Simulating pedestrian flow through narrow exits

Social force model is one of the well-known approaches that can successfully simulate pedestrians’ movements realistically. However, it is not suitable to simulate high-density crowd movement realistically due to the model having only three basic crowd characteristics which are goal, attraction, and repulsion. Therefore, it does not satisfy the high-density crowd condition which is complex yet unique, due to its capacity, density, and various demographic backgrounds of the agents. Thus, this research proposes a model that improves the social force model by introducing four new characteristics which are gender, walking speed, intention outlook, and grouping to make simulations more realistic. Besides, the high-density crowd introduces irregular behaviours in the crowd flow, which is stopping motion within the crowd. To handle these scenarios, another model has been proposed that controls each agent with two different states: walking and stopping. Furthermore, the stopping behaviour was categorized into a slow stop and sudden stop. Both of these proposed models were integrated to form a high-density crowd simulation framework. The framework has been validated by using the comparison method and fundamental diagram method. Based on the simulation of 45,000 agents, it shows that the proposed framework has a more accurate average walking speed (0.36 m/s) compared to the conventional social force model (0.61 m/s). Both of these results are compared to the real-world data which is 0.3267 m/s. The findings of this research will contribute to the simulation activities of pedestrians in a highly dense population.

In the present paper, we investigate arch-shaped equilibrium solutions in the social force model proposed by Helbing and Molnar (Phys Rev E 51:4282, 1995) and Helbing et al. (Nature 407:487, 2000). The social force model is a system of ordinary differential equations, which describe the motion of the pedestrians under a panic situation. In the simulation of the social force model, we observe an intermittent appearance of arch-shaped structures (i.e. the “Blocking clusters” Parisi and Dorso, Physica A 354:606, 2005; Physica A 385:343, 2007; Frank and Dorso, Physica A 390:2135, 2011) around an exit which block up the flow of pedestrians. To understand such a dynamic behavior, we study arch-shaped equilibrium solutions around an exit under the simplest configuration.

With the continuous expansion of the city scale and urbanization, urban road networks are becoming increasingly complex. Moreover, severe and extreme weather events, earthquakes, and other natural disasters occur frequently. Therefore, how to effectively and quickly evacuate urban crowd in dynamic environments is an urgent issue. To carry out the above objective, an unmanned system-guided crowd evacuation method is proposed in the current study. In the proposed method, the robot can perceive the environment in a timely and accurate manner to generate the evacuation map via advanced information technologies such as the Internet of Things or urban brain. Subsequently, an improved elliptic tangent graph approach based on global and local information (ETG-GLI) is utilized to plan a feasible and short evacuation path in large-scale scenarios. Finally, a novel crowd evacuation model based on the social force model is proposed to simulate the actual crowd evacuation process in complex and large-scale environments. To test the performance of the proposed path planning method, 25 different scenarios are proposed to simulate complex urban crowd evacuation environments. The experimental results show that the proposed algorithm outperforms other competitors in terms of path planning ability and computational time. Three actual evacuation cases with 324 pedestrians are modeled to further test the performance of the proposed algorithm. The simulation results demonstrate that the unmanned system-guided crowd evacuation method can find a shorter evacuation path for reducing the evacuation time in three complex and large-scale environments when compared with three other methods. Therefore, the proposed algorithm is a highly effective and promising approach to provide useful decision support and guidance for actual urban planning and urban emergence management. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In modern cities, the population density is high and the road network is complex. To evacuate the crowd in a timely and safe manner, planning feasible and short paths in large-scale and complex environments is a critical and challenging task. Therefore, the present study aims to provide a novel method to plan high-quality evacuation routes to guide the pedestrian flow. The performance of the proposed approach is validated in 25 test scenarios and 3 real-world instances. Experimental results demonstrate that the proposed algorithm performs well in terms of path length and computation time. Moreover, the proposed crowd evacuation model can simulate the actual process of crowd evacuation.

Walking habits can affect the self-organizing movement in pedestrian flow. In China, pedestrians prefer to walk along the right-hand side in the collision-avoidance process, and the same is true for the left-hand preference that is followed in several countries. Through experiments with pedestrian flow, we find that the relative position between pedestrians can affect their moving preferences. We propose a kind of collision-avoidance force based on the social force model, which considers the predictions of potential conflict and the relative position between pedestrians. In the simulation, we use the improved model to explore the effect of moving preference on the collision-avoidance process and self-organizing pedestrian movement. We conclude that the improved model can bring the simulation closer to reality and that moving preference is conducive to the self-adjustment of counterflow.

Unidirectional pedestrian movement is a special phenomenon in the evacuation process of large public buildings and urban environments at pedestrian scale. Several macroscopic models for collective behaviors have been built to predict pedestrian flow. However, current models do not explain the diffusion behavior in pedestrian crowd movement, which can be important in representing spatial-temporal crowd density differentiation in the movement process. This study builds a macroscopic model for describing crowd diffusion behavior and evaluating unidirectional pedestrian flow. The proposed model employs discretization of time and walking speed in geometric distribution to calculate downstream pedestrian crowd flow and analyze movement process based on upstream number of pedestrians and average walking speed. The simulated results are calibrated with video observation data in a baseball stadium to verify the model precision. Statistical results have verified that the proposed pedestrian diffusion model could accurately describe pedestrian macromovement behavior within the margin of error.

Pushing and overtaking others in a spatial game of exit congestion

Efficient interchange stations, where travelers are changing lines and/or travel modes, are essential for the functionality of the whole public transport system. By studying pedestrian movements, the level of service and effectiveness imposed by the design of the interchange station can be evaluated. We address the problem by microsimulation, where a social force model is used for the phenomenological description of pedestrian interactions. The contribution of this paper is the proposal of measures describing the density, delay, acceleration and discomfort for pedestrian flows. Simulation experiments are performed for the movements in two canonical pedestrian areas, a corridor and a corridor intersection. Clearly, each of the four measures gives a description for how pedestrians impede each other, and hence for the efficiency at the facility. There is, however, different information provided by each measure, and we conclude that they all are well-motivated for quantifying the level of service in a pedestrian flow. We also illustrate the outcome for a railway platform, with two trains arriving in parallel.

Experimental study and numerical simulation of evacuation from a dormitory

An improved social force model for pedestrian dynamics in shipwrecks

Modified social force model considering emotional contagion for crowd evacuation simulation

This paper puts forward a simple mean-field game that captures some of the key dynamic features of crowd and pedestrian flows in multilevel building evacuations. It considers both microscopic and macroscopic route choice by strategic agents. To achieve this, we use mean-field differential game with local congestion measure based on the location of the agent in the building. Including the local mean-field term and its evolution along the path causes a sort of dispersion of the flow: the agents will try to avoid high density areas in order to reduce their overall walking costs and queuing costs at the stairs and exits. Each agent state is represented by a center of a box that follows a simple first-order dynamical system in an Euclidean space. Each agent will move to one of the closest exits that is safer and with less congested path. First, we formulate the problem and derive optimality equations using maximum principle and dynamic programming with boundary conditions. Second, well posedness and existence results are provided. Numerics and simulations are carried out to illustrate mean-field equilibria of a safer evacuation process. Finally, the methodology is shown to be flexible enough to include movement noises and stochastic structural component of the building.

Pedestrian crowd flows in shared spaces: Investigating the impact of geometry based on micro and macro scale measures

Unlike conventional crowd simulations for what-if analysis, agent-based crowd simulations for real-time applications are an emerging research topic and an important tool for better crowd managements in smart cities. Recent studies have attempted to incorporate the real-time crowd observations into crowd simulations for real-time crowd forecasting and management; however, crowd flow forecasting considering individual-level microscopic interactions, especially for large crowds, is still challenging. Here, we present a method that incorporates crowd observation data to forecast a large crowd flow, including thousands of individuals, using a microscopic agent-based model. By sequentially estimating both the crowd state and the latent parameter behind the crowd flows from the aggregate crowd density observation with the particle filter algorithm, the present method estimates and forecasts the large crowd flow using agent-based simulations that incorporate observation data. Numerical experiments, including a realistic evacuation scenario with 5000 individuals, demonstrated that the present method could successfully provide reasonable crowd flow forecasting for different crowd scenarios, even with limited information on crowd movements. These results support the feasibility of real-time crowd flow forecasting and subsequent crowd management, even for large but microscopic crowd problems.

Emergency signage systems provide effective route guidance and evacuation information for pedestrians in case of emergencies such as fire, blackout, and explosion. This paper proposes a modified social force (SF) model to investigate crowd evacuation dynamics taking into account the influence of emergency signs. The perceiving probability model is formulated for the quantitative description of the probability that pedestrians can successfully notice the sign and clearly perceive the guidance information. Simulation experiments and controlled experiments are designed to calibrate the parameters of the proposed model. The effectiveness of the modified SF model is preliminarily verified by comparing the simulation results with experimental data and/or empirical results such as fundamental diagrams and self-organization phenomena. A case study of crowd evacuation simulations at a typical Beijing subway station is conducted to evaluate evacuation performance of three signage distribution schemes, i.e., Maximal Covering (MaxCover), Uniform, and Random, which are proposed by the maximal covering location and empirical approaches, as well as contrasted scheme without emergency signs. The effects of the quantity and distribution of emergency signs on crowd evacuation efficiency are studied quantitatively by simulations. The results show that installing emergency signs can improve evacuation efficiency no matter what distribution scheme is adopted. By choosing an appropriate distribution scheme i.e., MaxCover, the evacuation performance can be further improved and the evacuation time can be significantly reduced.

Crowd simulation has its greatest utility in the study of safety measures for crowded events. However, total evacuation time, which is the most important feature in crowd evacuation, can vary depending on the population, the environment, the adopted strategies to decide routes, but also because people can be panicked or not. This paper presents a model to parametrize crowd simulation allowing to increase or decrease the agents stress. We use BioCrowds model and proposed an extension to consider new parameters to deal with crowd relaxing and compression, as comfort and stress. These two new parameters impact the will to go to the goal and the individual panic in trying to save itself. Indeed, our model could be integrated in other crowd simulators. This work discusses some obtained results and also presents a case study regarding a real scenario. We simulate the Hillsborough Disaster happened in 1989 in order to discuss the reliability of our method. Results indicate that our method can simulate in a coherent way the densities observed in the real life event.