometry and explore the results with particular pedestrian and car-following models based on relaxation processes. The uniform solutions are stable if the relaxation times are sufficiently small. The analysis is focused on the relevance of the number of predecessors in the dynamics. Unexpected non-monotonic relations between $K$ and the stability are presented.Comment: 18 pages, 14 figure

Quantitative Description of Pedestrian Dynamics with a Force based Model

This paper introduces a space-continuous force-based 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.Comment: 4 pages, 7 figures, 2009 IEEE/WIC/ACM International Joint Conferences on Web Intelligence and Intelligent Agent Technologies (WI-IAT 2009), 15-18 September 2009, in Milano, Italy, 200

Quantitative Verification of a Force-based Model for Pedestrian Dynamics

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.Comment: 8 pages, 7 figures, Proceedings of Traffic and Granular Flow (TGF) 200

Ordering in bidirectional pedestrian flows and its influence on the fundamental diagram

Experiments under laboratory conditions were carried out to study the ordering in bidirectional pedestrian streams and its influence on the fundamental diagram (density-speed-flow relation). The Voronoi method is used to resolve the fine structure of the resulting velocity-density relations and spatial dependence of the measurements. The data show that the specific flow concept is applicable also for bidirectional streams. For various forms of ordering in bidirectional streams, no large differences among density-flow relationships are found in the observed density range. The fundamental diagrams of bidirectional streams with different forms of ordering are compared with that of unidirectional streams. The result shows differences in the shape of the relation for {\rho} > 1.0 m-2. The maximum of the specific flow in unidirectional streams is significantly larger than that in all bidirectional streams examined.Comment: 9 pages, 9 figures, 3 Table

Transitions in pedestrian fundamental diagrams of straight corridors and T-junctions

Many observations of pedestrian dynamics, including various self-organization phenomena, have been reproduced successfully by different models. But the empirical databases for quantitative calibration are still insufficient, e.g. the fundamental diagram as one of the most important relationships displays non-negligible differences among various studies. To improve this situation, experiments in straight corridors and T-junction are performed. Four different measurement methods are defined to study their effects on the fundamental diagram. It is shown that they have minor influences for {\rho} <3.5 m-2 but only the Voronoi method is able to resolve the fine-structure of the fundamental diagram. This enhanced measurement method permits to observe the occurrence of boundary-induced phase transition. For corridors of different widths we found that the specific flow concept works well for {\rho} <3.5 m-2. Moreover, we illustrate the discrepancies between the fundamental diagrams of a T-junction and a straight corridor.Comment: 17 pages, 10 figures, 3 table