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In this paper, we extend the nonlinear adaptive time gap car-following model to enhance the local and string stability for adaptive cruise control systems considering a time-lag in the lower level ...

Waves and oscillations are commonly observed in the dynamics of self-driven agents such as pedestrians or vehicles. Interestingly, many factors may perturb the stability of space homogeneous streaming, leading to the spontaneous formation of collective oscillations of the agents related to stop-and-go waves, jamiton, or phantom jam in the literature. In this article, we demonstrate that even a minimal additive stochastic noise in stable first-order dynamics can initiate stop-and-go phenomena. The noise is not a classic white one, but a colored noise described by a Gaussian Ornstein-Uhlenbeck process. It turns out that the joint dynamics of particles and noises forms again a (Gaussian) Ornstein-Uhlenbeck process whose characteristics can be explicitly expressed in terms of parameters of the model. We analyze its stability and characterize the presence of waves through oscillation patterns in the correlation and autocorrelation of the distance spacing between the particles. We determine exact solutions for the correlation functions for the finite system with periodic boundaries and in the continuum limit when the system size is infinite. Finally, we compare experimental trajectories of single-file pedestrian motions to simulation results., Comment: Preprint, 20 pages, 5 figures

Stop-and-go waves are commonly observed in traffic and pedestrian flows. In most traffic models they occur through a phase transition after fine tuning of parameters when the model has unstable homogeneous solutions. Inertia effects are believed to play an important role in this mechanism. Here, we present a novel explanation for stop-and-go waves based on stochastic effects in the absence of inertia. The introduction of specific coloured noises in a stable microscopic first order model allows to describe realistic stop-and-go behaviour without requiring instabilities or phase transitions. We apply the approach to pedestrian single-file motion and compare simulation results to real pedestrian trajectories. Plausible values for the model parameters are discussed., Comment: 10 pages, 8 figures. This is an extended version of the contribution arXiv:1801.09791

We apply the concept of time-to-collision (TTC) to the modeling of pedestrian dynamics. The TTC combines the spatial distances with the velocities to quantify the 'distance' to a collision. Therefore, it is a promising candidate for modeling the interactions between pedestrians. Empirical studies also indicate that the interaction between pedestrians can be described by the TTC: While the pair distribution of the distances, i.e. the probability of two pedestrians to have a certain spatial distance, was found to strongly depend on the relative velocity, the TTC accurately parametrizes its pair distribution. However, there are still few pedestrian models that use the TTC. After giving a general definition of the TTC, we present the widely used approximations for its calculation, especially in a one-dimensional setting. Combined with a desired time-gap, these give rise to different models, namely an Optimal-Velocity model and a new Time-to-Collision model. The TTC model exhibits, however, generic inconsistencies which are related to the estimates we use to approximate the speed of the predecessor. The estimates have a large impact on the dynamics and must therefore be interpreted as reflecting the pedestrians behavior, i.e. as anticipation strategies. We propose new estimates for the predecessor's speed. These give rise to a rich family of models based on the TTC which are analyzed by means of linear stability analysis and simulations.

Identifying the factors that control the dynamics of pedestrians is a crucial step towards modeling and building various pedestrian-oriented simulation systems. In this article, we empirically explore the influential factors that control the single-file movement of pedestrians and their impact. Our goal in this context is to apply feed-forward neural networks to predict and understand the individual speeds for different densities of pedestrians. With artificial neural networks, we can approximate the fitting function that describes pedestrians’ movement without having modeling bias. Our analysis is focused on the distances and range of interactions across neighboring pedestrians. As indicated by previous research, we find that the speed of pedestrians depends on the distance to the predecessor. Yet, in contrast to classical purely anisotropic approaches—which are based on vision fields and assume that the interaction mainly depends on the distance in front—our results demonstrate that the distance to the follower also significantly influences movement. Using the distance to the follower combined with the subject pedestrian’s headway distance to predict the speed improves the estimation by 18% compared to the prediction using the space in front alone.

Many models and algorithms allow predicting driver lane-changing intents in highway. Generally speaking, the challenge consists of inferring lane-changing maneuvers from speed difference and spacing with the surrounding vehicles on current and intended lanes. In this contribution, we empirically compare two approaches: the MOBIL model and the naive Bayes algorithm. The model MOBIL is a well-established rule-based approach, while naive Bayes is a data-based classifier by machine learning. The analysis is done using naturalistic trajectories of two-lane German highways (HighD project). We identify characteristic relationships between the spacing and speed difference variables and the intent to keep lane, overtake, or fold-down. It turns out that the mechanisms initiating fold-down and overtaking are different, requiring analysing the maneuvers separately. The fold-down maneuver is a more complex process involving more surrounding vehicles in interaction. False-positive and true-negative prediction errors of lane-changing and lane-keeping intents are computed using cross-validation. The quality of prediction with the rule-based model is satisfying for overtaking and limited for the fold-down maneuver. On the other hand, the data-based algorithm, devoid of modeling bias, can improve prediction for both lane-changing maneuvers. We quantify the prediction improvement using ROC curves and demonstrate statistical significance by taking into account the number of parameters.

Pedestrian behavior tends to depend on the type of facility. The flow at bottlenecks, for instance, can exceed the maximal rates observed in straight corridors. Consequently, accurate predictions of pedestrians movements in complex buildings including corridors, corners, bottlenecks, or intersections are difficult tasks for minimal models with a single setting of the parameters. Artificial neural networks are robust algorithms able to identify various types of patterns. In this paper, we will investigate their suitability for forecasting of pedestrian dynamics in complex architectures. Therefore, we develop, train, and test several artificial neural networks for predictions of pedestrian speeds in corridor and bottleneck experiments. The estimations are compared with those of a classical speed-based model. The results show that the neural networks can distinguish the two facilities and significantly improve the prediction of pedestrian speeds.

Stop-and-go waves are a common feature of vehicular traffic and have also been observed in pedestrian flows. Usually the occurrence of this self-organization phenomenon is related to an inertia mechanism. It requires fine-tuning of the parameters and is described by instability and phase transitions. Here, we present a novel explanation for stop-and-go waves in pedestrian dynamics based on stochastic effects. By introducing coloured noise in a stable microscopic inertia-free (i.e. first order) model, pedestrian stop-and-go behaviour can be described realistically without requirement of instability and phase transition. We compare simulation results to empirical pedestrian trajectories and discuss plausible values for the model’s parameters.

Classical second order models of pedestrian dynamics, like the social-force model, suffer from various unrealistic behaviors in the dynamics, e.g. backward motion, oscillations and overlapping of pedestrians. These effects are intrinsic to the dynamics and the consequence of strong inertia effects that usually appear in second order models. The experimentally observed stop-and-go behavior, which is an important test for any pedestrian model, can be reproduced with a stochastic first order model that does not suffer from the dynamical artefacts resulting from strong inertia. The model provides a new mechanism for stop-and-go behavior which is based on correlated noise. We show that this mechanism exists in a large class of models.

Adaptive cruise control (ACC) systems are fundamental components of driving automation. At the upper control level, ACC systems are based on car-following models determining the acceleration rate of a vehicle according to the distance gap to the predecessor and the speed difference. The pursuit strategy consists in keeping a constant time gap with the predecessor, as recommended by industrial norms. The systematic active safety of the systems is tackled thanks to local and string stability analysis. In this contribution, we analyze and compare several classical constant time gap linear and non-linear car-following models. We critically evaluate the stability robustness of the models against latency, noise and measurement error, heterogeneity, or kinetic constraints operating in the dynamics at the lower control level. The results highlight that many factors can perturb or even break the stability and induce the formation of stop-and-go waves or collisions, for intrinsically stable car-following models.

A mesoscopic pedestrian model is proposed, considering pedestrians as individuals and describing their movement by means of aggregate density-flow relationships. The model builds on a stochastic process, describing transition rates among adjacent sites on a lattice. Each lattice can contain several pedestrians. The approach is minimal and fast to simulate, and, by construction, capable of capturing population heterogeneity as well as variability in walking behaviour and en-route path choice. The model is more efficient than microscopic models, and potentially more accurate than macroscopic ones. We calibrate and validate the model using real data and carry out several numerical experiments to present its key properties and possible applications for simulation of large-scale scenarios.

The prediction of pedestrian movements in complex buildings is a difficult task. Recent experiments have shown that the behaviour of pedestrians tends to depend on the type of facility. For instance, flows at bottlenecks often exceed the maximal rates observed in straight corridors. This makes pedestrian behaviours geometry-dependent. Yet the types of geometries are various, and their systematic identification in complex buildings is not straightforward. Artificial neural networks are able to identify various types of patterns without supervision. They could be a suitable alternative for forecasts of pedestrian dynamics in complex architectures. In this paper, we test this assertion. We develop, train and test artificial neural networks for the prediction of pedestrian speeds in corridor and bottleneck experiments. The estimations are compared to those of an elementary speed-based model. The results show that neural networks distinguish the flow characteristics for the two different types of facilities and significantly improve the prediction of pedestrian speeds.

Voronoi diagrams are an established method in the analysis of pedestrian motion for constructing a density from two-dimensional positions. It is in turn used to give pointwise values for speed, movement direction, flow etc. The method was first described for high-density situations inside a crowd moving in a simple geometry without considering the influence of walls. However, more complicated distance calculations are needed for more complicated geometries where there are several obstacles or corners. In addition, partially empty spaces also require special treatment to avoid excessively big cells. These problems can lead to estimation errors when not handled correctly in subsequent use. In this work, we give details on how to adapt the calculations of Voronoi diagrams to make them fit for the presence of walls and obstacles in complex geometries. Furthermore, we show how that for persons at the edge of a group the personal space can be reasonably restricted. Based on these modifications, having pointwise values for quantities of interest allows to give average values for arbitrary geometries, not just for lines or rectangles of measurements. However, in order to obtain reasonable measurement values, different quantities may need different kind of averages—arithmetic or harmonic, or weighted with density.

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.

In this work we propose a methodology for assessment of pedestrian models continuous in space. With respect to the Kolmogorov-Smirnov distance between two data clouds, representing for instance simulated and the corresponding empirical data, we calculate an evaluation factor between zero and one. Based on the value of the herein developed factor, we make a statement about the goodness of the model under evaluation. Moreover this process can be repeated in an automatic way in order to maximize the above mentioned factor and hence determine the optimal set of model parameters., 8 pages, 3 figures, accepted at the Proceedings of Traffic and Granular Flow '17

Pedestrian behaviours tend to depend on the type of facility. Therefore accurate predictions of pedestrians movements in complex geometries (including corridor, bottleneck or intersection) are difficult to achieve for classical models with few parameters. Artificial neural networks have multiple parameters and are able to identify various types of patterns. They could be a suitable alternative for forecasts. We aim in this paper to present first steps testing this approach. We compare estimations of pedestrian speed with a classical model and a neural network for combinations of corridor and bottleneck experiments. The results show that the neural network is able to differentiate the two geometries and to improve the estimation of pedestrian speeds when the geometries are mixed., 8 pages, 5 figures; Traffic and Granular Flow 2017 Conference (TGF'17)

Stop-and-go waves are commonly observed in traffic and pedestrian flows. In traffic theory they are described by phase transitions of metastable models. The self-organization phenomenon occurs due to inertia mechanisms but requires fine tuning of the parameters. Here, a novel explanation for stop-and-go waves based on stochastic effects is presented for pedestrian dynamics. We show that the introduction of specific coloured noises in a stable microscopic model allows to describe realistic pedestrian stop-and-go behaviour without requirement of metastability and phase transition. We compare simulation results of the stochastic model to real pedestrian trajectories and discuss plausible values for the model's parameters., 8 pages, 5 figures; Traffic and Granular Flow 2017 Conference (TGF'17)

In a crowd, individuals make different motion choices such as "moving to destination", "following another pedestrian", and "making a detour". For the sake of convenience, the three direction choices are respectively called destination direction, following direction and detour direction in this paper. Here, it is found that the featured direction choices could be inspired by the shape characteristics of Voronoi diagram. To be specific, in the Voronoi cell of a pedestrian, the direction to a Voronoi node is regarded as a potential "detour" direction, and the direction perpendicular to a Voronoi link is regarded as a potential "following" direction. A pedestrian generally owns several alternative Voronoi nodes and Voronoi links in a Voronoi cell, and the optimal detour and following direction are determined by considering related factors such as deviation. Plus the destination direction which is directly pointing to the destination, the three basic direction choices are defined in a Voronoi cell. In order to evaluate the Voronoi diagram based basic directions, the empirical trajectory data in both uni- and bi-directional flow experiments are extracted. A time series method considering the step frequency is used to reduce the original trajectories' swaying phenomena which might disturb the recognition of actual forward direction. The deviations between the empirical velocity direction and the basic directions are investigated, and each velocity direction is classified into a basic direction or regarded as an inexplicable direction according to the deviations. The analysis results show that each basic direction could be a potential direction choice for a pedestrian. The combination of the three basic directions could cover most empirical velocity direction choices in both uni- and bi-directional flow experiments., Comment: 10pages, 12 figures

In this contribution, we review the state of the art of the interplay between empirical and theoretical studies of pedestrian dynamics. First, we introduce the main physical quantities characterizing the properties of a homogeneous crowd. A brief summary of some important empirical findings is given. Finally, we discuss the properties of microscopic pedestrian models. Different classifications of the models are proposed. We emphasize the relevance of empirical results and show how they can be used for validation and calibration.

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 figures