双出口房间人群疏散的实验研究和数学建模

禹尔东; 吴正; 郭明旻

doi:10.7498/aps.63.094501

摘要

本文设计了一个双出口房间内人群疏散的实验方案，通过不同条件下疏散过程的实况录像及视频检测，得到不同人数疏散时间的许多定量结果. 提出了双出口房间吸引区间的概念，证明了较小出口吸引区间的边界总是一段圆弧，可以解释行人流出口处的圆形成拱现象. 通过类比地铁候车厅内人群疏散过程，建立了双出口房间内疏散时间的二次函数模型，成功拟合不同条件下的实测数据. 疏散人数较少时，疏散时间随着人数增加而线性增长；人数较多，在出口附近出现待行区域时，疏散时间则呈二次函数增长. 与一些已知疏散时间数学模型相比，本文模型对出口宽度变化的反应更敏感.

关键词:

Abstract

A set of experimental schemes of pedestrian evacuation from a room having two exits is proposed and applied to experiments. Some quantitative results of evacuation time varying with the number of pedestrians in different circumstances are obtained from the video recordings. The concept of attraction domain of a two-exit room is established. It is proved that the boundary curve of attraction domain of the smaller exit is always a circular arch, by which the mechanism of arch formation near an exit can be illustrated. Compared with the passenger evacuation procedure in a subway waiting hall, we have established a quadratic function model of evacuation time which can fit the measured data well for various cases. The evacuation time increases linearly with the number of people without waiting, and increases as a quadratic function of the number of people after the formation of a waiting region. It is also found that the expression is affected by the width of exit more sensitively than in other well-known models.

Keywords:

作者及机构信息

1.
复旦大学力学与工程科学系, 上海 200433

基金项目: 国家自然科学基金（批准号：11002035）资助的课题.

Authors and contacts

1.
Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11002035).

参考文献

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[25]	Kretz T, Grnebohm A, Schreckenberg M 2006 J. Statistics Mech. : Theory & ExperimentP 10014
[26]	Zhang J, Song W, Xu X 2008 Physica A 387 5901
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施引文献

[1]	Li X 2012 M. S. Thesis (Shanghai: Shanghai University) (in Chinese) [李翔 2012 硕士学位论文 (上海: 上海大学)]
[2]	Hughs R L 2002 Transpn. Res. B 36 507
[3]	Xiong T, Zhang P, Wong S C, Shu C W, Zhang M P 2011 Chin. Phys. Lett. 28 108901
[4]	Xu W N, Wu Z 2005 J. Railway Sci. & Eng. 2 70 (in Chinese) [徐尉南, 吴正 2005 铁道科学与工程学报 2 70]
[5]	Wu Z, Wang Y, Shen J Y 2006 J. Fudan Univ. (Natural Sci. ) 45 594 (in Chinese) [吴正, 王昀, 沈俊彦 2006 复旦学报(自然科学版) 45 594]
[6]	Helbing D, Molnár P 1995 Phys. Rev. E 51 4282
[7]	Yu W J, Chen R, Dong L Y, Dai S Q 2005 Phys. Rev. E 72 026112
[8]	Yu W J 2006 M. S. Thesis (Shanghai: Shanghai University) (in Chinese) [郁文剑 2006硕士学位论文 (上海: 上海大学)]
[9]	Burstedde C, Klauck K, Schadschneider A, Zittartz J 2001 Physica A 295 507
[10]	Zhou J W, Chen X L, Kong L J, Liu M R, Tan H L, Zhou J H 2009 Acta Phys. Sin. 58 2281 (in Chinese) [周金旺, 陈秀丽, 孔令江, 刘慕仁, 谭惠丽, 周建槐2009 58 2281]
[11]	Yue H, Shao F C, Guan H Z, Duan L M 2010 Acta Phys. Sin. 59 4499 (in Chinese) [岳昊, 邵春福, 关宏志, 段龙梅2010 59 4499]
[12]	Jiang R, Wu R S 2007 Physica A 373 683
[13]	Tian H H, Xue Y, Wen J 2010 Acta Phys. Sin. 59 3817 (in Chinese) [田欢欢, 薛郁, 温坚 2010 59 3817]
[14]	Kuang H, Li X L, Wei Y F, Song T, Dai S Q 2010 Chin. Phys. B 19 070517
[15]	Muramatsu M, Irie T, Nagatani T 1999 Physica A 267 487
[16]	Chen X M, Hao H R, Shao C F 2008 Acta Phys. Sin. 57 6901 (in Chinese) [陈晓明, 郝合瑞, 邵春福 2008 57 6901]
[17]	Helbing D, Farkas I, Vicsek T 2000 Nature 407 487
[18]	Sun L, Zhao L D 2007 J. Safe. & Environ. 2007 7 124 (in Chinese) [孙立, 赵林度2007 安全与环境学报 7 124]
[19]	Zhou J W, Kuang H, Liu M R, Kong L J 2009 Acta Phys. Sin. 58 3001 (in Chinese) [周金旺, 邝华, 刘慕仁, 孔令江2009 58 3001]
[20]	Zhou J W, Deng M Y, Liu M R, Kong L J 2009 GuangXi Sci. 16 277 (in Chinese) [周金旺, 邓敏艺, 刘慕仁, 孔令江 2009 广西科学 16 277]
[21]	Ge H X, Cheng R J, Lo S M 2013 Chin. Phys. B 22 070507
[22]	Shi Z W, Chen Z Y, Zhou L, Ling J W 2010 Sys. Eng. 28 51 (in Chinese) [施正威, 陈治亚, 周乐, 凌景文 2010 系统工程 28 51]
[23]	Tan H L, Qiu B, Liu M R, Kong L J 2004 J. GuangXi Norm. Univ. (Natural Sci.) 22 1 (in Chinese) [谭惠丽, 邱冰, 刘慕仁, 孔令江 2004 广西师范大学学报 22 1]
[24]	Chen T, Song W G, Fan W C, Lu S X 2004 Eng. Sci. 6 56 (in Chinese) [陈涛, 宋卫国, 范维澄, 陆守香 2004 中国工程科学 6 56]
[25]	Kretz T, Grnebohm A, Schreckenberg M 2006 J. Statistics Mech. : Theory & ExperimentP 10014
[26]	Zhang J, Song W, Xu X 2008 Physica A 387 5901
[27]	Zhu K J, Yang L Z 2010 Acta Phys. Sin. 59 7701 (in Chinese) [朱孔金, 杨立中 2010 59 7701]
[28]	Zarita Z, Lim E A 2012 Chin. Phys. Lett. 29 078901
[29]	Yue H, Yao S Z, Shao C F 2009 Acta Phys. Sin. 58 4523 (in Chinese) [岳昊, 姚智胜, 邵春福 2009 58 4523]

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