A modified heuristics-based model for simulating realistic pedestrian movement behavior

Pedestrian movement simulation models are used in various areas, such as building evacuation, transportation engineering, and safety management of large events. It also provides effective means to uncover underlying mechanisms of collective behaviors. In this work, a modified heuristics-based model is presented. In this model, the potential collisions in the moving process are explicitly considered. Meanwhile, a series of simulations is conducted in two typical scenarios to demonstrate the influence of critical parameters on model performance. It is found that when facing a wide obstacle in a corridor, the larger the visual radius, the earlier the pedestrian starts to make a detour. In addition, when a pedestrian observes a large crowd walking toward him, he chooses to make a detour and moves in the flow in a uniform direction. Furthermore, the model can reproduce the lane formation pedestrian flow phenomena in relatively high-density situations. With the increase of pedestrian visual radius and the weight of potential collision resistance, more stable pedestrian lanes and fewer moving-through-the-counterflow pedestrians can be observed. In terms of model validation, the density-speed relationship of simulation results accords well with that of the published empirical data. Our results demonstrate that the modified heuristics-based model can overcome the deficiency of the original model, and reproduce more realistic pedestrian movement behavior.     

A higher-order macroscopic model for pedestrian flows

This paper develops a higher-order macroscopic model of pedestrian crowd dynamics derived from fluid dynamics that consists of two-dimensional Euler equations with relaxation. The desired directional motion of pedestrians is determined by an Eikonal-type equation, which describes a problem that minimizes the instantaneous total walking cost from origin to destination. A linear stability analysis of the model demonstrates its ability to describe traffic instability in crowd flows. The algorithm to solve the macroscopic model is composed of a splitting technique introduced to treat the relaxation terms, a second-order positivity-preserving central-upwind scheme for hyperbolic conservation laws, and a fast-sweeping method for the Eikonal-type equation on unstructured meshes. To test the applicability of the model, we study a challenging pedestrian crowd flow problem of the presence of an obstruction in a two-dimensional continuous walking facility. The numerical results indicate the rationality of the model and the effectiveness of the computational algorithm in predicting the flux or density distribution and the macroscopic behavior of the pedestrian crowd flow. The simulation results are compared with those obtained by the two-dimensional Lighthill-Whitham-Richards pedestrian flow model with various model parameters, which further shows that the macroscopic model is able to correctly describe complex phenomena such as “stop-and-go waves” observed in empirical pedestrian flows.     

Biomechanically inspired modelling of pedestrian-induced forces on laterally oscillating structures

Despite considerable interest among engineers and scientists, bi-directional interaction between walking pedestrians and lively bridges has still not been well understood. In an attempt to bridge this gap a biomechanically inspired model of the human response to lateral bridge motion is presented and explored. The simple inverted pendulum model captures the key features of pedestrian lateral balance and the resulting forces on the structure. The forces include self-excited components that can be effectively modelled as frequency-dependent added damping and mass to the structure. The results of numerical simulations are in reasonable agreement with recent experimental measurements of humans walking on a laterally oscillating treadmill, and in very good agreement with measurements on full-scale bridges. In contrast to many other models of lateral pedestrian loading, synchronisation with the bridge motion is not involved. A parametric study of the model is conducted, revealing that as pedestrians slow down as a crowd becomes more dense, their resulting lower pacing rates generate larger self-excited forces. For typical pedestrian parameters, the potential to generate negative damping arises for any lateral bridge vibration frequency above 0.43 Hz, depending on the walking frequency. Stability boundaries of the combined pedestrian–structure system are presented in terms of the structural damping ratio and pedestrian-to-bridge mass ratio, revealing complex relations between damping demand and bridge and pedestrian frequencies, due to the added mass effect. Finally it is demonstrated that the model can produce simultaneous self-excited forces on multiple structural modes, and a realistic full simulation of a large number of pedestrians, walking randomly and interacting with a bridge, produces structural behaviour in very good agreement with site observations.     

Characterisation of walking loads by 3D inertial motion tracking

The present contribution analyses the walking behaviour of pedestrians in situ by 3D inertial motion tracking. The technique is first tested in laboratory experiments with simultaneous registration of the ground reaction forces. The registered motion of the pedestrian allows for the identification of stride-to-stride variations, which is usually disregarded in the simulation of walking forces. Subsequently, motion tracking is used to register the walking behaviour of (groups of) pedestrians during in situ measurements on a footbridge. The calibrated numerical model of the structure and the information gathered using the motion tracking system enables detailed simulation of the step-by-step pedestrian induced vibrations. Accounting for the in situ identified walking variability of the test-subjects leads to a significantly improved agreement between the measured and the simulated structural response.     

Pedestrian choice behavior analysis and simulation of vertical walking facilities in transfer station

Considering the interlayer height, luggage, the difference between queuing pedestrians, and walking speed, the pedestrian choice model of vertical walking facilities is established based on a support vector machine. This model is verified with the pedestrian flow data of Changchun light-rail transfer station and Beijing Xizhimen transfer station. Adding the pedestrian choice model of vertical walking facilities into the pedestrian simulation model which is based on cellular automata, the pedestrian choice behavior is simulated. In the simulation, the effects of the dynamic influence factors are analyzed. To reduce the conflicts between pedestrians in opposite directions, the layout of vertical walking facilities is improved. The simulations indicate that the improved layout of vertical walking facilities can improve the efficiency of pedestrians passing.     

Self-organized phenomena of pedestrian counter flow in a channel under periodic boundary conditions

In this paper we investigate self-organized phenomena such as lane formation generated by pedestrian counter flow in a channel.The lattice gas model is extended to take the effect of walkers in the opposite direction into account simultaneously when they are in the view field of a walker,i.e.,walkers tend to follow the leaders in the same direction and avoid conflicts with those walking towards them.The improved model is then used to mimic pedestrian counter flow in a channel under periodic boundary conditions.Numerical simulations show that lane formation is well reproduced,and this process is rather rapid which coincides with real pedestrian traffic.The average velocity and critical density are found to increase to some degree with the consideration of view field.     

基于元胞自动机和复杂网络理论的双向行人流建模

通过设计行人行走倾向性调查实验,分析了行人的行走倾向性特征. 引入前进系数、右倾系数、超越系数以及影响修正系数等对元胞自动机(CA) 基本模型中的转移概率进行修正,建立了考虑行人行走倾向性特征的CA行人仿真模型. 针对该模型中的行人群体,依据k-近邻作用原理,构建行人复杂网络. 通过计算机仿真,揭示了行人流密度、速度和流量的关系以及仿真过程中出现的自组织现象.进一步分析仿真输出的行人流基本参数和行人复杂网络主要特征参数,发现对同一行人流,其平均速度和网络平均路径长度均随着行人流状态的改变而变化.最后, 通过平均路径长度和平均速度的数据拟合,得出两者之间存在着线性负相关关系的结论, 即具有较小网络平均路径长度的行人流具有较高的平均速度.     

基于元胞传输模型的楼梯区域行人运动

针对楼梯区域行人运动进行观测实验,获得行人上下楼过程中的运动数据,通过对数据进行整理与分析,绘制不同过程中流量-密度变化关系图.通过对流密关系图进行定量分析,掌握楼梯区域行人运动特征,并改进原有元胞传输模型,提出楼梯行人运动模型,仿真模拟行人运动过程.模型中,引入势能修正系数,利用异向行人对元胞势能的影响来改变行人的路径选择;引入流量修正系数,描述不同的物理参数对元胞边界最大流量的影响;引入偏移系数,修正移动规则,增强优先方向对行人路径选择行为的影响.然后,通过比较仿真结果与实验数据,对模型及引入参数进行验证和校准.最后,利用校正模型,模拟研究楼梯区域对向行人运动过程,并对势能修正参数进行了灵敏度分析,进一步研究模型参数对行人运动的影响.研究表明,该模型可以模拟刻画楼梯区域行人运动过程,同时验证了楼梯区域行人集散效率跟行人到达率与行人路径选择有关.     

Kinetic theory of situated agents applied to pedestrian flow in a corridor

A situated agent-based model for simulation of pedestrian flow in a corridor is presented. In this model, pedestrians choose their paths freely and make decisions based on local criteria for solving collision conflicts. The crowd consists of multiple walking agents equipped with a function of perception as well as a competitive rule-based strategy that enables pedestrians to reach free access areas. Pedestrians in our model are autonomous entities capable of perceiving and making decisions. They apply socially accepted conventions, such as avoidance rules, as well as individual preferences such as the use of specific exit points, or the execution of eventual comfort turns resulting in spontaneous changes of walking speed. Periodic boundary conditions were considered in order to determine the density-average walking speed, and the density-average activity with respect to specific parameters: comfort angle turn and frequency of angle turn of walking agents. The main contribution of this work is an agent-based model where each pedestrian is represented as an autonomous agent. At the same time the pedestrian crowd dynamics is framed by the kinetic theory of biological systems.     

基于元胞自动机的行人和机动车相互干扰机理研究

在行人流量大的人行横道处,机动车和行人之间存在较为严重的干扰.通过引入行人和机动车的冲突干扰规则, 构建了能够刻画人行横道处机动车和行人相互干扰行为的元胞自动机模型.通过数值模拟研究了行人到达率、机动车到达率、 行人冒险穿越机动车道的阈值以及行人对机动车敏感系数等因素对机动车和行人流量的影响. 模拟结果显示,所提出的模型很好地反映了行人与机动车之间的干扰特性;随着行人冒险穿越机动车道的阈值的增加, 机动车流量增大,行人流量减小;随着行人对机动车敏感系数的增加,行人避让概率减小,机动车流量减小,行人流量增大. 所得结果对混合交通的控制和管理具有一定的指导意义.     

Effect of following strength on pedestrian counter flow

This paper proposes a modified lattice gas model to simulate pedestrian counter flow by considering the effect of following strength which can lead to appropriate responses to some complicated situations.Periodic and open boundary conditions are adopted respectively.The simulation results show that the presented model can reproduce some essential features of pedestrian counter flows,e.g.,the lane formation and segregation effect.The fundamental diagrams show that the complete jamming density is independent of the system size only when the width W and the length L are larger than some critical values respectively,and the larger asymmetrical conditions can better avoid the occurrence of deadlock phenomena.For the mixed pedestrian flow,it can be found that the jamming cluster is mainly caused by those walkers breaking the traffic rules,and the underlying mechanism is analysed.Furthermore,the comparison of simulation results and the experimental data is performed,it is shown that this modified model is reasonable and more realistic to simulate and analyse pedestrian counter flow.     

步行通道内行人流拉链现象的生成机理与仿真研究

以步行通道内的单向行人流为研究对象,分析研究行人拉链现象的生成机理,并建立基于Voronoi图的速度修正模型对其仿真研究.首先,从行人追求视野最佳和步行舒适的角度分析拉链现象的生成机理,以行人的视野关注和视野遮挡描述影响行人移动过程中产生拉链偏移的因素;以行人局部密度描述行人的步行舒适度;引入拉链敏感系数描述行人客观偏移的意愿程度;提出单个行人侧向偏移的机制,获得行人最佳的偏移位置.然后,构建基于Voronoi图的行人速度修正仿真模型,考虑行人是否有偏移倾向的主观意愿,并嵌入偏移规则,模拟再现行人的拉链现象.仿真发现:行人的拉链层数与通道宽度成正比,该模型速度密度关系图与实证数据吻合较好;与不考虑拉链效应相比,倾向主动进行侧向偏移的行人占比越大,越有助于提高通道内行人的移动速度、舒适度和空间利用率.     

基于改进格子气模型的对向行人流分层现象的随机性研究

在考虑行人视野范围的随机偏走格子气模型基础上, 引入行人对前方开阔区域的移动偏好特性, 提出改进的格子气模型, 对通道内对向行人流进行仿真研究. 模型再现了对向行人流在不同密度下出现的3种演化过程, 发现了行人密度与对向行人流分层现象的形成具有随机性, 以及统计了概率的变化趋势, 同时分析了分层现象形成概率与系统几何尺寸参数、移动强度参数、右行人流比例参数和视野范围参数等的关系. 分析结果表明, 改进的模型能够再现实际低密度下对向行人流不会出现分层现象的特性. 根据分层形成的概率, 可将对向行人流的密度分为5个区间, 不同区间的行人流演化过程各有差异. 模型和分析结果对理解对向行人流的动态演化过程, 提高通道内对向行人流的走行效率有一定帮助.     

Simulation study of pedestrian flow in a station hall during the Spring Festival travel rush

The Spring Festival is the most important festival in China. How can passengers go home smoothly and quickly during the Spring Festival travel rush, especially when emergencies of terrible winter weather happen? By modifying the social force model, we simulated the pedestrian flow in a station hall. The simulation revealed casualties happened when passengers escaped from panic induced by crowd turbulence. The results suggest that passenger numbers, ticket checking patterns, baggage volumes, and anxiety can affect the speed of passing through the waiting corridor. Our approach is meaningful in understanding the feature of a crowd moving and can be served to reproduce mass events. Therefore, it not only develops a realistic modeling of pedestrian flow but also is important for a better preparation of emergency management.     

Modeling the capability of penetrating a jammed crowd to eliminate freezing transition

Frozen state from jammed state is one of the most interesting aspects produced when simulating the multidirectional pedestrian flow of high density crowds. Cases of real life situations for such a phenomenon are not exhaustively treated.Our observations in the Hajj crowd show that freezing transition does not occur very often. On the contrary, penetrating a jammed crowd is a common aspect. We believe the kindness of pedestrians facing others whose walking is blocked is a main factor in eliminating the frozen state as well as in relieving the jammed state. We refine the social force model by incorporating a new social force to enable the simulated pedestrians to mimic the real behavior observed in the Hajj area.Simulations are performed to validate the work qualitatively.     

Multi-grid simulation of pedestrian counter flow with topological interaction

We investigate the dynamics of pedestrian counter flow by using a multi-grid topological pedestrian counter flow model.In the model,each pedestrian occupies multi-rather than only one grid,and interacts with others in the form of topological interaction,which means that a moving pedestrian interacts with a fixed number of those nearest neighbours coming from the opposite direction to determine his/her own moving direction.Thus the discretization of space and time are much finer,the decision making process of the pedestrian is more reliable,which all together makes the moving behaviour and boundary conditions much more realistic.When compared with field observations,it can be found that the modified model is able to reproduce well fitted pedestrian collective behaviour such as dynamical variation of lane formation,clustering of pedestrians in the same direction,etc.The fundamental diagram produced by the model fits also well with field data in the free flow region.Further analyses indicate that with the increase of the size of pedestrian counter flow system,it becomes harder for the system to transit into a jamming state,while the increase of interaction range does not change the transition point from free flow to jamming flow in the multi-grid topological counter flow model.It is also found that the asymmetry of the injection rate of pedestrians on the boundaries has direct influence on the process of transition from free flow to jamming flow,i.e.,a symmetric injection makes it easier for the system to transit into jamming flow.     

地铁站内交织行人流的简化模型和数值模拟

地铁站内多方向行人流以不同方式通过瓶颈时具有不同的效率,发生拥堵的机制也有所不同. 本文将地铁站内行人流的交织运动简化为连通双通道内两股行人通过瓶颈的情形. 采用推广的格子气模型,通过引入背景场,使改进的模型可以刻画地铁站内行人流的运动特征, 通过数值模拟研究了两股行人以两种不同方式经过研究区域的清空时间以及瓶颈宽度的影响. 研究发现,在模型中考虑行人沿对角线的运动可以更加准确地描述真实行人运动. 当瓶颈宽度小于临界宽度时,逆向交织的行人经过研究区域具有更高的效率, 验证了行人流实验的结果.此外还详细讨论了在瓶颈处发生拥堵的机理.     

Analysis of dynamic features in intersecting pedestrian flows

This paper focuses on the simulation analysis of stripe formation and dynamic features of intersecting pedestrian flows.The intersecting flows consist of two streams of pedestrians and each pedestrian stream has a desired walking direction.The model adopted in the simulations is the social force model, which can reproduce the self-organization phenomena successfully. Three scenarios of different cross angles are established. The simulations confirm the empirical observations that there is a stripe formation when two streams of pedestrians intersect and the direction of the stripes is perpendicular to the sum of the directional vectors of the two streams. It can be concluded from the numerical simulation results that smaller cross angle results in higher mean speed and lower level of speed fluctuation. Moreover, the detailed pictures of pedestrians' moving behavior at intersections are given as well.     

Determining an influencing area affecting walking speed on footpath: A case study of a footpath in CBD Bangkok,Thailand

Intuitively, the crowd density in front of a pedestrian will affect his walking speed along a footpath. Nevertheless, the size of the influencing area affecting walking speed has rarely been scrutinized in the past. This study attempts to determine the distance in front of pedestrians that principally affects their walking speed under normal conditions, using a case study of a footpath in Bangkok. We recorded pedestrian activities along a test section of 20 m, with an effective walking width of 2.45 m in the morning and at noon. The morning dataset was extracted for analyzing various influencing distances, ranging from 1 to 20 m in front of the pedestrian. The bi-directional walking speed–pedestrian density models were developed, for each tested distance, using linear regression analysis. It was found that an influencing length in the range of 5–8 m yields the highest correlation coefficients. In the case of high density conditions, the walking speed of the equally-split flow (50:50) was found to be higher than other proportional flow analyzed. The finding has useful implications on the improvement of the walking simulations in mesoscopic models.     

Study on bi-direction pedestrian flow using cellular automata simulation

A simulation of bi-direction pedestrian flow based on cellular automata (CA) will be presented from two aspects: direction split and pedestrians’ walking habit in this paper. The simulation uses Dynamic Parameters Model (DPM) to simplify tactically the decision-making process of pedestrians in their movements. A new parameter right-hand parameter is introduced to describe the pedestrians’ walking preference. The relationships of velocity–density and flow–density will be studied and analyzed. It is found that there are phase transitions at the critical density point, and the pedestrian flow shows distinctive characteristics at different phases with different relationships of velocity–density and flow–density. It is also found that direction split and pedestrians’ walking habit affect the value of critical density point and the figures of velocity–density and volume–density curves. In conclusion, the simulation can reflect and describe some pedestrian flow self-organization phenomena and transition trend of empirical pedestrian flow curves.