Designing mobile application messages to impact route choice: A survey and simulation study.

Crowd congestion is a common issue at train stations around major sports events, and puts passengers at risk and lowers service quality. Guiding arriving fans along less traveled routes may alleviate congestion. Smartphone apps provide a medium to deliver route suggestions but the messages they provide are pivotal to adherence. We explore how message design affects pedestrians' willingness to follow route instructions. We present an online survey conducted with two groups: football fans, and students and faculty associates. We vary the presence of top down views of the route choices at train station Münchner Freiheit in Munich, real-time information on congestion, and appeals to team spirit. We compute a distribution of route choices that suggests that congestion may be reduced with the right combination of message components for each target group. We then use a computer simulation to investigate the congestion situation. Our results suggest that lowest congestion is achieved when people base their decisions on real-time information. The social identity approach is highlighted in our study as having a possible influence on message design. Moreover, it indicates that the implementation of such apps in real-life applications can improve safety. Our methodology can be applied to other scenarios to test the suitability of apps and message designs.

Guiding crowds when facing limited compliance: Simulating strategies.

At traffic hubs, it is important to avoid congestion of pedestrian streams to ensure safety and a good level of service. This presents a challenge, since distributing crowds on different routes is much more difficult than opening valves to, for example, regulate fluid flow. Humans may or may not comply with re-directions suggested to them typically with the help of signage, loudspeakers, apps, or by staff. This remains true, even if they perceive and understand the suggestions. Yet, simulation studies so far have neglected the influence of compliance. In view of this, we complement a state-of-the-art model of crowd motion and crowd behavior, so that we can vary the compliance rate. We consider an abstracted scenario that is inspired by a metro station in the city of Munich, where traffic regulators wish to make some passengers abandon the obviously shortest route so that the flow evens out. We investigate the effect of compliance for two very simple guiding strategies. In the first strategy, we alternate routes. In the second strategy, we recommend the path with the lowest crowd density. We observe that, in both cases, it suffices to reroute a small fraction of the crowd to reduce travel times. But we also find that taking densities into account is much more efficient when facing low compliance rates.

Modelling airborne transmission of SARS-CoV-2 at a local scale.

The coronavirus disease (COVID-19) pandemic has changed our lives and still poses a challenge to science. Numerous studies have contributed to a better understanding of the pandemic. In particular, inhalation of aerosolised pathogens has been identified as essential for transmission. This information is crucial to slow the spread, but the individual likelihood of becoming infected in everyday situations remains uncertain. Mathematical models help estimate such risks. In this study, we propose how to model airborne transmission of SARS-CoV-2 at a local scale. In this regard, we combine microscopic crowd simulation with a new model for disease transmission. Inspired by compartmental models, we describe virtual persons as infectious or susceptible. Infectious persons exhale pathogens bound to persistent aerosols, whereas susceptible ones absorb pathogens when moving through an aerosol cloud left by the infectious person. The transmission depends on the pathogen load of the aerosol cloud, which changes over time. We propose a 'high risk' benchmark scenario to distinguish critical from non-critical situations. A parameter study of a queue shows that the new model is suitable to evaluate the risk of exposure qualitatively and, thus, enables scientists or decision-makers to better assess the spread of COVID-19 and similar diseases.

Agent-based simulation of collective cooperation: from experiment to model.

Simulation models of pedestrian dynamics have become an invaluable tool for evacuation planning. Typically, crowds are assumed to stream unidirectionally towards a safe area. Simulated agents avoid collisions through mechanisms that belong to each individual, such as being repelled from each other by imaginary forces. But classic locomotion models fail when collective cooperation is called for, notably when an agent, say a first-aid attendant, needs to forge a path through a densely packed group. We present a controlled experiment to observe what happens when humans pass through a dense static crowd. We formulate and test hypotheses on salient phenomena. We discuss our observations in a psychological framework. We derive a model that incorporates: agents' perception and cognitive processing of a situation that needs cooperation; selection from a portfolio of behaviours, such as being cooperative; and a suitable action, such as swapping places. Agents' ability to successfully get through a dense crowd emerges as an effect of the psychological model.

Walking on stairs: Experiment and model.

An increasing global population forces urban planners to construct buildings and infrastructure that is extremely deep and high. Elevators and escalators serve skyscrapers and tunnels, but in an emergency people still have to walk on stairs. Computer simulations can mitigate risks of escape situations. For these situations, pedestrian locomotion models need to match reality well. Motion on stairs, however, is not nearly as well understood as motion in the plane. Publications are scarce and some are contradictory. As a result, movement on stairs is usually modeled by slowing down pedestrians by a fixed factor. But is this justified? And what happens at intermediate landings? This contribution aims to clarify inconclusive results of previous research and provide new information to directly incorporate empirical results into a parsimonious computer model. The algorithms are freely available through an open-source framework. After outlining the shortcomings of existing approaches, we present three experiments, from which we derive requirements for the computer model. Reenacting computer experiments shows the extent to which our model meets our observations. We conclude with an applied example, simulating an evacuation of Germany's famous Neuschwanstein Castle.

Investigating the Randomness of Passengers' Seating Behavior in Suburban Trains.

In pedestrian dynamics, individual-based models serve to simulate the behavior of crowds so that evacuation times and crowd densities can be estimated or the efficiency of public transportation optimized. Often, train systems are investigated where seat choice may have a great impact on capacity utilization, especially when passengers get in each other's way. Therefore, it is useful to reproduce passengers' behavior inside trains. However, there is surprisingly little research on the subject. Do passengers distribute evenly as it is most often assumed in simulation models and as one would expect from a system that obeys the laws of thermodynamics? Conversely, is there a higher degree of order? To answer these questions, we collect data on seating behavior in Munich's suburban trains and analyze it. Clear preferences are revealed that contradict the former assumption of a uniform distribution. We subsequently introduce a model that matches the probability distributions we observed. We demonstrate the applicability of our model and present a qualitative validation with a simulation example. The model's implementation is part of the free and open-source Vadere simulation framework for pedestrian dynamics and thus available for further studies. The model can be used as one component in larger systems for the simulation of public transport.

How cognitive heuristics can explain social interactions in spatial movement.

The movement of pedestrian crowds is a paradigmatic example of collective motion. The precise nature of individual-level behaviours underlying crowd movements has been subject to a lively debate. Here, we propose that pedestrians follow simple heuristics rooted in cognitive psychology, such as 'stop if another step would lead to a collision' or 'follow the person in front'. In other words, our paradigm explicitly models individual-level behaviour as a series of discrete decisions. We show that our cognitive heuristics produce realistic emergent crowd phenomena, such as lane formation and queuing behaviour. Based on our results, we suggest that pedestrians follow different cognitive heuristics that are selected depending on the context. This differs from the widely used approach of capturing changes in behaviour via model parameters and leads to testable hypotheses on changes in crowd behaviour for different motivation levels. For example, we expect that rushed individuals more often evade to the side and thus display distinct emergent queue formations in front of a bottleneck. Our heuristics can be ranked according to the cognitive effort that is required to follow them. Therefore, our model establishes a direct link between behavioural responses and cognitive effort and thus facilitates a novel perspective on collective behaviour.

Gradient navigation model for pedestrian dynamics.

We present a microscopic ordinary differential equation (ODE)-based model for pedestrian dynamics: the gradient navigation model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is then integrated to obtain the location. The approach differs fundamentally from force-based models needing only three equations to derive the ODE system, as opposed to four in, e.g., the social force model. Also, as a result, pedestrians are no longer subject to inertia. Several other advantages ensue: Model-induced oscillations are avoided completely since no actual forces are present. The derivatives in the equations of motion are smooth and therefore allow the use of fast and accurate high-order numerical integrators. At the same time, the existence and uniqueness of the solution to the ODE system follow almost directly from the smoothness properties. In addition, we introduce a method to calibrate parameters by theoretical arguments based on empirically validated assumptions rather than by numerical tests. These parameters, combined with the accurate integration, yield simulation results with no collisions of pedestrians. Several empirically observed system phenomena emerge without the need to recalibrate the parameter set for each scenario: obstacle avoidance, lane formation, stop-and-go waves, and congestion at bottlenecks. The density evolution in the latter is shown to be quantitatively close to controlled experiments. Likewise, we observe a dependence of the crowd velocity on the local density that compares well with benchmark fundamental diagrams.

Avoiding numerical pitfalls in social force models.

The social force model of Helbing and Molnár is one of the best known approaches to simulate pedestrian motion, a collective phenomenon with nonlinear dynamics. It is based on the idea that the Newtonian laws of motion mostly carry over to pedestrian motion so that human trajectories can be computed by solving a set of ordinary differential equations for velocity and acceleration. The beauty and simplicity of this ansatz are strong reasons for its wide spread. However, the numerical implementation is not without pitfalls. Oscillations, collisions, and instabilities occur even for very small step sizes. Classic solution ideas from molecular dynamics do not apply to the problem because the system is not Hamiltonian despite its source of inspiration. Looking at the model through the eyes of a mathematician, however, we realize that the right hand side of the differential equation is nondifferentiable and even discontinuous at critical locations. This produces undesirable behavior in the exact solution and, at best, severe loss of accuracy in efficient numerical schemes even in short range simulations. We suggest a very simple mollified version of the social force model that conserves the desired dynamic properties of the original many-body system but elegantly and cost efficiently resolves several of the issues concerning stability and numerical resolution.

Predicting pedestrian flow: a methodology and a proof of concept based on real-life data.

Building a reliable predictive model of pedestrian motion is very challenging: Ideally, such models should be based on observations made in both controlled experiments and in real-world environments. De facto, models are rarely based on real-world observations due to the lack of available data; instead, they are largely based on intuition and, at best, literature values and laboratory experiments. Such an approach is insufficient for reliable simulations of complex real-life scenarios: For instance, our analysis of pedestrian motion under natural conditions at a major German railway station reveals that the values for free-flow velocities and the flow-density relationship differ significantly from widely used literature values. It is thus necessary to calibrate and validate the model against relevant real-life data to make it capable of reproducing and predicting real-life scenarios. In this work we aim at constructing such realistic pedestrian stream simulation. Based on the analysis of real-life data, we present a methodology that identifies key parameters and interdependencies that enable us to properly calibrate the model. The success of the approach is demonstrated for a benchmark model, a cellular automaton. We show that the proposed approach significantly improves the reliability of the simulation and hence the potential prediction accuracy. The simulation is validated by comparing the local density evolution of the measured data to that of the simulated data. We find that for our model the most sensitive parameters are: the source-target distribution of the pedestrian trajectories, the schedule of pedestrian appearances in the scenario and the mean free-flow velocity. Our results emphasize the need for real-life data extraction and analysis to enable predictive simulations.

Natural discretization of pedestrian movement in continuous space.

Is there a way to describe pedestrian movement with simple rules, as in a cellular automaton, but without being restricted to a cellular grid? Inspired by the natural stepwise movement of humans, we develop a model that uses local discretization on a circle around virtual pedestrians. This allows for movement in arbitrary directions, only limited by the chosen optimization algorithm and numerical resolution. The radii of the circles correspond to the step lengths of pedestrians and thus are model parameters, which must be derived from empirical observation. Therefore, we conducted a controlled experiment, collected empirical data for step lengths in relation with different speeds, and used the findings in our model. We complement the model with a simple calibration algorithm that allows reproducing known density-velocity relations, which constitutes a proof of concept. Further validation of the model is achieved by reenacting an evacuation scenario from experimental research. The simulated egress times match the values reported for the experiment very well. A new normalized measure for space occupancy serves to visualize the results.