Generalized Centrifugal Force Model for Pedestrian Dynamics

A spatially continuous force-based model for simulating pedestrian dynamics is introduced which includes an elliptical volume exclusion of pedestrians. We discuss the phenomena of oscillations and overlapping which occur for certain choices of the forces. The main intention of this work is the quantitative description of pedestrian movement in several geometries. Measurements of the fundamental diagram in narrow and wide corridors are performed. The results of the proposed model show good agreement with empirical data obtained in controlled experiments.Comment: 10 pages, 14 figures, accepted for publication as a Regular Article in Physical Review E. This version contains minor change

Quantitative analysis of pedestrian counterflow in a cellular automaton model

Pedestrian dynamics exhibits various collective phenomena. Here we study bidirectional pedestrian flow in a floor field cellular automaton model. Under certain conditions, lane formation is observed. Although it has often been studied qualitatively, e.g., as a test for the realism of a model, there are almost no quantitative results, neither empirically nor theoretically. As basis for a quantitative analysis we introduce an order parameter which is adopted from the analysis of colloidal suspensions. This allows to determine a phase diagram for the system where four different states (free flow, disorder, lanes, gridlock) can be distinguished. Although the number of lanes formed is fluctuating, lanes are characterized by a typical density. It is found that the basic floor field model overestimates the tendency towards a gridlock compared to experimental bounds. Therefore an anticipation mechanism is introduced which reduces the jamming probability.Comment: 11 pages, 12 figures, accepted for publication in Phys. Rev.

Constant net-time headway as key mechanism behind pedestrian flow dynamics

We show that keeping a constant lower limit on the net-time headway is the key mechanism behind the dynamics of pedestrian streams. There is a large variety in flow and speed as functions of density for empirical data of pedestrian streams, obtained from studies in different countries. The net-time headway however, stays approximately constant over all these different data sets. By using this fact, we demonstrate how the underlying dynamics of pedestrian crowds, naturally follows from local interactions. This means that there is no need to come up with an arbitrary fit function (with arbitrary fit parameters) as has traditionally been done. Further, by using not only the average density values, but the variance as well, we show how the recently reported stop-and-go waves [Helbing et al., Physical Review E, 75, 046109] emerge when local density variations take values exceeding a certain maximum global (average) density, which makes pedestrians stop.Comment: 7 pages, 7 figure

Solving the Direction Field for Discrete Agent Motion

Models for pedestrian dynamics are often based on microscopic approaches allowing for individual agent navigation. To reach a given destination, the agent has to consider environmental obstacles. We propose a direction field calculated on a regular grid with a Moore neighborhood, where obstacles are represented by occupied cells. Our developed algorithm exactly reproduces the shortest path with regard to the Euclidean metric.Comment: 8 pages, 4 figure

The Fundamental Diagram of Pedestrian Movement Revisited

The empirical relation between density and velocity of pedestrian movement is not completely analyzed, particularly with regard to the `microscopic' causes which determine the relation at medium and high densities. The simplest system for the investigation of this dependency is the normal movement of pedestrians along a line (single-file movement). This article presents experimental results for this system under laboratory conditions and discusses the following observations: The data show a linear relation between the velocity and the inverse of the density, which can be regarded as the required length of one pedestrian to move. Furthermore we compare the results for the single-file movement with literature data for the movement in a plane. This comparison shows an unexpected conformance between the fundamental diagrams, indicating that lateral interference has negligible influence on the velocity-density relation at the density domain $1 m^{-2}<\rho<5 m^{-2}$. In addition we test a procedure for automatic recording of pedestrian flow characteristics. We present preliminary results on measurement range and accuracy of this method.Comment: 13 pages, 9 figure

Statistical mechanics of non-hamiltonian systems: Traffic flow

Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car ahead. Distribution of car velocities for various densities of a group of cars are derived as well as probabilities of density fluctuations of the group for different velocities. For high braking abilities of cars free-flow and congested phases are found. Platoons of cars are formed for system of cars with inefficient brakes. A first order phase transition between free-flow and congested phase is suggested.Comment: 12 pages, 6 figures, presented at TGF, Paris, 200

Calibrating Car-Following Models using Trajectory Data: Methodological Study

The car-following behavior of individual drivers in real city traffic is studied on the basis of (publicly available) trajectory datasets recorded by a vehicle equipped with an radar sensor. By means of a nonlinear optimization procedure based on a genetic algorithm, we calibrate the Intelligent Driver Model and the Velocity Difference Model by minimizing the deviations between the observed driving dynamics and the simulated trajectory when following the same leading vehicle. The reliability and robustness of the nonlinear fits are assessed by applying different optimization criteria, i.e., different measures for the deviations between two trajectories. The obtained errors are in the range between~11% and~29% which is consistent with typical error ranges obtained in previous studies. In addition, we found that the calibrated parameter values of the Velocity Difference Model strongly depend on the optimization criterion, while the Intelligent Driver Model is more robust in this respect. By applying an explicit delay to the model input, we investigated the influence of a reaction time. Remarkably, we found a negligible influence of the reaction time indicating that drivers compensate for their reaction time by anticipation. Furthermore, the parameter sets calibrated to a certain trajectory are applied to the other trajectories allowing for model validation. The results indicate that ``intra-driver variability'' rather than ``inter-driver variability'' accounts for a large part of the calibration errors. The results are used to suggest some criteria towards a benchmarking of car-following models

Criterion for traffic phases in single vehicle data and empirical test of a microscopic three-phase traffic theory

A microscopic criterion for distinguishing synchronized flow and wide moving jam phases in single vehicle data measured at a single freeway location is presented. Empirical local congested traffic states in single vehicle data measured on different days are classified into synchronized flow states and states consisting of synchronized flow and wide moving jam(s). Then empirical microscopic characteristics for these different local congested traffic states are studied. Using these characteristics and empirical spatiotemporal macroscopic traffic phenomena, an empirical test of a microscopic three-phase traffic flow theory is performed. Simulations show that the microscopic criterion and macroscopic spatiotemporal objective criteria lead to the same identification of the synchronized flow and wide moving jam phases in congested traffic. It is found that microscopic three-phase traffic models can explain both microscopic and macroscopic empirical congested pattern features. It is obtained that microscopic distributions for vehicle speed difference as well as fundamental diagrams and speed correlation functions can depend on the spatial co-ordinate considerably. It turns out that microscopic optimal velocity (OV) functions and time headway distributions are not necessarily qualitatively different, even if local congested traffic states are qualitatively different. The reason for this is that important spatiotemporal features of congested traffic patterns are it lost in these as well as in many other macroscopic and microscopic traffic characteristics, which are widely used as the empirical basis for a test of traffic flow models, specifically, cellular automata traffic flow models.Comment: 27 pages, 16 figure

Experimental study of pedestrian flow through a bottleneck

In this work the results of a bottleneck experiment with pedestrians are presented in the form of total times, fluxes, specific fluxes, and time gaps. A main aim was to find the dependence of these values from the bottleneck width. The results show a linear decline of the specific flux with increasing width as long as only one person at a time can pass, and a constant value for larger bottleneck widths. Differences between small (one person at a time) and wide bottlenecks (two persons at a time) were also found in the distribution of time gaps.Comment: accepted for publication in J. Stat. Mec

Two-way multi-lane traffic model for pedestrians in corridors

We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian density cannot exceed a maximal density corresponding to contact between pedestrians. In a first step, we propose a singularly perturbed pressure relation which models the fact that the pedestrian velocity is considerably reduced, if not blocked, at congestion. In a second step, we carry over the singular limit into the model and show that abrupt transitions between compressible flow (in the uncongested regions) to incompressible flow (in congested regions) occur. We also investigate the hyperbolicity of the two-way models and show that they can lose their hyperbolicity in some cases. We study a diffusive correction of these models and discuss the characteristic time and length scales of the instability