Antoine Tordeux

Measuring the steady state of pedestrian flow in bottleneck experiments

Experiments with pedestrians could depend strongly on initial conditions. Comparisons of the results of such experiments require to distinguish carefully between transient state and steady state. Thus a modified version of the Cumulative Sum Control Chart algorithm is proposed to robustly detect steady states from density and speed time series of bottleneck experiments. The threshold of the detection parameter in the algorithm is calibrated using an autoregressive model. Comparing the detected steady states with manually selected ones, the modified algorithm gives robust and reproducible results. For the applications, three groups of bottleneck experiments are analysed and the steady states are detected. The results reconfirm that the specific flow is constant as bottleneck width changes. Moreover, we proposed a criterion to judge the difference between the flows in all states and in steady states, which is the ratio of pedestrian number to bottleneck width. The critical value of the ratio is found to be approximately 115 persons/m. This conclusion applies not only for the analysis of existing bottleneck experiments but also for the design of new bottleneck experiments and the validation of evacuation models. Furthermore, the range of steady state in time series of pedestrian characteristics could be effectively controlled by adjusting the value of the ratio.

Understanding human queuing behaviour at exits: an empirical study

The choice of the exit to egress from a facility plays a fundamental role in pedestrian modelling and simulation. Yet, empirical evidence for backing up simulation is scarce. In this contribution, we present three new groups of experiments that we conducted in different geometries. We varied parameters such as the width of the doors, the initial location and number of pedestrians which in turn affected their perception of the environment. We extracted and analysed relevant indicators such as distance to the exits and density levels. The results put in evidence the fact that pedestrians use time-dependent information to optimize their exit choice, and that, in congested states, a load balancing over the exits occurs. We propose a minimal modelling approach that covers those situations, especially the cases where the geometry does not show a symmetrical configuration. Most of the models try to achieve the load balancing by simulating the system and solving optimization problems. We show statistically and by simulation that a linear model based on the distance to the exits and the density levels around the exit can be an efficient dynamical alternative.

Jamming transitions in force-based models for pedestrian dynamics

Force-based models describe pedestrian dynamics in analogy to classical mechanics by a system of second order ordinary differential equations. By investigating the linear stability of two main classes of forces, parameter regions with unstable homogeneous states are identified. In this unstable regime it is then checked whether phase transitions or stop-and-go waves occur. Results based on numerical simulations show, however, that the investigated models lead to unrealistic behavior in the form of backwards moving pedestrians and overlapping. This is one reason why stop-and-go waves have not been observed in these models. The unrealistic behavior is not related to the numerical treatment of the dynamic equations but rather indicates an intrinsic problem of this model class. Identifying the underlying generic problems gives indications how to define models that do not show such unrealistic behavior. As an example we introduce a force-based model which produces realistic jam dynamics without the appearance of unrealistic negative speeds for empirical desired walking speeds.

Collision-Free Speed Model for Pedestrian Dynamics

We propose in this paper a minimal speed-based pedestrian model for which particle dynamics are intrinsically collision-free. The speed model is an optimal velocity function depending on the agent length (i.e.\ particle diameter), maximum speed and time gap parameters. The direction model is a weighted sum of exponential repulsion from the neighbors, calibrated by the repulsion rate and distance. The models main features like the reproduction of empirical phenomena are analysed by simulation. We point out that phenomena of self-organisation observable in force-based models and field studies can be reproduced by the collision-free model with low computational effort.

Quantitative comparison of estimations for the density within pedestrian streams

In this work, the precision of estimators for the density within unidirectional pedestrian streams is evaluated. The analysis is done in controllable systems where the density is homogeneous and all the characteristics are known. The objectives are to estimate the global density with local measurements or density profile at high spatial resolution with no bias and low fluctuations. The classical estimation using discrete numbers of observed pedestrians is compared to continuous estimators using spacing distance, Voronoi diagram, Gaussian kernel as well as maximum likelihood. Mean squared error and bias of the estimators are calculated from empirical data and Monte Carlo experiments. The results show quantitatively how continuous approaches improve the precision of the estimations.

A stochastic optimal velocity model for pedestrian flow

We propose a microscopic stochastic model to describe 1D pedestrian trajectories obtained in laboratory experiments. The model is based on optimal velocity (OV) functions and an additive noise determined by the inertial Ornstein-Uhlenbeck process. After statistical estimation of the OV function and noise parameters, we explore the model by simulation. The results show that the stochastic approach gives a good description of the characteristic relation between speed and spacing (fundamental diagram) and its variability. Moreover, it can reproduce the observed stop-and-go waves, bimodal speed distributions, and nonzero speed or spacing autocorrelations.

Jam avoidance with autonomous systems

Many car-following models have been developed for jam avoidance in highways. Two mechanisms are used to improve the stability: feedback control with autonomous models and increasing of the interaction within cooperative ones. In this paper, we compare the linear autonomous and collective optimal velocity (OV) models. We observe that the stability is significantly increased by adding predecessors in interaction with collective models. Yet, autonomous and collective approaches are close when the speed difference term is taken into account. In the linear OV models tested, the autonomous models including speed difference are sufficient to maximise the stability.

Detection of Steady State in Pedestrian Experiments

Initial conditions could have strong influences on the dynamics of pedestrian experiments. Thus, a careful differentiation between transient state and steady state is important and necessary for a thorough study. In this contribution a modified CUSUM algorithm is proposed to automatically detect steady state from time series of pedestrian experiments. Major modifications on the statistics include introducing a step function to enhance the sensitivity, adding a boundary to limit the increase, and simplifying the calculation to improve the computational efficiency. Furthermore, the threshold of the detection parameter is calibrated using an autoregressive process. By testing the robustness, the modified CUSUM algorithm is able to reproduce identical steady state with different references. Its application well contributes to accurate analysis and reliable comparison of experimental results.

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. These 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 is provided. The conditions match those 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 th...

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