相向行人流自组织行为机理研究
|
摘要
拥挤人群的运动,包含单向、双向、交叉、往复等形式,可能引发诸如踩踏之类的严重事故。在这类事故中,行人可能遭受身体伤害甚至失去生命。因此,建筑设施内行人运动的舒适性及安全性问题日益引起建筑设计及管理人员的关注。已有的研究表明,影响建筑服务水平(Level of Service)的因素和行人流自组织的模式紧密相关。但是,目前尚缺乏对导致行人流自组织的行人行为机理的研究。
本文中,我们首先开展可控的实验,研究通道内行人运动的微观特征。基于数字图像处理的方法,提取出实验录像中行人的运动轨迹,并对这些运动轨迹做直接线性变换得到相应的现实坐标。依据行人的现实坐标研究单个行人的运动特征、行人与走廊间的作用以及行人与行人间的相互作用。结果表明,当在通道中运动时,典型学生行人的平均弛豫时间为0.71秒,平均最大行走速度为1.51米／秒。同时,行人在运动的过程中与墙壁保持一定的距离。当与墙之间的距离太近时,行人有朝远离墙壁方向运动以避免潜在碰撞的趋势。这种运动趋势最终被量化为行人与墙壁间随距离增长指数衰减的力。当通道内一个运动的行人规避在其运动方向上其他静止行人时,他们间的作用力呈现出各向异性的特点。典型中国学生行人在运动过程中有显著的右行偏向。进一步定量的分析表明,当静止的行人处于运动行人的右前方,那么其对运动行人的力变化不明显；当静止行人处于运动行人的左前方,其对运动行人的力随他们间距离的增加变化显著。其次,对于环形通道内单列同向运动的行人间相互作用的分析则表明,运动个体受其直接前驱最近邻的影响显著,而几乎不受其他行人影响。
基于上述实验结果,我们建立κ近邻模型和全近邻模型两个模型以研究相向行人流中运动个体间的基本作用。这两个模型的更新规则与随机行走元胞自动机模型(即基本模型)一致：通道内运动的个体依照其运动方向被分成左行行人和右行行人两种。不同的是,行人因不同的相互作用形式而具有不同的方向选择行为。在全近邻模型中,运动个体的方向选择行为受到距其一定距离范围内迎面.而来的所有的运动个体的影响；在κ近邻模型中,运动个体的方向选择则受到从对面走来的与其距离最近的κ近个体的分布的影响。通过研究相向行人流中自发形成的行人分层以及影响通道内行人分层数目的因素,我们发现随着通道内行人密度的变化,全近邻模型中行人分层的模式变化显著,而κ近邻模型中行人分层模式基本不变且与实际观测相符。这意味着κ近邻作用在行人集群行为涌现中起着更基本的作用。基于演化博弈理论,我们分析了模型中行人分层的涌现机制。并研究了通道内行人的平均速度,密度与边界密度间的关系,讨论了速度、流量增强的原因。
通过比较模型中行人分层的模式与实际观测的相向行人流模式、模型计算得到的基本图与行人流经验基本图,我们对κ近邻模型进行了验证。结果表明κ近邻模型可以改善交通环境,进而增加自由流区域内行人的运动速度,并且能够重现高密度时的相分离及自由流向壅塞流转变的特征。考虑到实际行人流中行人相对.位置有错位的现象,我们对κ近邻模型进行了改进,建立了多格子κ近邻模型,并采用多格子κ近邻模型研究了相向行人流受系统尺寸、行人视野范围以及非对称边界条件等影响下的动力学行为。
在深入理解相向行人流中行人行为机理的基础上,我们将κ近邻模型嵌入地理信息系统(GIS)平台,开发了基于GIS的行人流模拟软件。并进一步以不同的车站站台设计方案为例,讨论为改善行人交通环境采取不同拥挤人群控制措施时,地铁站台上行人运动的基本图以及实时的设施服务水平图,评估人行设施的服务水平,研究探讨拥挤人群的控制方法。
Pedestrian crowd movement, including single direction, bi-directional flow etc, may trigger serious crowd disasters such as trampling. People may be injured or even killed in these disasters. As a result, the effect of building facilities on the comfort and safety of people's movement becomes one of the important concerns of building designers and facility managers. Factors affecting the level of service relate closely to pedestrian flow pattern. Previous studies indicate that self-organized patterns emerging in pedestrian counter flows may affect the flow rate and velocity of crowds. However, the studies rarely discussed the inter-personal interaction in pedestrians.
In this study, we first performed well-controlled experiments to capture the moving characteristics of pedestrians in a corridor. Pedestrians'moving trajectories were first extracted with digital image processing method and then mapped into real space coordinates by adopting a direct linear transformation approach. Moving characteristics of single pedestrian, interaction between pedestrian and the corridor as well as interaction between pair pedestrians were analyzed. It was found that when walking in the corridor, the average relaxation time of typical Chinese pedestrians was about 0.71s, and the maximum mean velocity of free walking was about 1.51m/s. Meanwhile, these pedestrians also kept a suitable distance to the wall to avoid potential collisions. When walking too close to the wall, the pedestrian had a tendency to walk away. This phenomenon was then expressed as an exponential decay force function. When one pedestrian tried to evade another standing still pedestrian in the corridor, the interaction between them showed a non-isotropic feature. The experimental results indicated that the participants preferred to walk with right preference more significantly. We further quantified the interaction among pedestrians, and found that the force from those who located on the right-forward direction did not change much while from those who located on the left-forward direction did vary with the increase of distance. Interaction among pedestrians in a single file uni-directional flow show that the moving pedestrian is affected by his direct predecessor most while is barely affected by others.
Based on the experimental findings, two models were established, namely a metric distance based model and a k-Nearest-Neighbor (kNN) counterflow model, which could be used to investigate the fundamental interaction ruling pedestrian counter. flow. The basic update schemes of these two models were the same with a cellular automaton (CA) random walker model, which is entitled as basic model hereafter. Pedestrians moving in a long channel will evolve into left moving pedestrians and right moving pedestrians. These pedestrians interact with each other in different forms in different models. In the metric distance based model, the direction chosen behavior of an individual is influenced by all those who are in a small metric distance and come from the opposite direction; while in the kNN counterflow model, the direction chosen behavior of an individual is influenced by the distribution of a fixed number of the k-Nearest neighbors coming from the opposite direction. The self-organized lane formation was captured and factors affecting the number of lanes formed in the channel were investigated. Results implied that with varying the density, the lane formation pattern varies substantially in the case of metric distance based model while is nearly the same in the kNN counterflow model which matches field observations. This means that the kNN interaction plays a more fundamental role in the emergence of collective pedestrian phenomena. The relations among mean velocity, occupancy and total entrance density at the boundaries of the counter flow system were also studied. Reasons for the lane formation in the CA models were theoretically investigated on the basis of game theory. Reasons for the velocity enhancement and flow improvement were also discussed.
The kNN counterflow model was further validated by comparing lane formation pattern and the fundamental diagram with real pedestrian counter flow. The results indicated that the kNN interaction enhances the mean velocity in the free flow phase by providing more efficient traffic condition, and is able to quantify features such as segregation and phase transition at high density of pedestrian traffic. Considering the facts such as the pedestrians'locations are out of alignment in reality, we further modified the kNN model into multi-grid kNN model to mimic pedestrian flow. Dynamics of the multi-grid kNN model were studied to detail traffic characteristics of pedestrian counter flow.
With these insights in the behavioral mechanism of pedestrian counter flow, we illustrated the present study in the area of crowd control by an example of improving traffic situation for pedestrian counter flow in a long corridor in respect of a series of layout design. To facilitate application, we further embed the kNN counterflow model into a Geographic Information System (GIS) platform and try to derive fundamental diagram, as well as real-time level-of-service map so as to evaluate levels of services of pedestrian traffic facilities and efficiencies of different crowd control methods.
本文中,我们首先开展可控的实验,研究通道内行人运动的微观特征。基于数字图像处理的方法,提取出实验录像中行人的运动轨迹,并对这些运动轨迹做直接线性变换得到相应的现实坐标。依据行人的现实坐标研究单个行人的运动特征、行人与走廊间的作用以及行人与行人间的相互作用。结果表明,当在通道中运动时,典型学生行人的平均弛豫时间为0.71秒,平均最大行走速度为1.51米／秒。同时,行人在运动的过程中与墙壁保持一定的距离。当与墙之间的距离太近时,行人有朝远离墙壁方向运动以避免潜在碰撞的趋势。这种运动趋势最终被量化为行人与墙壁间随距离增长指数衰减的力。当通道内一个运动的行人规避在其运动方向上其他静止行人时,他们间的作用力呈现出各向异性的特点。典型中国学生行人在运动过程中有显著的右行偏向。进一步定量的分析表明,当静止的行人处于运动行人的右前方,那么其对运动行人的力变化不明显；当静止行人处于运动行人的左前方,其对运动行人的力随他们间距离的增加变化显著。其次,对于环形通道内单列同向运动的行人间相互作用的分析则表明,运动个体受其直接前驱最近邻的影响显著,而几乎不受其他行人影响。
基于上述实验结果,我们建立κ近邻模型和全近邻模型两个模型以研究相向行人流中运动个体间的基本作用。这两个模型的更新规则与随机行走元胞自动机模型(即基本模型)一致：通道内运动的个体依照其运动方向被分成左行行人和右行行人两种。不同的是,行人因不同的相互作用形式而具有不同的方向选择行为。在全近邻模型中,运动个体的方向选择行为受到距其一定距离范围内迎面.而来的所有的运动个体的影响；在κ近邻模型中,运动个体的方向选择则受到从对面走来的与其距离最近的κ近个体的分布的影响。通过研究相向行人流中自发形成的行人分层以及影响通道内行人分层数目的因素,我们发现随着通道内行人密度的变化,全近邻模型中行人分层的模式变化显著,而κ近邻模型中行人分层模式基本不变且与实际观测相符。这意味着κ近邻作用在行人集群行为涌现中起着更基本的作用。基于演化博弈理论,我们分析了模型中行人分层的涌现机制。并研究了通道内行人的平均速度,密度与边界密度间的关系,讨论了速度、流量增强的原因。
通过比较模型中行人分层的模式与实际观测的相向行人流模式、模型计算得到的基本图与行人流经验基本图,我们对κ近邻模型进行了验证。结果表明κ近邻模型可以改善交通环境,进而增加自由流区域内行人的运动速度,并且能够重现高密度时的相分离及自由流向壅塞流转变的特征。考虑到实际行人流中行人相对.位置有错位的现象,我们对κ近邻模型进行了改进,建立了多格子κ近邻模型,并采用多格子κ近邻模型研究了相向行人流受系统尺寸、行人视野范围以及非对称边界条件等影响下的动力学行为。
在深入理解相向行人流中行人行为机理的基础上,我们将κ近邻模型嵌入地理信息系统(GIS)平台,开发了基于GIS的行人流模拟软件。并进一步以不同的车站站台设计方案为例,讨论为改善行人交通环境采取不同拥挤人群控制措施时,地铁站台上行人运动的基本图以及实时的设施服务水平图,评估人行设施的服务水平,研究探讨拥挤人群的控制方法。
Pedestrian crowd movement, including single direction, bi-directional flow etc, may trigger serious crowd disasters such as trampling. People may be injured or even killed in these disasters. As a result, the effect of building facilities on the comfort and safety of people's movement becomes one of the important concerns of building designers and facility managers. Factors affecting the level of service relate closely to pedestrian flow pattern. Previous studies indicate that self-organized patterns emerging in pedestrian counter flows may affect the flow rate and velocity of crowds. However, the studies rarely discussed the inter-personal interaction in pedestrians.
In this study, we first performed well-controlled experiments to capture the moving characteristics of pedestrians in a corridor. Pedestrians'moving trajectories were first extracted with digital image processing method and then mapped into real space coordinates by adopting a direct linear transformation approach. Moving characteristics of single pedestrian, interaction between pedestrian and the corridor as well as interaction between pair pedestrians were analyzed. It was found that when walking in the corridor, the average relaxation time of typical Chinese pedestrians was about 0.71s, and the maximum mean velocity of free walking was about 1.51m/s. Meanwhile, these pedestrians also kept a suitable distance to the wall to avoid potential collisions. When walking too close to the wall, the pedestrian had a tendency to walk away. This phenomenon was then expressed as an exponential decay force function. When one pedestrian tried to evade another standing still pedestrian in the corridor, the interaction between them showed a non-isotropic feature. The experimental results indicated that the participants preferred to walk with right preference more significantly. We further quantified the interaction among pedestrians, and found that the force from those who located on the right-forward direction did not change much while from those who located on the left-forward direction did vary with the increase of distance. Interaction among pedestrians in a single file uni-directional flow show that the moving pedestrian is affected by his direct predecessor most while is barely affected by others.
Based on the experimental findings, two models were established, namely a metric distance based model and a k-Nearest-Neighbor (kNN) counterflow model, which could be used to investigate the fundamental interaction ruling pedestrian counter. flow. The basic update schemes of these two models were the same with a cellular automaton (CA) random walker model, which is entitled as basic model hereafter. Pedestrians moving in a long channel will evolve into left moving pedestrians and right moving pedestrians. These pedestrians interact with each other in different forms in different models. In the metric distance based model, the direction chosen behavior of an individual is influenced by all those who are in a small metric distance and come from the opposite direction; while in the kNN counterflow model, the direction chosen behavior of an individual is influenced by the distribution of a fixed number of the k-Nearest neighbors coming from the opposite direction. The self-organized lane formation was captured and factors affecting the number of lanes formed in the channel were investigated. Results implied that with varying the density, the lane formation pattern varies substantially in the case of metric distance based model while is nearly the same in the kNN counterflow model which matches field observations. This means that the kNN interaction plays a more fundamental role in the emergence of collective pedestrian phenomena. The relations among mean velocity, occupancy and total entrance density at the boundaries of the counter flow system were also studied. Reasons for the lane formation in the CA models were theoretically investigated on the basis of game theory. Reasons for the velocity enhancement and flow improvement were also discussed.
The kNN counterflow model was further validated by comparing lane formation pattern and the fundamental diagram with real pedestrian counter flow. The results indicated that the kNN interaction enhances the mean velocity in the free flow phase by providing more efficient traffic condition, and is able to quantify features such as segregation and phase transition at high density of pedestrian traffic. Considering the facts such as the pedestrians'locations are out of alignment in reality, we further modified the kNN model into multi-grid kNN model to mimic pedestrian flow. Dynamics of the multi-grid kNN model were studied to detail traffic characteristics of pedestrian counter flow.
With these insights in the behavioral mechanism of pedestrian counter flow, we illustrated the present study in the area of crowd control by an example of improving traffic situation for pedestrian counter flow in a long corridor in respect of a series of layout design. To facilitate application, we further embed the kNN counterflow model into a Geographic Information System (GIS) platform and try to derive fundamental diagram, as well as real-time level-of-service map so as to evaluate levels of services of pedestrian traffic facilities and efficiencies of different crowd control methods.
引文
'Hajj'. (2010). "Wikipedia." viewed 10, March,2010, from http://en.wikipedia.org/wiki/Hajj.
'Jamaraat_Bridge'. (2010). "Wikipedia." viewed 10, March,2010, from http://en.wikipedia.org/wiki/Jamaraat_Bridge.
Algadhi, S. and Mahmassani, H. (1990). Modelling crowd behavior and movement:application to Makkah pilgrimage. Proc.11th Internat. Sympos. Transportation and Traffic Theory, Yokohama, Japan, Elsevier.
AlGadhi, S. A. and Still, G. K. (2004). Jamarat Bridge:Mathematical models, Computer Simulation and Hajjis Safety Analysis. Saudi Arabia, Ministry of Municipal and Rural Affairs. Final Report:75.
Antonini, G., Bierlaire, M. and Weber, M. (2006). "Discrete choice models of pedestrian walking behavior." Transportation Research Part B:Methodological 40(8):667-687.
Asano, M., Iryo, T. and Kuwahara, M. (2009). A Pedestrian Model Considering Anticipatory Behaviour for Capacity Evaluation. Transportation and Traffic Theory 2009:Golden Jubilee:559-581.
Ballerini, M., Calbibbo, N., Candeleir, R., Cavagna, A., Cisbani, E., Giardina, I., Lecomte, V, Orlandi, A., Parisi, G., et al. (2008). "Interaction ruling animal collective behavior depends on topological rather than metric distance:Evidence from a field study." Proceedings of the National Academy of Sciences of the United States of America 105(4): 1232-1237.
Bing, Q., Tan, H. L., Kong, L. J. and Liu, M. R. (2004). "Lattice-gas simulation of escaping pedestrian flow in corridor." Chinese Physics 13(7):990-995.
Burstedde, C., Klauck, K., Schadschneider, A. and Zittartz, J. (2001). "Simulation of pedestrian dynamics using a two-dimensional cellular automaton." Physica A:Statistical Mechanics and its Applications 295(3-4):507-525.
Chattaraj, U., Seyfried, A. and Chakroborty, P. (2009). "Comparison of Pedestrian Fundamental Diagram Across Cultures." Advances in Complex Systems 12(03):393-405.
Cheng, X. D., Zhang, H. P., Xie, Q. Y., Zhou, Y, Zhang, H. J. and Zhang, C. J. (2009). "Study of announced evacuation drill from a retail store." Building and Environment 44(5): 864-870.
Couzin, I. D., Krause, J., Franks, N. R. and Levin, S. A. (2005). "Effective leadership and
decision-making in animal groups on the move." Nature 433(7025):513-516.
Craig, W. R. (1987). Flocks, herds and schools:A distributed behavioral model. Proceedings of the 14th annual conference on Computer graphics and interactive techniques, ACM.
Cristiani, E. and Piccoli, B. (2009). "A unifying model for the structure of animal groups on the move." Arxiv preprint arXiv.0903.4056.
Daamen, W. and Hoogendoorn, S. (2007). Flow-Density Relations for Pedestrian Traffic. Traffic and Granular Flow'05:315-322.
Deneubourg, J., Halloy, J., Ame, J., Rivault, C. and Detrain, C. (2007). Self-organised choice based on inter-attraction:the example of gregarious animals. Pedestrian and Evacuation Dynamics 2005:455-463.
Fang, Z., Song, W., Zhang, J. and Wu, H. (2009). "Experiment and modeling of exit-selecting behaviors during a building evacuation." Physica A:Statistical Mechanics and its Applications.
Fang, Z., Yuan, J. P., Wang, Y. C. and Lo, S. M. (2008). "Survey of pedestrian movement and development of a crowd dynamics model." Fire Safety Journal 43(6):459-465.
Florian, M., Mahut, M. and Tremblay, N. (2001). "A hybrid optimization-mesoscopic simulation dynamic trafficassignment model." 2001 IEEE Intelligent Transportation Systems,2001. Proceedings:118-121.
Fruin, J. (1971a). Pedestrian planning and design, Metropolitan Association of Urban Designers and Environmental Planners.
Fruin, J. J. (1971b). "Designing for pedestrians:A level-of-service concept." Highway Research Record Number 355:Pedestrians, Highway Research Board(377):1-15.
Fujiyama, T. and Tyler, N. (2009). "Bidirectional collision-avoidance behaviour of pedestrians on stairs." Environment and Planning B:Planning and Design 36(1):128-148.
Fuks-acute, H. (1997). "Solution of the density classification problem with two cellular automata rules." Physical Review E 55(3):2081-2084.
GB10000-88 China National Standard Human Dimensions of Chinese Adults.
Guo, R., Wong, S., Huang, H., Zhang, P. and Lam, W. (2009). "A microscopic pedestrian-simulation model and its application to intersecting flows." Physica A: Statistical Mechanics and its Applications.
Hankin, B. D. and Wright, R. A. (1958). "Passenger Flow in Subways." Operational Research Quarterly 9(2):81-88.
Hartley, R. and Zisserman, A. (June 2000). Multiple View Geometry in Computer Vision, Cambridge Univ Pr
Helbing, D. (1992). "Interactions Between Stochastic-Equations For Systems With Pair Interactions." Physica A 181(1-2):29-52.
Helbing, D. (1996). "A stochastic behavioral model and a'Microscopic'foundation of evolutionary game theory." Theory and Decision 40(2):149-179.
Helbing, D. (2001). "Traffic and related self-driven many-particle systems." Reviews of Modern Physics 73(4):1067-1141.
Helbing, D., Buzna, L., Johansson, A. and Werner, T. (2005). "Self-Organized Pedestrian Crowd Dynamics:Experiments, Simulations, and Design Solutions." Transportation Science 39(1):1-24.
Helbing, D., Farkas, I. and Vicsek, T. (2000a). "Simulating dynamical features of escape panic." Nature 407(6803):487-490.
Helbing, D., Farkas, I. e. J., Molnar, P. e. and Vicsek, a. T. a. (2001a). Simulation of Pedestrian Crowds in Normal and Evacuation Situations. Pedestrian and evacuation dynamics, Springer.
Helbing, D., Farkas, I. J. and Vicsek, T. (2000b). "Freezing by heating in a driven mesoscopic System." Physical Review Letters 84(6):1240-1243.
Helbing, D., Isobe, M., Nagatani, T. and Takimoto, K. (2003). "Lattice gas simulation of experimentally studied evacuation dynamics." Physical Review E 67(6):067101.
Helbing, D., Johansson, A. and Al-Abideen, H. Z. (2007). "Dynamics of crowd disasters:An empirical study." Physical Review E 75(4):046109.
Helbing, D., Johansson, A. and Lammer, S. (2008). Self-Organization and Optimization of Pedestrian and Vehicle Traffic in Urban Environments. The Dynamics of Complex Urban Systems:287-309.
Helbing, D., Johansson, A., Mathiesen, J., Jensen, M. H. and Hansen, A. (2006). "Analytical approach to continuous and intermittent bottleneck flows." Physical Review Letters 97(16).
Helbing, D. and Molnar, P. (1995). "Social force model for pedestrian dynamics." Physical Review E 51(5):4282.
Helbing, D., Molnar, P., Farkas, I. J. and Bolay, K. (2001b). "Self-organizing pedestrian movement." Environment and Planning B-Planning & Design 28(3):361-383.
Hoogendoorn, S. and Bovy, P. (2002). Pedestrian travel behavior in walking areas by subjective utility optimization. Transportation Research Annual Meeting 2002.
Hoogendoorn, S. and Bovy, P. (2004). "Pedestrian route-choice and activity scheduling theory and models." Transportation Research Part B 38(2):169-190.
Hoogendoorn, S. and Bovy., P. (2003). "Simulation of pedestrian flows by optimal control and differential games." Optimal control applications and methods 24(3):153--172.
Hoogendoorn, S. and Daamen, W. (2005a). Self-Organization in Pedestrian Flow. Traffic and Granular Flow'03:373-382.
Hoogendoorn, S., Daamen, W. and Campanella, M. (3-6 June 2008). Self-organization and chaos in pedestrians flow:experiments and modelling. Proceedings of the Chaotic Modeling and Simulation International Conference (CHAOS 2008). Chania, Crete, Greece.
Hoogendoorn, S. P. and Daamen, W. (2005b). "Pedestrian behavior at bottlenecks." Transportation Science 39(2):147-159.
Hou, X. G., Siveter, D. J. and Aldridge, R. J. (2008). "Collective behavior in an early Cambrian arthropod." Science 322(5899):224-224.
Huang, D. W. (2001). "Stochastic exclusion processes with extended hopping." Physical Review E 6403(3).
Huang, H.-J. and Guo, R.-Y. (2008). "Static floor field and exit choice for pedestrian evacuation in rooms with internal obstacles and multiple exits." Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 78(2):021131-6.
Huang, L., Wong, S. C., Zhang, M., Shu, C.-W. and Lam, W. H. K. (2009). "Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm." Transportation Research Part B:Methodological 43(1):127-141.
Hughes, R. L. (2002). "A continuum theory for the flow of pedestrians." Transportation Research Part B:Methodological 36(6):507-535.
Hughes, R. L. (2003). "The flow of human crowds." Annual Review of Fluid Mechanics 35: 169-182.
Ispolatov, S., Krapivsky, P. L. and Redner, S. (1998). "Wealth distributions in asset exchange models." European Physical Journal B 2(2):267-276.
Jian, L., Lizhong, Y. and Daoliang, Z. (2005). "Simulation of bi-direction pedestrian movement in corridor." Physica A:Statistical Mechanics and its Applications 354:619-628.
Jiang, B., Yin, J. and Zhao, S. (2009a). "Characterizing the human mobility pattern in a large street network." Physical Review E 80(2):21136.
Jiang, C., Deng, Y, Hu, C., Ding, H. and Chow, W. (2009b). "Crowding in platform staircases of a subway station in China during rush hours." Safety Science 47(7):931-938.
Jiang, C. S., Li, W., Hu, C., Xiong, Y, Ding, H. and Chow, W. K. (2009c). "Emergency evacuation in places for public entertainment in Mainland China." Building and Environment 44(1): 169-176.
Jiang, C. S., Yuan, F. and Chow, W. K. (2010). "Effect of varying two key parameters in simulating evacuation for subway stations in China." Safety Science 48(4):445-451.
Jiang, R. and Wu, Q. S. (2007). "Pedestrian behaviors in a lattice gas model with large maximum velocity." Physica a-Statistical Mechanics and Its Applications 373:683-693.
Johansson, A. (2009a). "Constant-net-time headway as key mechanism behind pedestrian ow dynamics." Physical Review E 80:026120.
Johansson, A. (2009b). Data-Driven Modeling of Pedestrian Crowds, Saechsische Landesbibliothek-Staats-und Universitaetsbibliothek Dresden. Ph.D:185.
Johansson, A., Helbing, D. and Shukla, P. (2007). "Specification of the social force pedestrian model by evolutionary adjustment to video tracking data." Advances in Complex Systems 10(Supplementary Issue 2):271-288
John, A., Schadschneider, A., Chowdhury, D. and Nishinari, K. (2009). "Traffic like collective movement of ants on trails:Absence of a jammed phase." Physical Review Letters 102(10):108001.
Kholshevnikov, V. V., Shleds, T. J., Boyce, K. E. and Samoshin, D. A. (2008). "Recent developments in pedestrian flow theory and research in Russia." Fire Safety Journal 43(2): 108-118.
Kretz, T., Grunebohm, A., Kaufman, M., Mazur, F. and Schreckenberg, M. (2006). "Experimental study of pedestrian counterflow in a corridor." Journal of Statistical Mechanics-Theory and Experiment.
Kuang, H., Song, T., Li, X. L. and Dai, S. Q. (2008). "Subconscious effect on pedestrian counter flow." Chinese Physics Letters 25(4):1498-1501.
Lam, W. H. K. and Cheung, C. Y. (2000). "Pedestrian speed/flow relationships for walking facilities in Hong Kong." Journal of Transportation Engineering-Asce 126(4):343-349.
Lam, W. H. K., Lee, J. Y. S., Chan, K. S. and Goh, P. K. (2003). "A generalised function for modeling bi-directional flow effects on indoor walkways in Hong Kong." Transportation Research Part A:Policy and Practice 37(9):789-810.
Lam, W. H. K., Lee, J. Y. S. and Cheung, C. Y. (2002). "A study of the bi-directional pedestrian flow characteristics at Hong Kong signalized crosswalk facilities." Transportation 29(2): 169-192.
Lee, J. Y. S. and Lam, W. H. K. (2008). "Simulating pedestrian movements at signalized crosswalks in Hong Kong." Transportation Research Part A:Policy and Practice 42(10): 1314-1325.
Lee, R. S. C. and Hughes, R. L. (2005). "Exploring trampling arid crushing in a crowd." Journal of
Transportation Engineering-Asce 131(8):575-582.
Lee, R. S. C. and Hughes, R. L. (2007). "Minimisation of the risk of trampling in a crowd." Mathematics and Computers in Simulation 74(1):29-37.
Li, Q., Chen, X., Chen, J. and Tang, Q. (2009).“考虑危险源的城市应急交通疏散风险评价模型." Chinese Science Bulletine (in Chinese) 54(16):2431-2436.
Li, X. M., Chen, T., Pan, L. L., Shen, S. F. and Yuan, H. Y. (2008). "Lattice gas simulation and experiment study of evacuation dynamics." Physica a-Statistical Mechanics and Its Applications 387(22):5457-5465.
Liu, X., Song, W. and Zhang, J. (2009). "Extraction and quantitative analysis of microscopic evacuation characteristics based on digital image processing." Physica A:Statistical Mechanics and its Applications 388(13):2717-2726.
Lo, S. M. and Fang, Z. (2000). "A Spatial-Grid Evacuation Model for Buildings." Journal of Fire Sciences 18(5):376-394.
Lo, S. M., Huang, H. C., Wang, P. and Yuen, K. K. (2006). "A game theory based exit selection model for evacuation." Fire Safety Journal 41(5):364-369.
Lord, J., Meacham, B., Moore, A., Fahy, R. and Proulx, G. (2005). "Guide for evaluating the predictive capabilities of computer egress models." NIST GCR:06-886.
Low, D. J. (2000). "Statistical physics:Following the crowd." Nature 407(6803):465-466.
Lyman, E. and Schmittmann, B. (2005). "Steady states of a nonequilibrium lattice gas." Physical Review E 72(3):036127.
Ma, J., Song, W.-g., Zhang, J., Lo, S.-m. and Liao, G.-x. (2010). "k-Nearest-Neighbor interaction induced self-organized pedestrian counter flow." Physica A:Statistical Mechanics and its Applications 389:2101-2117.
Macdonald, J. (2009). "Lateral excitation of bridges by balancing pedestrians." Proceedings of the Royal Society A:Mathematical, Physical and Engineering Science 465(2104):1055.
Mori, M. and Tsukaguchi, H. (1987). "A new Method for Evaluation of Level of Service in Pedestrian Facilities." Transp. Res.-A 21(3):223-234.
Moussaid, M., Helbing, D., Gamier, S., Johansson, A., Combe, M. and Theraulaz, G. (2009). "Experimental study of the behavioural mechanisms underlying self-organization in human crowds." Proceedings of the Royal Society B:Biological Sciences 276(1668): 2755-2762.
Moussad, M., Helbing, D., Gamier, S., Johansson, A., Combe, M. and Theraulaz, G. (2009). "Experimental study of the behavioural mechanisms underlying self-organization in human crowds." Proceedings of the Royal Society B:Biological Sciences 276(1668): 2755-2762.
Muramatsu, M., Irie, T. and Nagatani, T. (1999). "Jamming transition in pedestrian counter flow." Physica A:Statistical and Theoretical Physics 267(3-4):487-498.
Muramatsu, M. and Nagatani, T. (2000). "Jamming transition of pedestrian traffic at a crossing with open boundaries." Physica A:Statistical Mechanics and its Applications 286(1-2): 377-390.
Nagatani, T. (1993). "Jamming transition in the traffic-flow model with two-level crossings." Physical Review E 48(5):3290.
Nagatani, T. (2009). "Freezing transition in bi-directional CA model for facing pedestrian traffic." Physics Letters A 373(33):2917-2921.
Nakayama, A., Hasebe, K. and Sugiyama, Y. (2005). "Instability of pedestrian flow and phase structure in a two-dimensional optimal velocity model." Physical Review E (Statistical. Nonlinear, and Soft Matter Physics) 71(3):036121-11.
Nilsson, D. and Johansson, A. (2009). "Social influence during the initial phase of a fire evacuation-Analysis of evacuation experiments in a cinema theatre." Fire Safety Journal 44(1):71-79.
Nilsson, D., Johansson, M. and Frantzich, H. (2009). "Evacuation experiment in a road tunnel:A study of human behaviour and technical installations." Fire Safety Journal 44(4): 458-468.
Older, S. J. (1968). "Movement of Pedestrians on Footways in Shopping Streets." Traffic Engineering & Control 10:160-163.
Parisi, D. R., Gilman, M. and Moldovan, H. (2009). "A modification of the Social Force Model can reproduce experimental data of pedestrian flows in normal conditions." Phvsica A: Statistical Mechanics and its Applications 388(17):3600-3608.
Pauls, J. (1984). "The movement of people in buildings and design solutions for means of egress." Fire Technology 20(1):27-47.
Pauls, J., Fruin, J. and Zupan, J. (2006). "Minimum stair-width for evacuation, overtaking movement and counterflow—Technical bases and suggestions for the past, present and future." Pedestrian and Evacuation Dynamics 2005:57.
Rangel-Huerta, A. and Mu oz-Melendez, A. (2010). "Kinetic theory of situated agents applied to pedestrian flow in a corridor." Physica A:Statistical Mechanics and its Applications 389(5):1077-1089.
Ricciardelli, F. and Pizzimenti, A. (2007). "Lateral Walking-Induced Forces on Footbridges." Journal of Bridge Engineering 12:677.
Robin, T., Antonini, G, Bierlaire, M. and Cruz, J. (2009). "Specification, estimation and validation of a pedestrian walking behavior model." Transportation Research Part B: Methodological 43(1):36-56.
Saloma, C., Perez, G. J., Tapang, G., Lim, M. and Palmes-Saloma, C. (2003). "Self-organized queuing and scale-free behavior in real escape panic." Proceedings of the National Academy of Sciences of the United States of America 100(21):11947-11952.
Schadschneider, A. and Seyfried, A. (2009). "Validation of CA Models of Pedestrian Dynamics with Fundamental Diagrams." Cybernetics and Systems:An International Journal 40(5): 367-389.
Schneirla, T. C. (1944). "A unique case of circular milling in ants, considered in relation to trail following and the general problem of orientation." American Museum novitates:no. 1253.
Seyfried, A., Bernhard, S., Wolfram, K. and Maik, B. (2005). "The fundamental diagram of pedestrian movement revisited." Journal of Statistical Mechanics:Theory and Experiment(10):P10002.
Seyfried, A., Passon, O., Steffen, B., Boltes, M., Rupprecht, T. and Klingsch, W. (2009). "New Insights into Pedestrian Flow Through Bottlenecks." Transportation Science 43(3): 395-406.
Seyfried, A., Steffen, B. and Lippert, T. (2006). "Basics of modelling the pedestrian flow." Physica a-Statistical Mechanics and Its Applications 368(1):232-238.
Shi, L., Xie, Q., Cheng, X., Chen, L., Zhou, Y. and Zhang, R. (2009). "Developing a database for emergency evacuation model." Building and Environment 44(8):1724-1729.
Smith, A., James, C., Jones, R., Langston, P., Lester, E. and Drury, J. (2009). "Modelling contra-flow in crowd dynamics DEM simulation." Safety Science 47(3):395-404.
So, S. K. and Daganzo, C. F. (2010). "Managing evacuation routes." Transportation Research Part B:Methodological 44(4):514-520.
Song, W.-G., Yu, Y.-F., Wang, B.-H. and Fan, W.-C. (2006a). "Evacuation behaviors at exit in CA model with force essentials:A comparison with social force model." Physica A:Statistical and Theoretical Physics 371(2):658-666.
Song, W., Xu, X., Wang, B. and Ni, S. (2006b). "Simulation of evacuation processes using a multi-grid model for pedestrian dynamics." Physica A 363:492-500.
Song, W., Zhang, J. and Seyfried, A. (2010). Experimental Study of Pedestrian Flow in the Channel through Bottleneck. Pedestrian and Evacuation Dynamics 2010. Gaithersburg, Maryland:In print.
Song, W. G., Yu, Y. F., Wang, B. H. and Fan, W. C. (2006c). "Evacuation behaviors at exit in CA model with force essentials:A comparison with social force model." Physica A:Statistical Mechanics and its Applications 371(2):658-666.
Song, W. G., Zhang,J., Xu, X., Liu, X. and Yu, Y. F. (2008). "A New Lattice-gas Model of Evacuation Considering the Uncertainty of Pedestrians' Number." Progress in Natural Science 18(5):552-558.
Sugiyama, Y, Fukui, M., Kikuchi, M., Hasebe, K., Nakayama, A., Nishinari, K., Tadaki, S. and Yukawa, S. (2008). "Traffic jams without bottlenecks-experimental evidence for the physical mechanism of the formation of a jam." New Journal of Physics 10.
SuperMap (2009). SuperMap User Guide. Beijing.
Tajima, Y, Takimoto, K. and Nagatani, T. (2002). "Pattern formation and jamming transition in pedestrian counter flow." Physica A:Statistical Mechanics and its Applications 313(3-4): 709-723.
Takimoto, K., Tajima, Y. and Nagatani, T. (2002). "Effect of partition line on jamming transition in pedestrian counter flow." Physica a-Statistical Mechanics and Its Applications 308(1-4): 460-470.
Tavares, R. M. and Galea, E. R. (2009). "Evacuation modelling analysis within the operational research context:A combined approach for improving enclosure designs." Building and Environment 44(5):1005-1016.
Teknomo, K. (2006). "Application of microscopic pedestrian simulation model." Transportation Research Part F:Traffic Psychology and Behaviour 9(1):15-27.
Tian, H., Xue, Y. and Wei, Y. F. (2009). "Influence of Inforamtion on Crowd Disperrsion Process." International Journal of Modern Physics C 20(7):1001-1010.
Venuti, F. and Bruno, L. (2009). "Crowd-structure interaction in lively footbridges under synchronous lateral excitation:A literature review." Physics of Life Reviews 6(3): 176-206.
Vicsek, T., Czirok, A., Benjacob, E., Cohen, I. and Shochet, O. (1995). "Novel Tyep of Phase Transition in A System of Self-drvien Particles." Physical Review Letters 75(6): 1226-1229.
Wang, Z., Liu, M. and Zhao, Y. (2008). "Analysis of trample disaster and a case study-Mihong bridge fatality in China in 2004." Safety Science 46(8):1255-1270.
Weidmann, U., Ed. (1993). Transporttechnik der Fuβganger, Schriftenreihe des Institut fur Verkehrsplanung, Transporttechnik, Straβen-und Eisenbahnbau, ETH Zurich.
Weng, W. G., Chen, T., Yuan, H. Y. and Fan, W. C. (2006). "Cellular automaton simulation of
pedestrian counter flow with different walk velocities." Physical Review E 74(3).
Weng, W. G., Pan, L. L., Shen, S. F. and Yuan, H. Y. (2007a). "Small-grid analysis of discrete model for evacuation from a hall." Physica a-Statistical Mechanics and Its Applications 374(2):821-826.
Weng, W. G., Shen, S. F., Yuan, H. Y. and Fan, W. C. (2007b). "A behavior-based model for pedestrian counter flow." Phvsica a-Statistical Mechanics and Its Applications 375(2): 668-678.
Weng, W. G., Yuan, H. Y., Fan, W. C. and Hasemi, Y. J. (2007c). "Experimental validation of motor schema-based cellular automaton model for pedestrian dynamics." International Journal of Modern Physics C 18(6):927-936.
Wong, S. C., Leung, W. L., Chan, S. H., Lam, W. H. K., Yung, N. H. C., Liu, C. Y. and Zhang, P. (2010). "Bidirectional Pedestrian Stream Model with Oblique Intersecting Angle." Journal of Transportation Engineering 136(3):234-242.
Xia, Y, Wong, S. C. and Shu, C.-W. (2009). "Dynamic continuum pedestrian flow model with memory effect." Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 79(6): 066113-8.
Xu, X. (2009). Theoretical and Experimental Study of a Multi-grid Model for Pedestrian Evacuation. State Key Laboratory of Fire Science Hefei, University of Science and Technology of China. Ph.D.:95.
Xu, X. and Song, W. G. (2009). "Staircase evacuation modeling and its comparison with an egress drill." Building and Environment 44(5):1039-1046.
Xue, Y., Tian, H. H., He, H. D., Lu, W. Z. and Wei, Y. F. (2009). "Exploring jamming transitions and density waves in bidirectional pedestrian traffic." European Physical Journal B 69(2): 289-295.
Yamamoto, K., Kokubo, S. and Nishinari, K. (2007). "Simulation for pedestrian dynamics by real-coded cellular automata (RCA)." Physica A:Statistical Mechanics and its Applications 379(2):654-660.
Yang, L., Li, J. and Liu, S. (2008). "Simulation of pedestrian counter-flow with right-moving preference." Physica A:Statistical Mechanics and its Applications 387(13):3281-3289.
Ye, J. H., Chen, X., Yang, C. and Wu, J. (2008). "Walking Behavior and Pedestrian Flow Characteristics for Different Types of Walking Facilities." Transportation Research Record(2048):43-51.
Yu, W. and Johansson, A. (2007). "Modeling crowd turbulence by many-particle simulations." Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 76(4):046105-5.
Yu, W. J., Chen, R., Dong, L. Y. and Dai, S. Q. (2005). "Centrifugal force model for pedestrian dynamics." Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 72(2): 026112-7.
Yu, Y. F. (2008). Evacuation Simulation using Cellular Automata Model with Forces Essentials. State Key Laboratory of Fire Science. Hefei, University of Science and Technology of China. Ph.D.:103.
Yu, Y. F. and Song, W. G. (2007a). "Cellular automaton simulation of pedestrian counter flow considering the surrounding environment." Physical Review E 75(4).
Yu, Y. F. and Song, W. G. (2007b). "Effect of traffic rule breaking behavior on pedestrian counterflow in a channel with a partition line." Physical Review E 76(2).
Yue, H., Shao, C. F., Chen, X. M. and Hao, H. R. (2009). "Simulation of bi-directional pedestrian flow based on cellular automata model." Acta Physica Sinica 57(11):8.
Zhang, J., Song, W. and Xu, X. (2008). "Experiment and multi-grid modeling of evacuation from a classroom." Physica A:Statistical Mechanics and its Applications 387(23):5901-5909.
Zhang, Q., Liu, M., Wu, C. and Zhao, G. (2007). "A stranded-crowd model (SCM) for performance-based design of stadium egress." Building and Environment 42(7): 2630-2636.
Zhang, Q., Zhao, G. and Liu, J. (2009). "Performance-Based Design for Large Crowd Venue Control Using a Multi-Agent Model." Tsinghua Science & Technology 14(3):352-359.
Zheng, X., Sun, J. and Cheng, Y. (2010). "Analysis of crowd jam in public buildings based on cusp-catastrophe theory." Building and Environment doi:10.1016/j.buildenv.2010.01.027
Zheng, X. P., Zhong, T. K. and Liu, M. T. (2009). "Modeling crowd evacuation of a building based on seven methodological approaches." Building and Environment 44(3):437-445.
'Jamaraat_Bridge'. (2010). "Wikipedia." viewed 10, March,2010, from http://en.wikipedia.org/wiki/Jamaraat_Bridge.
Algadhi, S. and Mahmassani, H. (1990). Modelling crowd behavior and movement:application to Makkah pilgrimage. Proc.11th Internat. Sympos. Transportation and Traffic Theory, Yokohama, Japan, Elsevier.
AlGadhi, S. A. and Still, G. K. (2004). Jamarat Bridge:Mathematical models, Computer Simulation and Hajjis Safety Analysis. Saudi Arabia, Ministry of Municipal and Rural Affairs. Final Report:75.
Antonini, G., Bierlaire, M. and Weber, M. (2006). "Discrete choice models of pedestrian walking behavior." Transportation Research Part B:Methodological 40(8):667-687.
Asano, M., Iryo, T. and Kuwahara, M. (2009). A Pedestrian Model Considering Anticipatory Behaviour for Capacity Evaluation. Transportation and Traffic Theory 2009:Golden Jubilee:559-581.
Ballerini, M., Calbibbo, N., Candeleir, R., Cavagna, A., Cisbani, E., Giardina, I., Lecomte, V, Orlandi, A., Parisi, G., et al. (2008). "Interaction ruling animal collective behavior depends on topological rather than metric distance:Evidence from a field study." Proceedings of the National Academy of Sciences of the United States of America 105(4): 1232-1237.
Bing, Q., Tan, H. L., Kong, L. J. and Liu, M. R. (2004). "Lattice-gas simulation of escaping pedestrian flow in corridor." Chinese Physics 13(7):990-995.
Burstedde, C., Klauck, K., Schadschneider, A. and Zittartz, J. (2001). "Simulation of pedestrian dynamics using a two-dimensional cellular automaton." Physica A:Statistical Mechanics and its Applications 295(3-4):507-525.
Chattaraj, U., Seyfried, A. and Chakroborty, P. (2009). "Comparison of Pedestrian Fundamental Diagram Across Cultures." Advances in Complex Systems 12(03):393-405.
Cheng, X. D., Zhang, H. P., Xie, Q. Y., Zhou, Y, Zhang, H. J. and Zhang, C. J. (2009). "Study of announced evacuation drill from a retail store." Building and Environment 44(5): 864-870.
Couzin, I. D., Krause, J., Franks, N. R. and Levin, S. A. (2005). "Effective leadership and
decision-making in animal groups on the move." Nature 433(7025):513-516.
Craig, W. R. (1987). Flocks, herds and schools:A distributed behavioral model. Proceedings of the 14th annual conference on Computer graphics and interactive techniques, ACM.
Cristiani, E. and Piccoli, B. (2009). "A unifying model for the structure of animal groups on the move." Arxiv preprint arXiv.0903.4056.
Daamen, W. and Hoogendoorn, S. (2007). Flow-Density Relations for Pedestrian Traffic. Traffic and Granular Flow'05:315-322.
Deneubourg, J., Halloy, J., Ame, J., Rivault, C. and Detrain, C. (2007). Self-organised choice based on inter-attraction:the example of gregarious animals. Pedestrian and Evacuation Dynamics 2005:455-463.
Fang, Z., Song, W., Zhang, J. and Wu, H. (2009). "Experiment and modeling of exit-selecting behaviors during a building evacuation." Physica A:Statistical Mechanics and its Applications.
Fang, Z., Yuan, J. P., Wang, Y. C. and Lo, S. M. (2008). "Survey of pedestrian movement and development of a crowd dynamics model." Fire Safety Journal 43(6):459-465.
Florian, M., Mahut, M. and Tremblay, N. (2001). "A hybrid optimization-mesoscopic simulation dynamic trafficassignment model." 2001 IEEE Intelligent Transportation Systems,2001. Proceedings:118-121.
Fruin, J. (1971a). Pedestrian planning and design, Metropolitan Association of Urban Designers and Environmental Planners.
Fruin, J. J. (1971b). "Designing for pedestrians:A level-of-service concept." Highway Research Record Number 355:Pedestrians, Highway Research Board(377):1-15.
Fujiyama, T. and Tyler, N. (2009). "Bidirectional collision-avoidance behaviour of pedestrians on stairs." Environment and Planning B:Planning and Design 36(1):128-148.
Fuks-acute, H. (1997). "Solution of the density classification problem with two cellular automata rules." Physical Review E 55(3):2081-2084.
GB10000-88 China National Standard Human Dimensions of Chinese Adults.
Guo, R., Wong, S., Huang, H., Zhang, P. and Lam, W. (2009). "A microscopic pedestrian-simulation model and its application to intersecting flows." Physica A: Statistical Mechanics and its Applications.
Hankin, B. D. and Wright, R. A. (1958). "Passenger Flow in Subways." Operational Research Quarterly 9(2):81-88.
Hartley, R. and Zisserman, A. (June 2000). Multiple View Geometry in Computer Vision, Cambridge Univ Pr
Helbing, D. (1992). "Interactions Between Stochastic-Equations For Systems With Pair Interactions." Physica A 181(1-2):29-52.
Helbing, D. (1996). "A stochastic behavioral model and a'Microscopic'foundation of evolutionary game theory." Theory and Decision 40(2):149-179.
Helbing, D. (2001). "Traffic and related self-driven many-particle systems." Reviews of Modern Physics 73(4):1067-1141.
Helbing, D., Buzna, L., Johansson, A. and Werner, T. (2005). "Self-Organized Pedestrian Crowd Dynamics:Experiments, Simulations, and Design Solutions." Transportation Science 39(1):1-24.
Helbing, D., Farkas, I. and Vicsek, T. (2000a). "Simulating dynamical features of escape panic." Nature 407(6803):487-490.
Helbing, D., Farkas, I. e. J., Molnar, P. e. and Vicsek, a. T. a. (2001a). Simulation of Pedestrian Crowds in Normal and Evacuation Situations. Pedestrian and evacuation dynamics, Springer.
Helbing, D., Farkas, I. J. and Vicsek, T. (2000b). "Freezing by heating in a driven mesoscopic System." Physical Review Letters 84(6):1240-1243.
Helbing, D., Isobe, M., Nagatani, T. and Takimoto, K. (2003). "Lattice gas simulation of experimentally studied evacuation dynamics." Physical Review E 67(6):067101.
Helbing, D., Johansson, A. and Al-Abideen, H. Z. (2007). "Dynamics of crowd disasters:An empirical study." Physical Review E 75(4):046109.
Helbing, D., Johansson, A. and Lammer, S. (2008). Self-Organization and Optimization of Pedestrian and Vehicle Traffic in Urban Environments. The Dynamics of Complex Urban Systems:287-309.
Helbing, D., Johansson, A., Mathiesen, J., Jensen, M. H. and Hansen, A. (2006). "Analytical approach to continuous and intermittent bottleneck flows." Physical Review Letters 97(16).
Helbing, D. and Molnar, P. (1995). "Social force model for pedestrian dynamics." Physical Review E 51(5):4282.
Helbing, D., Molnar, P., Farkas, I. J. and Bolay, K. (2001b). "Self-organizing pedestrian movement." Environment and Planning B-Planning & Design 28(3):361-383.
Hoogendoorn, S. and Bovy, P. (2002). Pedestrian travel behavior in walking areas by subjective utility optimization. Transportation Research Annual Meeting 2002.
Hoogendoorn, S. and Bovy, P. (2004). "Pedestrian route-choice and activity scheduling theory and models." Transportation Research Part B 38(2):169-190.
Hoogendoorn, S. and Bovy., P. (2003). "Simulation of pedestrian flows by optimal control and differential games." Optimal control applications and methods 24(3):153--172.
Hoogendoorn, S. and Daamen, W. (2005a). Self-Organization in Pedestrian Flow. Traffic and Granular Flow'03:373-382.
Hoogendoorn, S., Daamen, W. and Campanella, M. (3-6 June 2008). Self-organization and chaos in pedestrians flow:experiments and modelling. Proceedings of the Chaotic Modeling and Simulation International Conference (CHAOS 2008). Chania, Crete, Greece.
Hoogendoorn, S. P. and Daamen, W. (2005b). "Pedestrian behavior at bottlenecks." Transportation Science 39(2):147-159.
Hou, X. G., Siveter, D. J. and Aldridge, R. J. (2008). "Collective behavior in an early Cambrian arthropod." Science 322(5899):224-224.
Huang, D. W. (2001). "Stochastic exclusion processes with extended hopping." Physical Review E 6403(3).
Huang, H.-J. and Guo, R.-Y. (2008). "Static floor field and exit choice for pedestrian evacuation in rooms with internal obstacles and multiple exits." Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 78(2):021131-6.
Huang, L., Wong, S. C., Zhang, M., Shu, C.-W. and Lam, W. H. K. (2009). "Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm." Transportation Research Part B:Methodological 43(1):127-141.
Hughes, R. L. (2002). "A continuum theory for the flow of pedestrians." Transportation Research Part B:Methodological 36(6):507-535.
Hughes, R. L. (2003). "The flow of human crowds." Annual Review of Fluid Mechanics 35: 169-182.
Ispolatov, S., Krapivsky, P. L. and Redner, S. (1998). "Wealth distributions in asset exchange models." European Physical Journal B 2(2):267-276.
Jian, L., Lizhong, Y. and Daoliang, Z. (2005). "Simulation of bi-direction pedestrian movement in corridor." Physica A:Statistical Mechanics and its Applications 354:619-628.
Jiang, B., Yin, J. and Zhao, S. (2009a). "Characterizing the human mobility pattern in a large street network." Physical Review E 80(2):21136.
Jiang, C., Deng, Y, Hu, C., Ding, H. and Chow, W. (2009b). "Crowding in platform staircases of a subway station in China during rush hours." Safety Science 47(7):931-938.
Jiang, C. S., Li, W., Hu, C., Xiong, Y, Ding, H. and Chow, W. K. (2009c). "Emergency evacuation in places for public entertainment in Mainland China." Building and Environment 44(1): 169-176.
Jiang, C. S., Yuan, F. and Chow, W. K. (2010). "Effect of varying two key parameters in simulating evacuation for subway stations in China." Safety Science 48(4):445-451.
Jiang, R. and Wu, Q. S. (2007). "Pedestrian behaviors in a lattice gas model with large maximum velocity." Physica a-Statistical Mechanics and Its Applications 373:683-693.
Johansson, A. (2009a). "Constant-net-time headway as key mechanism behind pedestrian ow dynamics." Physical Review E 80:026120.
Johansson, A. (2009b). Data-Driven Modeling of Pedestrian Crowds, Saechsische Landesbibliothek-Staats-und Universitaetsbibliothek Dresden. Ph.D:185.
Johansson, A., Helbing, D. and Shukla, P. (2007). "Specification of the social force pedestrian model by evolutionary adjustment to video tracking data." Advances in Complex Systems 10(Supplementary Issue 2):271-288
John, A., Schadschneider, A., Chowdhury, D. and Nishinari, K. (2009). "Traffic like collective movement of ants on trails:Absence of a jammed phase." Physical Review Letters 102(10):108001.
Kholshevnikov, V. V., Shleds, T. J., Boyce, K. E. and Samoshin, D. A. (2008). "Recent developments in pedestrian flow theory and research in Russia." Fire Safety Journal 43(2): 108-118.
Kretz, T., Grunebohm, A., Kaufman, M., Mazur, F. and Schreckenberg, M. (2006). "Experimental study of pedestrian counterflow in a corridor." Journal of Statistical Mechanics-Theory and Experiment.
Kuang, H., Song, T., Li, X. L. and Dai, S. Q. (2008). "Subconscious effect on pedestrian counter flow." Chinese Physics Letters 25(4):1498-1501.
Lam, W. H. K. and Cheung, C. Y. (2000). "Pedestrian speed/flow relationships for walking facilities in Hong Kong." Journal of Transportation Engineering-Asce 126(4):343-349.
Lam, W. H. K., Lee, J. Y. S., Chan, K. S. and Goh, P. K. (2003). "A generalised function for modeling bi-directional flow effects on indoor walkways in Hong Kong." Transportation Research Part A:Policy and Practice 37(9):789-810.
Lam, W. H. K., Lee, J. Y. S. and Cheung, C. Y. (2002). "A study of the bi-directional pedestrian flow characteristics at Hong Kong signalized crosswalk facilities." Transportation 29(2): 169-192.
Lee, J. Y. S. and Lam, W. H. K. (2008). "Simulating pedestrian movements at signalized crosswalks in Hong Kong." Transportation Research Part A:Policy and Practice 42(10): 1314-1325.
Lee, R. S. C. and Hughes, R. L. (2005). "Exploring trampling arid crushing in a crowd." Journal of
Transportation Engineering-Asce 131(8):575-582.
Lee, R. S. C. and Hughes, R. L. (2007). "Minimisation of the risk of trampling in a crowd." Mathematics and Computers in Simulation 74(1):29-37.
Li, Q., Chen, X., Chen, J. and Tang, Q. (2009).“考虑危险源的城市应急交通疏散风险评价模型." Chinese Science Bulletine (in Chinese) 54(16):2431-2436.
Li, X. M., Chen, T., Pan, L. L., Shen, S. F. and Yuan, H. Y. (2008). "Lattice gas simulation and experiment study of evacuation dynamics." Physica a-Statistical Mechanics and Its Applications 387(22):5457-5465.
Liu, X., Song, W. and Zhang, J. (2009). "Extraction and quantitative analysis of microscopic evacuation characteristics based on digital image processing." Physica A:Statistical Mechanics and its Applications 388(13):2717-2726.
Lo, S. M. and Fang, Z. (2000). "A Spatial-Grid Evacuation Model for Buildings." Journal of Fire Sciences 18(5):376-394.
Lo, S. M., Huang, H. C., Wang, P. and Yuen, K. K. (2006). "A game theory based exit selection model for evacuation." Fire Safety Journal 41(5):364-369.
Lord, J., Meacham, B., Moore, A., Fahy, R. and Proulx, G. (2005). "Guide for evaluating the predictive capabilities of computer egress models." NIST GCR:06-886.
Low, D. J. (2000). "Statistical physics:Following the crowd." Nature 407(6803):465-466.
Lyman, E. and Schmittmann, B. (2005). "Steady states of a nonequilibrium lattice gas." Physical Review E 72(3):036127.
Ma, J., Song, W.-g., Zhang, J., Lo, S.-m. and Liao, G.-x. (2010). "k-Nearest-Neighbor interaction induced self-organized pedestrian counter flow." Physica A:Statistical Mechanics and its Applications 389:2101-2117.
Macdonald, J. (2009). "Lateral excitation of bridges by balancing pedestrians." Proceedings of the Royal Society A:Mathematical, Physical and Engineering Science 465(2104):1055.
Mori, M. and Tsukaguchi, H. (1987). "A new Method for Evaluation of Level of Service in Pedestrian Facilities." Transp. Res.-A 21(3):223-234.
Moussaid, M., Helbing, D., Gamier, S., Johansson, A., Combe, M. and Theraulaz, G. (2009). "Experimental study of the behavioural mechanisms underlying self-organization in human crowds." Proceedings of the Royal Society B:Biological Sciences 276(1668): 2755-2762.
Moussad, M., Helbing, D., Gamier, S., Johansson, A., Combe, M. and Theraulaz, G. (2009). "Experimental study of the behavioural mechanisms underlying self-organization in human crowds." Proceedings of the Royal Society B:Biological Sciences 276(1668): 2755-2762.
Muramatsu, M., Irie, T. and Nagatani, T. (1999). "Jamming transition in pedestrian counter flow." Physica A:Statistical and Theoretical Physics 267(3-4):487-498.
Muramatsu, M. and Nagatani, T. (2000). "Jamming transition of pedestrian traffic at a crossing with open boundaries." Physica A:Statistical Mechanics and its Applications 286(1-2): 377-390.
Nagatani, T. (1993). "Jamming transition in the traffic-flow model with two-level crossings." Physical Review E 48(5):3290.
Nagatani, T. (2009). "Freezing transition in bi-directional CA model for facing pedestrian traffic." Physics Letters A 373(33):2917-2921.
Nakayama, A., Hasebe, K. and Sugiyama, Y. (2005). "Instability of pedestrian flow and phase structure in a two-dimensional optimal velocity model." Physical Review E (Statistical. Nonlinear, and Soft Matter Physics) 71(3):036121-11.
Nilsson, D. and Johansson, A. (2009). "Social influence during the initial phase of a fire evacuation-Analysis of evacuation experiments in a cinema theatre." Fire Safety Journal 44(1):71-79.
Nilsson, D., Johansson, M. and Frantzich, H. (2009). "Evacuation experiment in a road tunnel:A study of human behaviour and technical installations." Fire Safety Journal 44(4): 458-468.
Older, S. J. (1968). "Movement of Pedestrians on Footways in Shopping Streets." Traffic Engineering & Control 10:160-163.
Parisi, D. R., Gilman, M. and Moldovan, H. (2009). "A modification of the Social Force Model can reproduce experimental data of pedestrian flows in normal conditions." Phvsica A: Statistical Mechanics and its Applications 388(17):3600-3608.
Pauls, J. (1984). "The movement of people in buildings and design solutions for means of egress." Fire Technology 20(1):27-47.
Pauls, J., Fruin, J. and Zupan, J. (2006). "Minimum stair-width for evacuation, overtaking movement and counterflow—Technical bases and suggestions for the past, present and future." Pedestrian and Evacuation Dynamics 2005:57.
Rangel-Huerta, A. and Mu oz-Melendez, A. (2010). "Kinetic theory of situated agents applied to pedestrian flow in a corridor." Physica A:Statistical Mechanics and its Applications 389(5):1077-1089.
Ricciardelli, F. and Pizzimenti, A. (2007). "Lateral Walking-Induced Forces on Footbridges." Journal of Bridge Engineering 12:677.
Robin, T., Antonini, G, Bierlaire, M. and Cruz, J. (2009). "Specification, estimation and validation of a pedestrian walking behavior model." Transportation Research Part B: Methodological 43(1):36-56.
Saloma, C., Perez, G. J., Tapang, G., Lim, M. and Palmes-Saloma, C. (2003). "Self-organized queuing and scale-free behavior in real escape panic." Proceedings of the National Academy of Sciences of the United States of America 100(21):11947-11952.
Schadschneider, A. and Seyfried, A. (2009). "Validation of CA Models of Pedestrian Dynamics with Fundamental Diagrams." Cybernetics and Systems:An International Journal 40(5): 367-389.
Schneirla, T. C. (1944). "A unique case of circular milling in ants, considered in relation to trail following and the general problem of orientation." American Museum novitates:no. 1253.
Seyfried, A., Bernhard, S., Wolfram, K. and Maik, B. (2005). "The fundamental diagram of pedestrian movement revisited." Journal of Statistical Mechanics:Theory and Experiment(10):P10002.
Seyfried, A., Passon, O., Steffen, B., Boltes, M., Rupprecht, T. and Klingsch, W. (2009). "New Insights into Pedestrian Flow Through Bottlenecks." Transportation Science 43(3): 395-406.
Seyfried, A., Steffen, B. and Lippert, T. (2006). "Basics of modelling the pedestrian flow." Physica a-Statistical Mechanics and Its Applications 368(1):232-238.
Shi, L., Xie, Q., Cheng, X., Chen, L., Zhou, Y. and Zhang, R. (2009). "Developing a database for emergency evacuation model." Building and Environment 44(8):1724-1729.
Smith, A., James, C., Jones, R., Langston, P., Lester, E. and Drury, J. (2009). "Modelling contra-flow in crowd dynamics DEM simulation." Safety Science 47(3):395-404.
So, S. K. and Daganzo, C. F. (2010). "Managing evacuation routes." Transportation Research Part B:Methodological 44(4):514-520.
Song, W.-G., Yu, Y.-F., Wang, B.-H. and Fan, W.-C. (2006a). "Evacuation behaviors at exit in CA model with force essentials:A comparison with social force model." Physica A:Statistical and Theoretical Physics 371(2):658-666.
Song, W., Xu, X., Wang, B. and Ni, S. (2006b). "Simulation of evacuation processes using a multi-grid model for pedestrian dynamics." Physica A 363:492-500.
Song, W., Zhang, J. and Seyfried, A. (2010). Experimental Study of Pedestrian Flow in the Channel through Bottleneck. Pedestrian and Evacuation Dynamics 2010. Gaithersburg, Maryland:In print.
Song, W. G., Yu, Y. F., Wang, B. H. and Fan, W. C. (2006c). "Evacuation behaviors at exit in CA model with force essentials:A comparison with social force model." Physica A:Statistical Mechanics and its Applications 371(2):658-666.
Song, W. G., Zhang,J., Xu, X., Liu, X. and Yu, Y. F. (2008). "A New Lattice-gas Model of Evacuation Considering the Uncertainty of Pedestrians' Number." Progress in Natural Science 18(5):552-558.
Sugiyama, Y, Fukui, M., Kikuchi, M., Hasebe, K., Nakayama, A., Nishinari, K., Tadaki, S. and Yukawa, S. (2008). "Traffic jams without bottlenecks-experimental evidence for the physical mechanism of the formation of a jam." New Journal of Physics 10.
SuperMap (2009). SuperMap User Guide. Beijing.
Tajima, Y, Takimoto, K. and Nagatani, T. (2002). "Pattern formation and jamming transition in pedestrian counter flow." Physica A:Statistical Mechanics and its Applications 313(3-4): 709-723.
Takimoto, K., Tajima, Y. and Nagatani, T. (2002). "Effect of partition line on jamming transition in pedestrian counter flow." Physica a-Statistical Mechanics and Its Applications 308(1-4): 460-470.
Tavares, R. M. and Galea, E. R. (2009). "Evacuation modelling analysis within the operational research context:A combined approach for improving enclosure designs." Building and Environment 44(5):1005-1016.
Teknomo, K. (2006). "Application of microscopic pedestrian simulation model." Transportation Research Part F:Traffic Psychology and Behaviour 9(1):15-27.
Tian, H., Xue, Y. and Wei, Y. F. (2009). "Influence of Inforamtion on Crowd Disperrsion Process." International Journal of Modern Physics C 20(7):1001-1010.
Venuti, F. and Bruno, L. (2009). "Crowd-structure interaction in lively footbridges under synchronous lateral excitation:A literature review." Physics of Life Reviews 6(3): 176-206.
Vicsek, T., Czirok, A., Benjacob, E., Cohen, I. and Shochet, O. (1995). "Novel Tyep of Phase Transition in A System of Self-drvien Particles." Physical Review Letters 75(6): 1226-1229.
Wang, Z., Liu, M. and Zhao, Y. (2008). "Analysis of trample disaster and a case study-Mihong bridge fatality in China in 2004." Safety Science 46(8):1255-1270.
Weidmann, U., Ed. (1993). Transporttechnik der Fuβganger, Schriftenreihe des Institut fur Verkehrsplanung, Transporttechnik, Straβen-und Eisenbahnbau, ETH Zurich.
Weng, W. G., Chen, T., Yuan, H. Y. and Fan, W. C. (2006). "Cellular automaton simulation of
pedestrian counter flow with different walk velocities." Physical Review E 74(3).
Weng, W. G., Pan, L. L., Shen, S. F. and Yuan, H. Y. (2007a). "Small-grid analysis of discrete model for evacuation from a hall." Physica a-Statistical Mechanics and Its Applications 374(2):821-826.
Weng, W. G., Shen, S. F., Yuan, H. Y. and Fan, W. C. (2007b). "A behavior-based model for pedestrian counter flow." Phvsica a-Statistical Mechanics and Its Applications 375(2): 668-678.
Weng, W. G., Yuan, H. Y., Fan, W. C. and Hasemi, Y. J. (2007c). "Experimental validation of motor schema-based cellular automaton model for pedestrian dynamics." International Journal of Modern Physics C 18(6):927-936.
Wong, S. C., Leung, W. L., Chan, S. H., Lam, W. H. K., Yung, N. H. C., Liu, C. Y. and Zhang, P. (2010). "Bidirectional Pedestrian Stream Model with Oblique Intersecting Angle." Journal of Transportation Engineering 136(3):234-242.
Xia, Y, Wong, S. C. and Shu, C.-W. (2009). "Dynamic continuum pedestrian flow model with memory effect." Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 79(6): 066113-8.
Xu, X. (2009). Theoretical and Experimental Study of a Multi-grid Model for Pedestrian Evacuation. State Key Laboratory of Fire Science Hefei, University of Science and Technology of China. Ph.D.:95.
Xu, X. and Song, W. G. (2009). "Staircase evacuation modeling and its comparison with an egress drill." Building and Environment 44(5):1039-1046.
Xue, Y., Tian, H. H., He, H. D., Lu, W. Z. and Wei, Y. F. (2009). "Exploring jamming transitions and density waves in bidirectional pedestrian traffic." European Physical Journal B 69(2): 289-295.
Yamamoto, K., Kokubo, S. and Nishinari, K. (2007). "Simulation for pedestrian dynamics by real-coded cellular automata (RCA)." Physica A:Statistical Mechanics and its Applications 379(2):654-660.
Yang, L., Li, J. and Liu, S. (2008). "Simulation of pedestrian counter-flow with right-moving preference." Physica A:Statistical Mechanics and its Applications 387(13):3281-3289.
Ye, J. H., Chen, X., Yang, C. and Wu, J. (2008). "Walking Behavior and Pedestrian Flow Characteristics for Different Types of Walking Facilities." Transportation Research Record(2048):43-51.
Yu, W. and Johansson, A. (2007). "Modeling crowd turbulence by many-particle simulations." Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 76(4):046105-5.
Yu, W. J., Chen, R., Dong, L. Y. and Dai, S. Q. (2005). "Centrifugal force model for pedestrian dynamics." Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 72(2): 026112-7.
Yu, Y. F. (2008). Evacuation Simulation using Cellular Automata Model with Forces Essentials. State Key Laboratory of Fire Science. Hefei, University of Science and Technology of China. Ph.D.:103.
Yu, Y. F. and Song, W. G. (2007a). "Cellular automaton simulation of pedestrian counter flow considering the surrounding environment." Physical Review E 75(4).
Yu, Y. F. and Song, W. G. (2007b). "Effect of traffic rule breaking behavior on pedestrian counterflow in a channel with a partition line." Physical Review E 76(2).
Yue, H., Shao, C. F., Chen, X. M. and Hao, H. R. (2009). "Simulation of bi-directional pedestrian flow based on cellular automata model." Acta Physica Sinica 57(11):8.
Zhang, J., Song, W. and Xu, X. (2008). "Experiment and multi-grid modeling of evacuation from a classroom." Physica A:Statistical Mechanics and its Applications 387(23):5901-5909.
Zhang, Q., Liu, M., Wu, C. and Zhao, G. (2007). "A stranded-crowd model (SCM) for performance-based design of stadium egress." Building and Environment 42(7): 2630-2636.
Zhang, Q., Zhao, G. and Liu, J. (2009). "Performance-Based Design for Large Crowd Venue Control Using a Multi-Agent Model." Tsinghua Science & Technology 14(3):352-359.
Zheng, X., Sun, J. and Cheng, Y. (2010). "Analysis of crowd jam in public buildings based on cusp-catastrophe theory." Building and Environment doi:10.1016/j.buildenv.2010.01.027
Zheng, X. P., Zhong, T. K. and Liu, M. T. (2009). "Modeling crowd evacuation of a building based on seven methodological approaches." Building and Environment 44(3):437-445.