Social distancing with the Optimal Steps Model

With the Covid-19 pandemic an urgent need to simulate social distancing arises. The Optimal Steps Model (OSM) is a pedestrian locomotion model that operationalizes an individual's need for personal space. We present new parameter values for personal space in the Optimal Steps Model to simulate social distancing in the pedestrian dynamics simulator Vadere. Our approach is pragmatic. We consider two use cases: in the first we demand that a set social distance must never be violated. In the second the social distance must be kept only on average. For each use case we conduct simulation studies in a typical bottleneck scenario and measure contact times, that is, violations of the social distance rule. We derive rules of thumb for suitable parameter choices in dependency of the desired social distance. We test the rules of thumb for the social distances 1.5m and 2.0m and observe that the new parameter values indeed lead to the desired social distancing. Thus, the rules of thumb will quickly enable Vadere users to conduct their own studies without understanding the intricacies of the OSM implementation and without extensive parameter adjustment.Comment: 9 pages, 8 figures, 4 table

Physics-based modeling and data representation of pedestrian pairwise interactions

The possibility to understand and to quantitatively model the physics of the interactions between pedestrians walking in crowds has compelling relevant applications, e.g. related to the design and safety of civil infrastructures. In this work we study pedestrian-pedestrian interactions from observational experimental data in diluted crowds. While in motion, pedestrians adapt their walking paths trying to preserve mutual comfort distances and to avoid collisions. In mathematical models this behavior is typically modeled via "social" interaction forces. Leveraging on a high-quality, high-statistics dataset - composed of few millions of real-life trajectories acquired from state-of-the-art observational experiments - we develop a quantitative model capable of addressing interactions in the case of binary collision avoidance. We model interactions in terms of both long- and short-range forces, which we superimpose to our Langevin model for non-interacting pedestrian motion [Corbetta et al. Phys.Rev.E 95, 032316, 2017]. The new model that we propose here features a Langevin dynamics with "fast" random velocity fluctuations that are superimposed to the "slow" dynamics of a hidden model variable: the "intended" walking path. The model is capable of reproducing relevant statistics of the collision avoidance motion, such as the statistics of the side displacement and of the passing speed. Rare occurrences of bumping events are also recovered. Furthermore, comparing with large datasets of real-life tracks involves an additional challenge so far neglected: identifying, within a database containing very heterogeneous conditions, only the relevant events corresponding to binary avoidance interactions. To tackle this challenge, we propose a novel approach based on a graph representation of pedestrian trajectories, which allows us to operate complexity reduction for efficient data selection.Comment: 17 figures, 18 page

Quickest Paths in Simulations of Pedestrians

This contribution proposes a method to make agents in a microscopic simulation of pedestrian traffic walk approximately along a path of estimated minimal remaining travel time to their destination. Usually models of pedestrian dynamics are (implicitly) built on the assumption that pedestrians walk along the shortest path. Model elements formulated to make pedestrians locally avoid collisions and intrusion into personal space do not produce motion on quickest paths. Therefore a special model element is needed, if one wants to model and simulate pedestrians for whom travel time matters most (e.g. travelers in a station hall who are late for a train). Here such a model element is proposed, discussed and used within the Social Force Model.Comment: revised version submitte

The Effect of Integrating Travel Time

This contribution demonstrates the potential gain for the quality of results in a simulation of pedestrians when estimated remaining travel time is considered as a determining factor for the movement of simulated pedestrians. This is done twice: once for a force-based model and once for a cellular automata-based model. The results show that for the (degree of realism of) simulation results it is more relevant if estimated remaining travel time is considered or not than which modeling technique is chosen -- here force-based vs. cellular automata -- which normally is considered to be the most basic choice of modeling approach.Comment: preprint of Pedestrian and Evacuation 2012 conference (PED2012) contributio

GPU accelerated Nature Inspired Methods for Modelling Large Scale Bi-Directional Pedestrian Movement

Pedestrian movement, although ubiquitous and well-studied, is still not that well understood due to the complicating nature of the embedded social dynamics. Interest among researchers in simulating pedestrian movement and interactions has grown significantly in part due to increased computational and visualization capabilities afforded by high power computing. Different approaches have been adopted to simulate pedestrian movement under various circumstances and interactions. In the present work, bi-directional crowd movement is simulated where an equal numbers of individuals try to reach the opposite sides of an environment. Two movement methods are considered. First a Least Effort Model (LEM) is investigated where agents try to take an optimal path with as minimal changes from their intended path as possible. Following this, a modified form of Ant Colony Optimization (ACO) is proposed, where individuals are guided by a goal of reaching the other side in a least effort mode as well as a pheromone trail left by predecessors. The basic idea is to increase agent interaction, thereby more closely reflecting a real world scenario. The methodology utilizes Graphics Processing Units (GPUs) for general purpose computing using the CUDA platform. Because of the inherent parallel properties associated with pedestrian movement such as proximate interactions of individuals on a 2D grid, GPUs are well suited. The main feature of the implementation undertaken here is that the parallelism is data driven. The data driven implementation leads to a speedup up to 18x compared to its sequential counterpart running on a single threaded CPU. The numbers of pedestrians considered in the model ranged from 2K to 100K representing numbers typical of mass gathering events. A detailed discussion addresses implementation challenges faced and averted

The Inflection Point of the Speed-Density Relation and the Social Force Model

It has been argued that the speed-density digram of pedestrian movement has an inflection point. This inflection point was found empirically in investigations of closed-loop single-file pedestrian movement. The reduced complexity of single-file movement does not only allow a higher precision for the evaluation of empirical data, but it occasionally also allows analytical considerations for micosimulation models. In this way it will be shown that certain (common) variants of the Social Force Model (SFM) do not produce an inflection point in the speed-density diagram if infinitely many pedestrians contribute to the force computed for one pedestrian. We propose a modified Social Force Model that produces the inflection point.Comment: accepted for presentation at conference Traffic and Granular Flow 201

Pedestrian vision and collision avoidance behavior: investigation of the information process space of pedestrians using an eye tracker

This study investigates the Information Process Space (IPS) of pedestrians, which has been widely used in microscopic pedestrian movement simulation models. IPS is a conceptual framework to define the spatial extent within which all objects are considered as potential obstacles for each pedestrian when computing where to move next. The particular focus of our study was identifying the size and shape of IPS by examining observed gaze patterns of pedestrians. A series of experiments was conducted in a controlled laboratory environment, in which up to 4 participants walked on a platform at their natural speed. Their gaze patterns were recorded by a head-mounted eye tracker and walking paths by laser-range-scanner–based tracking systems at the frequency of 25Hz. Our findings are threefold: pedestrians pay much more attention to ground surfaces to detect immediate potential environmental hazards than fixating on obstacles; most of their fixations fall within a cone-shape area rather than a semicircle; and the attention paid to approaching pedestrians is not as high as that paid to static obstacles. These results led to an insight that the structure of IPS should be re-examined by researching directional characteristics of pedestrians’ vision