A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS

In this paper, a reactive dynamic user equilibrium model is extended to simulate two groups of pedestrians traveling on crossing paths in a continuous walking facility. Each group makes path choices to minimize the travel cost to its destination in a reactive manner based on instantaneous information. The model consists of a conservation law equation coupled with an Eikonal-type equation for each group. The velocity-density relationship of pedestrian movement is obtained via an experimental method. The model is solved using a finite volume method for the conservation law equation and a fast-marching method for the Eikonal-type equation on unstructured grids. The numerical results verify the rationality of the model and the validity of the numerical method. Based on this continuum model, a number of results, e.g., the formation of strips or moving clusters composed of pedestrians walking to the same destination, are also observed.

Analysis of interrelationship between pedestrian flow parameters using artificial neural network

Pedestrian flow parameters are analysed in this study considering linear and non-linear relationships between stream flow parameters using conventional and soft computing approach. Speed-density relationship serves as a fundamental relationship, Single-regime con- cepts and deterministic models like Greenshield and Underwood were applied in the study to describe bidirec- tional flow characteristics on sidewalks and carriageways around transport terminals in India. Artificial Neural Net- work （ANN） approach is also used for traffic flow mod- elling to build a relationship between different pedestrian flow parameters. A non-linear model based on ANN is suggested and compared with the other deterministic models. Out of the aforesaid models, ANN model demonstrated good results based on accuracy measure- ment. Also these ANN models have an advantage in terms of their self-processing and intelligent behaviour. Flow parameters are estimated by ANN model using MFD （Macroscopic Fundamental Diagram）. Estimated mean absolute error （MAE） and root mean square error （RMSE）values for the best fitted ANN model are 3.83 and 4.73 m/ min, respectively, less than those for the other models for sidewalk movement. Further estimated MAE and RMSE values of ANN model for carriageway movement are 4.02 and 4.98 m/min, respectively, which are comparatively less than those of the other models. ANN model gives better performance in fitness of model and future prediction of flow parameters. Also when using linear regression model between observed and estimated values for speed and flow parameters, performance of ANN model gives better fitness to predict data as compared to deterministic model. R value for speed data prediction is 0.756 and for flow data pre- diction is 0.997 using ANN model at sidewalk movement around transport terminal.

The Korteweg-de Vires equation for the bidirectional pedestrian flow model considering the next-nearest-neighbor effect

This paper focuses on a two-dimensional bidirectional pedestrian flow model which involves the next-nearest-neighbor effect. The stability condition and the Korteweg-de Vries （KdV） equation are derived to describe the density wave of pedestrian congestion by linear stability and nonlinear analysis. Through theoretical analysis, the soliton solution is obtained.

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.

Numerical simulation of pedestrian flow past a circular obstruction

In this paper, a revisiting Hughes’ dynamic continuum model is used to investigate and predict the essential macroscopic characteristics of pedestrian flow, such as flow, density and average speed, in a two dimensional continuous walking facility scattered with a circular obstruction. It is assumed that pedestrians prefer to walk a path with the lowest instantaneous travel cost from origin to destination, under the consideration of the current traffic conditions and the tendency to avoid a high-density region and an obstruction. An algorithm for the pedestrian flow model is based on a cellcentered finite volume method for a scalar conservation law equation, a fast sweeping method for an Eikonal-type equation and a second-order TVD Runge-Kutta method for the time integration on unstructured meshes. Numerical results demonstrate the effectiveness of the algorithm. It is verified that density distribution of pedestrian flow is influenced by the position of the obstruction and the path-choice behavior of pedestrians.

Model and application of bidirectional pedestrian flows at signalized crosswalks

This research of bidirectional pedestrian flows at signalized crosswalks is divided into two parts： model and applica- tion. In the model part, a mixed survey including the questionnaire investigation and tracking investigation is conducted to gain the basic data about walking tendentiousness of a pedestrian crossing. Then, the forward, right-hand, outstripping, and influential coefficients are outlined to quantize walking tendentiousness of pedestrian crossing and estimate transition probabilities of pedestrians. At last, an improved cellular automation model is proposed to describe walking tendentious- ness and crossing behaviors of pedestrians. In the application part, channelization research of bidirectional pedestrian flows is presented for real signalized crosswalk. In this process, the effects of right-side-walking and conformity behaviors on the efficiency of pedestrian crossing are thoroughly analyzed based on simulations and experiments to obtain a final channelization method to raise the efficiency of a pedestrian crossing at the crosswalk.

Influence of bottleneck on single-file pedestrian flow:Findings from two experiments

In order to investigate the influence of bottleneck on single-file pedestrian flow,we conduct two different bottleneck experiments.The first one is on ring road,while the second one is on straight route.For the first one,the global density is always set to be 1.5 ped/m.The corresponding critical flow rate for the bottleneck activation is about 0.57 ped/s.The data of the detectors set at different locations,including the velocities and time-headways,show that the amplitude of the oscillation of the stop-and-go waves gradually increases during the upstream propagation.Besides,when the measured flow rates are the same,the different situations in the single-file experiments with and without bottleneck are compared and discussed.For the second one,lower flow rates are used and the bottleneck is always activated.In all the runs,the system can reach one stable state,and the time needed is nearly the same.Inside the stable area,the statistics of pedestrians'velocities keeps nearly constant in both time and space.Outside this area,when the waiting time is not long(X=10 s),the phenomenon observed is similar to that found on ring road,e.g.,the statistics of pedestrians'velocities also gradually increases during the upstream propagation.This phenomenon is similar to that found in vehicular traffic flow,which shows the universality of different traffic flows.But when the waiting time becomes longer(X=20 s),this situation will be broken since the actions of many pedestrians become much slower.All these results can facilitate understanding more about the influence of bottleneck on single-file pedestrian flow.

THE ONE-DIMENSIONAL HUGHES MODEL FOR PEDESTRIAN FLOW:RIEMANN-TYPE SOLUTIONS

This paper deals with a coupled system consisting of a scalar conservation law and an eikonal equation, called the Hughes model. Introduced in [24], this model attempts to describe the motion of pedestrians in a densely crowded region, in which they are seen as a ＇thinking＇ （continuum） fluid. The main mathematical difficulty is the discontinuous gradient of the solution to the eikonal equation appearing in the flux of the conservation law. On a one dimensional interval with zero Dirichlet conditions （the two edges of the interval are interpreted as ＇targets＇）, the model can be decoupled in a way to consider two classical conservation laws on two sub-domains separated by a turning point at which the pedestrians change their direction. We shall consider solutions with a possible jump discontinuity around the turning point. For simplicity, we shall assume they are locally constant on both sides of the discontinuity. We provide a detailed description of the local- in-time behavior of the solution in terms of a ＇global＇ qualitative property of the pedestrian density （that we call ＇relative evacuation rate＇）, which can be interpreted as the attitude of the pedestrians to direct towards the left or the right target. We complement our result with explicitly computable examples.

Time-dependent Ginzburg-Landau equation for lattice hydrodynamic model describing pedestrian flow

A thermodynamic theory is formulated to describe the phase transition and critical phenomena in pedestrian flow. Based on the extended lattice hydrodynamic pedestrian model taking the interaction of the next-nearest-neighbor persons into account, the time-dependent Ginzburg-Landau （TDGL） equation is derived to describe the pedestrian flow near the critical point through the nonlinear analysis method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line, and critical point are obtained by the first and second derivatives of the thermodynamic potential.

Simulation of High Density Pedestrian Flow: A Microscopic Model

In recent years, modelling crowd and evacuation dynamics has become very important, with increasing huge numbers of people gathering around the world for many reasons and events. The fact that our global population grows dramatically every year and the current public transport systems are able to transport large amounts of people heightens the risk of crowd panic or crush. Pedestrian models are based on macroscopic or microscopic behaviour. In this paper, we are interested in developing models that can be used for evacuation control strategies. This model will be based on microscopic pedestrian simulation models, and its evolution and design requires a lot of information and data. The people stream will be simulated, based on mathematical models derived from empirical data about pedestrian flows. This model is developed from image data bases, so called empirical data, taken from a video camera or data obtained using human detectors. We consider the individuals as autonomous particles interacting through social and physical forces, which is an approach that has been used to simulate crowd behaviour. The target of this work is to describe a comprehensive approach to model a huge number of pedestrians and to simulate high density crowd behaviour in overcrowding places, e.g. sport, concert and pilgrimage places, and to assist engineering in the resolution of complicated problems through integrating a number of models from different research domains.

An extended social force model on unidirectional flow considering psychological and behavioral impacts of hazard source

An accurate assessment of the evacuation efficiency in case of disasters is of vital importance to the safety design of buildings and street blocks.Hazard sources not only physically but psychologically affect the pedestrians,which may further alter their behavioral patterns.This effect is especially significant in narrow spaces,such as corridors and alleys.This study aims to integrate a non-spreading hazard source into the social force model following the results from a previous experiment and simulation,and to simulate unidirectional pedestrian flows over various crowd densities and clarity–intensity properties of the hazard source.The integration include a virtual repulsion force from the hazard source and a decay on the social force term.The simulations reveal(i)that the hazard source creates virtual bottlenecks that suppress the flow,(ii)that the inter-pedestrian push forms a stabilisation phase on the flow-density curve within medium-to-high densities,and(iii)that the pedestrians are prone to a less orderly and stable pattern of movement in low clarity–intensity scenarios,possibly with lateral collisions passing the hazard source.

Extended social force model with a dynamic navigation field for bidirectional pedestrian flow

An extended social force model with a dynamic navigation field is proposed to study bidirectional pedestrian movement. The dynamic navigation field is introduced to describe the desired direction of pedestrian motion resulting from the decision-making processes of pedestrians. The macroscopic fundamental diagrams obtained using the extended model are validated against camera-based observations. Numerical results show that this extended model can reproduce collective phenomena in pedestrian traffic, such as dynamic multilane flow and stable separate-lane flow. Pedestrians＇ path choice behavior significantly affects the probability of congestion and the number of self-organized lanes.

Fundamental diagrams for pedestrian flows in a channel via an extended social force model

In this paper, an extended social force model was applied to investigate fundamental diagrams of pedestrian flows. In the presented model, both the static floor field and the view field were taken into account. Then each pedestrian can determine his/her desired walking directions according to both global and local information. The fundamental diagrams were obtained numerically under periodic boundary condition. It was found that the fundamental diagrams show good agreement with the measured data in the case of unidirectional flow, especially in the medium density range. However, the fundamental diagram for the case of bidirectional flow gave larger values than the measured data. Furthermore, the bidirectional flux is larger than the tmidirectional flux in a certain density range. It is indicated that the bidirectional flow may be more efficient than the unidirectional flow in some cases. The process of lane formation is quite quick in the model. Typical flow patterns in three scenarios were given to show some realistic applications.

Investigation on lane-formation in pedestrian flow with a new cellular automaton model

In this paper, we investigate pedestrian flows by using a newly-proposed cellular automaton （CA） model, which is based on the floor-field model. The interaction of pedestrians includes completion and cooperation, respectively reflected by a modified dynamic field and a position-changing behavior. Then we utilize this model to research lane formation phase in counter flow problem, involving the probability of lane formation phase, the average number of lanes and the microscopic behavior of pedestrians. It is found that the interaction between pedestrians and the different significant influences of average density of pedestrian flow on the features of lane formation phase.

A Bayesian modeling approach to bi-directional pedestrian flows in carnival events

Bi-directional pedestrian flows are common at crosswalks, footpaths, and shopping areas. However, the properties of pedestrian movement may vary in urban areas according to the type of walking facility. In recent years,crowd movements at carnival events have attracted the attention of researchers. In contrast to pedestrian behavior in other walking facilities, pedestrians whose attention is attracted by carnival displays or activities may slow down and even stop walking. The Lunar New Year Market is a traditional carnival event in Hong Kong held annually one week before the Lunar New Year. During the said event,crowd movements can be easily identified, particularly in Victoria Park, where the largest Lunar New Year Market in Hong Kong is hosted. In this study, we conducted a videobased observational survey to collect pedestrian flow and speed data at the Victoria Park Lunar New Year Market on the eve of the Lunar New Year. Using the collected data, an extant mathematical model was calibrated to capture the relationships between the relevant macroscopic quantities,thereby providing insight into pedestrian behavior at the carnival event. Bayesian inference was employed to calibrate the model by using prior data obtained from a previous controlled experiment. Results obtained enhance our understanding of crowd behavior under different conditions at carnival events, thus facilitating the improvement of the safety and efficiency of similar events in the future.

A Lattice Model for Bidirectional Pedestrian Flow on Gradient Road

Ramps and sloping roads appear everywhere in the built environment. It is obvious that the movement pattern of people in the sloping path may be different as compared with the pattern on level roads. Previously, most of the studies, especially the mathematical and simulation models, on pedestrian movement consider the flow at level routes.This study proposes a new lattice model for bidirectional pedestrian flow on gradient road. The stability condition is obtained by using linear stability theory. The nonlinear analysis method is employed to derive the modified Korteweg-de Vries(mKdV) equation, and the space of pedestrian flow is divided into three regions: the stable region, the metastable region, and the unstable region respectively. Furthermore, the time-dependent Ginzburg–Landan(TDGL) equation is deduced and solved through the reductive perturbation method. Finally, we present detailed results obtained from the model, and it is found that the stability of the model is enhanced in uphill situation while reduced in downhill situation with increasing slope.

双足运动微观视角下单列行人流建模与仿真研究

为从双足运动的微观视角直接呈现行人的移动特性,本文分析行人连续交替步伐行为的运动机理,建立单列行人流迈步运动模型,模拟行人位置在迈步周期内的非线性变化过程。模型根据行人重心和双足中心相对位置,将每次迈步周期内的迈步过程分为单支撑与双支撑阶段,并根据双足瞬时速度具备的波形时序特性,确定迈步周期内任意时刻的位置坐标。基于单列行人流实验数据,标定单列行人流迈步模型中的相关参数,每个行人根据前向距离确定下一次迈步运动所需的步长与步时,并进一步考虑行人的迈步调整行为,避免与前方行人发生踩踏。模拟仿真结果表明:模型能够较好呈现行人迈步运动的微观特性,并复刻了基本图与时空特性;根据行人迈步速度的波形特征,本文基于模拟结果计算步进动力学特性参数,发现行人在面对拥挤空间时,倾向于采用低步长与低步频的迈步风格;模型呈现人群同步自组织现象,发现全局密度为1.9 ped·m^(-1)时,同步现象发生概率最高。行人迈步模型的有效建立,可为行人运动状态评估与预测工作提供参考。

基于扩展卡尔曼滤波的疏散行人密度预测算法研究

疏散效率的提升是疏散系统研究的核心关注点。由于疏散系统通常呈现局部可观测性,而异常的局部观测信息会降低疏散效率,因此需对观测信息进行预测校正。为此,提出一种基于扩展卡尔曼滤波的人员密度信息预测校正算法。该算法采用神经网络拟合方法对扩展卡尔曼滤波算法中状态函数和观测函数的参数进行辨识,完成非线性疏散系统的近似线性化,提高了建模的精度;同时算法通过误差协方差矩阵的迭代更新机制实现疏散人员密度的快速预测和校正。在此基础上,还结合密度控制算法构建异常疏散场景下的行人流疏散控制策略。为验证所提算法的有效性,在设计和构建异常疏散场景仿真模型的基础上进行了对比仿真和真人疏散可控实验。结果表明,相较无数据校正的疏散控制策略,算法在异常疏散仿真和真人可控场景中分别获得最高38.9%和23.26%的效率提升,为异常疏散场景中的控制策略提供了有效的解决思路。

Route optimization model for pedestrian evacuation in metro hubs

The route optimization problem for road networks was applied to pedestrian flow.Evacuation path networks with nodes and arcs considering the traffic capacities of facilities were built in metro hubs,and a path impedance function for metro hubs which used the relationships among circulation speed,density and flow rate for pedestrians was defined.Then,a route optimization model which minimizes the movement time of the last evacuee was constructed to optimize evacuation performance.Solutions to the proposed mathematical model were obtained through an iterative optimization process.The route optimization model was applied to Xidan Station of Beijing Metro Line 4 based on the actual situations,and the calculation results of the model were tested using buildingExodus microscopic evacuation simulation software.The simulation result shows that the proposed model shortens the evacuation time by 16.05%,3.15% and 2.78% compared with all or none method,equally split method and Logit model,respectively.Furthermore,when the population gets larger,evacuation efficiency in the proposed model has a greater advantage.

数字增强下的城市步行空间设计与优化方法——以广州火车站片区详细规划为例

在梳理步行空间复合立体化发展趋势以及人流分析方法演进的基础上,迎合人本需求与数字手段结合的契机,基于“以流定形”设计范式,提出以数据分析人流进而指导步行空间设计的“数流定形”方法,通过提炼人流在不同观测尺度下的流动特征及其与步行空间从结构网络到空间形态的互动关系,利用动态定位分析、sDNA空间句法分析、MassMotion仿真等数字技术,建立数字协同的步行空间设计优化方法,并以广州火车站片区详细规划为例开展实证研究。