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.

Modelling supported driving as an optimal control cycle: Framework and model characteristics

Driver assistance systems support drivers in operating vehicles in a safe, comfortable and efficient way, and thus may induce changes in traffic flow characteristics. This paper puts forward a receding horizon control framework to model driver assistance and cooperative systems. The accelerations of automated vehicles are controlled to optimise a cost function, assuming other vehicles driving at stationary conditions over a prediction horizon. The flexibility of the framework is demonstrated with controller design of Adaptive Cruise Control (ACC) and Cooperative ACC (C-ACC) systems. The proposed ACC and C-ACC model characteristics are investigated analytically, with focus on equilibrium solutions and stability properties. The proposed ACC model produces plausible human car-following behaviour and is unconditionally locally stable. By careful tuning of parameters, the ACC model generates similar stability characteristics as human driver models. The proposed C-ACC model results in convective downstream and absolute string instability, but not convective upstream string instability observed in human-driven traffic and in the ACC model. The control framework and analytical results provide insights into the influences of ACC and C-ACC systems on traffic flow operations.Comment: Submitted to Transportation Research Part C: Emerging Technologie

An Area-Aggregated Dynamic Traffic Simulation Model

Microscopic and macroscopic dynamic traffic models not fast enough to run in an optimization loop to coordinate traffic measures over areas of twice a trip length (50x50 km). Moreover, in strategic planning there are models with a spatial high level of detail, but lacking the features of traffic dynamics. This paper introduces the Network Transmission Model (NTM), a model based on areas, exploiting the Macroscopic or Network Fundamental Diagram (NFD). For the first time, a full operational model is proposed which can be implemented in a network divided into multiple subnetworks, and the physical properties of spillback of traffic jams for subnetwork to subnetwork is ensured. The proposed model calculates the traffic flow between to cell as the minimum of the demand in the origin cell and the supply in the destination cell. The demand first increasing and then decreasing as function of the accumulation in the cell; the supply is first constant and then decreasing as function of the accumulation. Moreover, demand over the boundaries of two cells is restricted by a capacity. This system ensures that traffic characteristics move forward in free flow, congestion moves backward and the NFD is conserved. Adding the capacity gives qualitatively reasonable effects of inhomogeneity. The model applied on a test case with multiple destinations, and re-routing and perimeter control are tested as control measures

Pedestrian flows in bounded domains with obstacles

In this paper we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space occupancy by pedestrians is described via a sequence of Radon positive measures generated by a push-forward recursive relation. We assume that two fundamental aspects of pedestrian behavior rule the dynamics of the system: On the one hand, the will to reach specific targets, which determines the main direction of motion of the walkers; on the other hand, the tendency to avoid crowding, which introduces interactions among the individuals. The resulting model is able to reproduce several experimental evidences of pedestrian flows pointed out in the specialized literature, being at the same time much easier to handle, from both the analytical and the numerical point of view, than other models relying on nonlinear hyperbolic conservation laws. This makes it suitable to address two-dimensional applications of practical interest, chiefly the motion of pedestrians in complex domains scattered with obstacles.Comment: 25 pages, 9 figure

A Framework for Imbalanced Time-Series Forecasting

Time-series forecasting plays an important role in many domains. Boosted by the advances in Deep Learning algorithms, it has for instance been used to predict wind power for eolic energy production, stock market fluctuations, or motor overheating. In some of these tasks, we are interested in predicting accurately some particular moments which often are underrepresented in the dataset, resulting in a problem known as imbalanced regression. In the literature, while recognized as a challenging problem, limited attention has been devoted on how to handle the problem in a practical setting. In this paper, we put forward a general approach to analyze time-series forecasting problems focusing on those underrepresented moments to reduce imbalances. Our approach has been developed based on a case study in a large industrial company, which we use to exemplify the approach

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