对包含障碍墙的某建筑空间内的人群疏散效果的仿真研究
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摘要
公共行人场所的服务水平主要取决于行人交通需求与基础设施供给之间的差异情况。作为对拥堵事故的预防,建筑物在安全疏散方面的设计越来越重要。而要评价各种设计是否合理有效,就需要引入一系列的评价指标以判断其方案的合理性。目前,研究者们在安全疏散的评价程序当中已经引入了多种评价指标。可以把这些指标按照其在评价程序当中所处的层级划分为三类：(1)人员疏散能力评价指标,包括：人群流动速度、人群密度、疏散时间等；(2)建筑环境评价指标,包括：疏散出口的数量及布局、疏散路线的合理性及疏散设备的效果等；(3)灾难(如火灾)场景评价指标,例如：烟气量的大小、毒气下降到临界高度的时间等。
一个值得研究的问题是含有障碍墙的封闭空间内的人群疏散情况。
在本论文里,建立起一个元胞自动机模型用以模拟该空间内的人群流动情况。该模型不仅定义了一个地面场,并且考虑到行人对于出口的选择和社会力效应这两方面的因素。一些模拟结果显示了该模型的有效性,它能够有效的展现人群疏散的一些动力学特征。而总疏散时间和某一特定区域内的人群拥挤程度均被作为考察疏散改进情况和测量疏散效率的指标。结合这两项考察指标,提出一些关于障碍墙疏散设计的观点：(1)改变障碍墙的长度可以减少疏散时间,但也有可能使得某一特定区域的人群更为拥挤,这可能带来潜在的严重人员伤害；(2)在优先考虑疏散时间选择障碍墙的长度时,优先考虑疏散时间指标,当疏散时间相同时,应选择使得人群拥挤程度更小的障碍墙长度。
The level of service in public walking spaces is mainly determined by the differences in pedestrian traffic demand and infrastructure supply. In order to provide against human traffic accidents resulting from serious jamming, the building design for safe evacuation should be highly respected. Many indicators of evacuation efficiency evaluation have been presented by the researches. These indicators can be roughly classified into three kinds:(1) the capability of passenger evacuation; (2) objective concept of environment index; (3) evaluation indicators of disaster (take fire for example) scenario.
A problem worth studying is the evacuation process in a closed square with partition wall.
In this paper, a cellular automaton model is presented to simulate the evacuation process in the square. This model defines a floor field and considers the selection of an exit and effect of social forces. Some simulation results show the model's correct description of the pedestrian dynamics. Both the total evacuation time and the degree of pedestrians jamming in a certain area are regarded as the indicators of the evacuation progress and the measure of evacuation efficiency. Concerning the two indicators, some viewpoints on the evacuation design of the partition wall are put forward:(1) changing the length of the partition wall could reduce the evacuation time, however, it could also bring the serious pedestrians jamming in a certain area, which may cause potential injury; (2) with the prior consideration for evacuation time, the length of the partition wall should be better chosen to make the pedestrians jamming less severe.
一个值得研究的问题是含有障碍墙的封闭空间内的人群疏散情况。
在本论文里,建立起一个元胞自动机模型用以模拟该空间内的人群流动情况。该模型不仅定义了一个地面场,并且考虑到行人对于出口的选择和社会力效应这两方面的因素。一些模拟结果显示了该模型的有效性,它能够有效的展现人群疏散的一些动力学特征。而总疏散时间和某一特定区域内的人群拥挤程度均被作为考察疏散改进情况和测量疏散效率的指标。结合这两项考察指标,提出一些关于障碍墙疏散设计的观点：(1)改变障碍墙的长度可以减少疏散时间,但也有可能使得某一特定区域的人群更为拥挤,这可能带来潜在的严重人员伤害；(2)在优先考虑疏散时间选择障碍墙的长度时,优先考虑疏散时间指标,当疏散时间相同时,应选择使得人群拥挤程度更小的障碍墙长度。
The level of service in public walking spaces is mainly determined by the differences in pedestrian traffic demand and infrastructure supply. In order to provide against human traffic accidents resulting from serious jamming, the building design for safe evacuation should be highly respected. Many indicators of evacuation efficiency evaluation have been presented by the researches. These indicators can be roughly classified into three kinds:(1) the capability of passenger evacuation; (2) objective concept of environment index; (3) evaluation indicators of disaster (take fire for example) scenario.
A problem worth studying is the evacuation process in a closed square with partition wall.
In this paper, a cellular automaton model is presented to simulate the evacuation process in the square. This model defines a floor field and considers the selection of an exit and effect of social forces. Some simulation results show the model's correct description of the pedestrian dynamics. Both the total evacuation time and the degree of pedestrians jamming in a certain area are regarded as the indicators of the evacuation progress and the measure of evacuation efficiency. Concerning the two indicators, some viewpoints on the evacuation design of the partition wall are put forward:(1) changing the length of the partition wall could reduce the evacuation time, however, it could also bring the serious pedestrians jamming in a certain area, which may cause potential injury; (2) with the prior consideration for evacuation time, the length of the partition wall should be better chosen to make the pedestrians jamming less severe.
引文
[1]Daoliang Zhao, Lizhong Zhong, Jian Li. Exit dynamics of occupant evacuation in an emergency[J]. Physica A,2006,363(2):501-511.
[2]D.L. Zhao, J. Li, Y. Zhu, et al. The application of a two-dimensional cellular automata random model to the performance-based design of building exit[J]. Building and Environment,2008, 43(4):518-522.
[3]Ris S.C. Lee, Roger L. Hughes. Prediction of human crowd pressures [J].Accident Analysis and Prevention,2006,38:712-722.
[4]S. Ko, M. Spearpoint, A. Teo. Trial evacuation of an industrial premises and evacuation model comparison[J]. Fire Safety Journal,2007,42(2):91-105.
[5]Helbing D, Molnar P. Social force model for pedestrian dynamics. Physical Review E,1995, 51(5):4282-4286.
[6]Helbing D, Farkas I, Vicsek T. Simulating dynamical features of escape panic[J]. Nature, 2000,407:487-490.
[7]John Toner, Yuhai Tu and Sirram Ramaswamy. Hydrodynamics and phases of flocks[J]. Annals of Physics,2005,318:170-244.
[8]A. Fax and R. M. Murray. Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control, September 2004,49:1465-1475.
[9]Yang L Z, Zhao D L, Li J, et al. Simulation of the kin behavior in building occupant evacuation based on Cellular automaton[J].Building and Environment,2005,40:411-415
[10]Kholshevnikov VV. The study of human flows and methodology of evacuation standardisation. Moscow:MIFS; 1999.
[11]Hughes R. L., A continuum theory for the flow of pedestrians[J]. Transportation Research Part B,2002,36 (6):507-535.
[12]Huang L, Wong S C, Zhang R C, et al. Revisiting Hughes's dynamics continuum model for pedestrian flow and the development of an efficient solution algorithm[J]. Transportation Research Part B,2009,43 (1):127-141.
[13]Henein C M, White T, Macroscopic effects of microscopic forces between agents in crowd models[J]. Physica A,2007,373:694-712.
[14]Kholshevnikov V V, Shields T J, Boyce K E, et al. Recent development in pedestrian flow theory and research in Russia[J]. Fire Safety Journal,2008,43 (2):108-118.
[15]Burstedde C, Klauck K, Schadschneider A, et al. Simulation of pedestrian dynamics using a two-dimensional cellular automaton[J]. Physica A,2001,295:507-525.
[16]Li J, Yang L, Zhao D L. Simulation of bi-direction pedestrian movement in corridor [J]. Physica A,2005,354:619-628.
[17]Blue V J, Adler J L. Cellular automata microsimulation for modeling bi-directional pedestrian walkways[J]. Transportation Research Part B,2001,35 (3):293-312.
[18]Ito S, Nagatani T, Saegusa T. Volatile jam and flow fluctuation in counter flow of slender particles[J]. Physica A,2007,373:672-682.
[19]Vicsek T, Czirok A, Farkas I J. Application of statistical mechanics to collective motion in
biology[J]. Physics A,1999,274(1-2):182-189.
[20]Zheng X P, Zhong T K, Liu M T. Modeling crowd evacuation of a building based on seven methodological approaches [J]. Building and Environment,2009,44 (3):437-445.
[21]Graat E, Midden C, Bockholts P. Complex evacuation:effects of motivation level and slope of stairs on emergency egress time in a sports stadium [J]. Safety Science,1999,31(2):127-141.
[22]Lack KB. Means of escape from fire in high building[J]. Municipal Engineer,1997, 63:223-231.
[23]Gupta A K, Yadav P K. SAFE-R:a new model to study the evacuation profile of a building [J]. Fire Safety Journal,2004,39:539-556.
[24]Zhang Q S, Liu M, Wu C H. A stranded-crowd model (SCM) for performance-based design of stadium egress [J]. Building and Environment,2007,42:2630-2636.
[25]Sime, J.D.,1986. Perceived Rime Available:the Margin of Safety in Fires. In:Grant, C.E., Pagni, P.J.(Eds.), Fire Safety Science:Proceedings of the First International Symposium. Hemisphere, Wshing-ton.
[26]Chu G Q, Chen T, Sun J H. Probabilistic risk assessment for evacuees in building fires[J]. Building and Environment,2007,42:1283-1290.
[27]Hanea D M, Jagtman H M, Sillem S. Modelling self-reliance, evacuation and fire fighting activities during a large fire in a public building [J]. Safety Science Monitor,2007,11(2): 1-17.
[28]Tang C H, Lin C Y, Hsu Y M. Exploratory research on reading cognition and escape-route planning using building evacuation plan diagrams [J]. Applied Egronomics,2008,39: 209-217.
[29]Chow W K, Candy M.Y. Waiting time in emergency evacuation of crowded public transport terminals [J]. Safety Science,2008,46:844-857.
[30]Fang Z, Lo S M, Lu J.A. On the relationship between crowd density and movement velocity [J]. Fire Safety Journal,2003,38:271-283.
[31]Parisi D R, Marcelo G. Herman Moldovan. A modification of Social Force Model can reproduce experimental data of pedestrian flows in normal conditions [J]. Physica A,2009, 388:3600-3608.
[32]Seyfried A, Steffen B, Lippert T. Basics of modeling the pedestrian flow [J]. Physica A,2006, 368:232-238.
[33]Fang Z M, Song W G, Zhang J, et al. Experiment and modeling of exit-selecting behaviors during a building evacuation[J]. Physica A,2007,45:978-985.
[34]Gwynne S M V, Kuligowski E D, Kratchman J. Questioning the linear relationship between doorway width and achievable flow rate [J]. Fire Safety Journal,2009,44:80-87.
[35]Liu Shaobo, Yang Lizhong, Fang Tingyong, Li Jian. Evacuation from a classroom considering the occupant density around exits [J]. Physica A,2009,388:1921-1928.
[36]Zhang Q, Han B M, Li D. Modeling and simulation of passenger alighting and boarding movement in Beijing metro station [J]. Transportation Research Part C,2008,16:635-649.
[37]Sun C Y, Vries B D. Automated human choice extraction for evacuation route prediction [J]. Automation in Constrcuction,2009,18:751-761.
[38]Jiang C S, Yuan F, Chow W K. Effect of varing two key parameters in simulating evacuation for subway stations in China [J]. Safety Science,2010, xxx:xxx-xxx.
[39]Feng C, Wu Q B, Zang H H, et al. Relationship Analysis on Station Capacity and Passenger
Flow:A Case of Beijing Subway Line 1[J]. J Transpn Sys Eng & IT,2009,9(2):93-98.
[40]Zhang Q S, Liu M, Wu C H, et al. A stranded-crowd model (SCM) for performance-based design of stadium egress [J]. Building and Environment,2007,42:2630-2636.
[41]Fang J, Yuan H Y. Experimental measurements, integral modeling and smoke detection of early fire in thermally stratified environments [J]. Fire Safety Journal,2007,42:11-24.
[42]Choi H T, Beven K. Multi-period and multi-criteria model conditioning to reduce prediction uncertainty in an application of TOPMODEL within the GLUE framework[J]. Journal of Hydrology 2007; 332:316-336.
[43]Packard N H, Wolfram. Two-Dimensional Cellular Automata [J]. Journal of Statistical Physics,1985,38:901-946.
[44]Kirchner A, Schadschneider A. Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics [J]. Physica A,2002,312:260-276.
[45]Rigo L O, Barbosa V C. Two-dimensional cellular automata and the analysis of correlated time series [J]. Pattern Recognition Letters,2006,27:1353-1360.
[46]Li J, Yang L Z, Zhao D L. Simulation of bi-direction pedestrian movement in corridor [J]. Physica A,2005,354:619-628.
[47]Wang R L, Jiang R, Wu Q S. Synchronized flow and phase separations in single-lane mixed traffic flow [J]. Physica A,2007,378:475-484.
[48]Lum K M, Halim H. A before-and-after study on green signal countdown device installation [J]. Transportation Research Part F,2006,9:29-41.
[49]Shang P, Lu Y B, Kama S. The application of Holder exponent to traffic congestion warning [J]. Physica A,2006,370:769-776.
[50]Lee R S C, Hughes R L. Prediction of human crowd pressures [J].Accident Analysis and Prevention,2006,38:712-722.
[51]Shi Jiangang, Li Yang, Zhao Guanghua, Chen Yanyan. Research on pedestrianmanagement method and simulation evaluation practice in Olympic Games. TheFirst International Conference of Transportation Engineering (ICTE). ChengduChina, July 22-24 2007.
[52]Deinekoa V G, Klinz B, Woegingerc G J. Exact algorithms for the Hamiltonian cycle problem in planar graphs [J]. Operations Research Letters,2006,34:269-274.
[53]Smith B L, Williams B M, Oswald R K. Comparison of parametric and nonparametric models for traffic flow forecasting [J]. Transportation Research Part C:Emerging Technologies,2002, 10:303-321.
[54]Varas A, Cornejo M D, Mainemer D, et al. Cellular automaton model for evacuation process with obstacles [J]. Physica A,2007,382:631-642.
[55]Chen C X, Li Q, Kaneko S, et al. Location optimization algorithm for emergency signs in public facilities and its application to a single-floor supermarket [J]. Fire Safety Journal,2009, 44(1):113-120.
[56]Kirchner A, Klupfel H, Nishinari K, et al. Simulation of competitive egress behavior: comparison with aircraft evacuation data [J]. Physica A,2003,324(3-4):689-697.
[57]Parisi D R, Dorso C O. Microscopic dynamics of pedestrian evacuation [J]. Physica A,2005, 354:606-618.
[58]Izquierdo J, Montalvo I, Perez R, et al. Forecasting pedestrian evacuation times by using swarm intelligence [J]. Physica A,2009,388 (7):1213-1220.
[59]Liu S B, Yang L Z, Fang T Y, et al. Evacuation from a classroom considering the occupant density around exits [J]. Physica A,2009,388 (9):1921-1928.
[60]Yuan W F, Tan K H, An evacuation model using cellular automata [J]. Physica A,2007,384 (2):549-566.
[61]Song W G, Yu Y F, Wang B H, et al. Evacuation behaviors at exit in CA model with force essentials:A comparison with social force model[J]. Physica A,2006,371 (2):658-666.
[62]Yamamoto K, Kokubo S, Nishinari K. Simulation for pedestrian dynamics by real-coded cellular automata (RCA) [J]. Physica A,2007,379 (2):654-660.
[2]D.L. Zhao, J. Li, Y. Zhu, et al. The application of a two-dimensional cellular automata random model to the performance-based design of building exit[J]. Building and Environment,2008, 43(4):518-522.
[3]Ris S.C. Lee, Roger L. Hughes. Prediction of human crowd pressures [J].Accident Analysis and Prevention,2006,38:712-722.
[4]S. Ko, M. Spearpoint, A. Teo. Trial evacuation of an industrial premises and evacuation model comparison[J]. Fire Safety Journal,2007,42(2):91-105.
[5]Helbing D, Molnar P. Social force model for pedestrian dynamics. Physical Review E,1995, 51(5):4282-4286.
[6]Helbing D, Farkas I, Vicsek T. Simulating dynamical features of escape panic[J]. Nature, 2000,407:487-490.
[7]John Toner, Yuhai Tu and Sirram Ramaswamy. Hydrodynamics and phases of flocks[J]. Annals of Physics,2005,318:170-244.
[8]A. Fax and R. M. Murray. Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control, September 2004,49:1465-1475.
[9]Yang L Z, Zhao D L, Li J, et al. Simulation of the kin behavior in building occupant evacuation based on Cellular automaton[J].Building and Environment,2005,40:411-415
[10]Kholshevnikov VV. The study of human flows and methodology of evacuation standardisation. Moscow:MIFS; 1999.
[11]Hughes R. L., A continuum theory for the flow of pedestrians[J]. Transportation Research Part B,2002,36 (6):507-535.
[12]Huang L, Wong S C, Zhang R C, et al. Revisiting Hughes's dynamics continuum model for pedestrian flow and the development of an efficient solution algorithm[J]. Transportation Research Part B,2009,43 (1):127-141.
[13]Henein C M, White T, Macroscopic effects of microscopic forces between agents in crowd models[J]. Physica A,2007,373:694-712.
[14]Kholshevnikov V V, Shields T J, Boyce K E, et al. Recent development in pedestrian flow theory and research in Russia[J]. Fire Safety Journal,2008,43 (2):108-118.
[15]Burstedde C, Klauck K, Schadschneider A, et al. Simulation of pedestrian dynamics using a two-dimensional cellular automaton[J]. Physica A,2001,295:507-525.
[16]Li J, Yang L, Zhao D L. Simulation of bi-direction pedestrian movement in corridor [J]. Physica A,2005,354:619-628.
[17]Blue V J, Adler J L. Cellular automata microsimulation for modeling bi-directional pedestrian walkways[J]. Transportation Research Part B,2001,35 (3):293-312.
[18]Ito S, Nagatani T, Saegusa T. Volatile jam and flow fluctuation in counter flow of slender particles[J]. Physica A,2007,373:672-682.
[19]Vicsek T, Czirok A, Farkas I J. Application of statistical mechanics to collective motion in
biology[J]. Physics A,1999,274(1-2):182-189.
[20]Zheng X P, Zhong T K, Liu M T. Modeling crowd evacuation of a building based on seven methodological approaches [J]. Building and Environment,2009,44 (3):437-445.
[21]Graat E, Midden C, Bockholts P. Complex evacuation:effects of motivation level and slope of stairs on emergency egress time in a sports stadium [J]. Safety Science,1999,31(2):127-141.
[22]Lack KB. Means of escape from fire in high building[J]. Municipal Engineer,1997, 63:223-231.
[23]Gupta A K, Yadav P K. SAFE-R:a new model to study the evacuation profile of a building [J]. Fire Safety Journal,2004,39:539-556.
[24]Zhang Q S, Liu M, Wu C H. A stranded-crowd model (SCM) for performance-based design of stadium egress [J]. Building and Environment,2007,42:2630-2636.
[25]Sime, J.D.,1986. Perceived Rime Available:the Margin of Safety in Fires. In:Grant, C.E., Pagni, P.J.(Eds.), Fire Safety Science:Proceedings of the First International Symposium. Hemisphere, Wshing-ton.
[26]Chu G Q, Chen T, Sun J H. Probabilistic risk assessment for evacuees in building fires[J]. Building and Environment,2007,42:1283-1290.
[27]Hanea D M, Jagtman H M, Sillem S. Modelling self-reliance, evacuation and fire fighting activities during a large fire in a public building [J]. Safety Science Monitor,2007,11(2): 1-17.
[28]Tang C H, Lin C Y, Hsu Y M. Exploratory research on reading cognition and escape-route planning using building evacuation plan diagrams [J]. Applied Egronomics,2008,39: 209-217.
[29]Chow W K, Candy M.Y. Waiting time in emergency evacuation of crowded public transport terminals [J]. Safety Science,2008,46:844-857.
[30]Fang Z, Lo S M, Lu J.A. On the relationship between crowd density and movement velocity [J]. Fire Safety Journal,2003,38:271-283.
[31]Parisi D R, Marcelo G. Herman Moldovan. A modification of Social Force Model can reproduce experimental data of pedestrian flows in normal conditions [J]. Physica A,2009, 388:3600-3608.
[32]Seyfried A, Steffen B, Lippert T. Basics of modeling the pedestrian flow [J]. Physica A,2006, 368:232-238.
[33]Fang Z M, Song W G, Zhang J, et al. Experiment and modeling of exit-selecting behaviors during a building evacuation[J]. Physica A,2007,45:978-985.
[34]Gwynne S M V, Kuligowski E D, Kratchman J. Questioning the linear relationship between doorway width and achievable flow rate [J]. Fire Safety Journal,2009,44:80-87.
[35]Liu Shaobo, Yang Lizhong, Fang Tingyong, Li Jian. Evacuation from a classroom considering the occupant density around exits [J]. Physica A,2009,388:1921-1928.
[36]Zhang Q, Han B M, Li D. Modeling and simulation of passenger alighting and boarding movement in Beijing metro station [J]. Transportation Research Part C,2008,16:635-649.
[37]Sun C Y, Vries B D. Automated human choice extraction for evacuation route prediction [J]. Automation in Constrcuction,2009,18:751-761.
[38]Jiang C S, Yuan F, Chow W K. Effect of varing two key parameters in simulating evacuation for subway stations in China [J]. Safety Science,2010, xxx:xxx-xxx.
[39]Feng C, Wu Q B, Zang H H, et al. Relationship Analysis on Station Capacity and Passenger
Flow:A Case of Beijing Subway Line 1[J]. J Transpn Sys Eng & IT,2009,9(2):93-98.
[40]Zhang Q S, Liu M, Wu C H, et al. A stranded-crowd model (SCM) for performance-based design of stadium egress [J]. Building and Environment,2007,42:2630-2636.
[41]Fang J, Yuan H Y. Experimental measurements, integral modeling and smoke detection of early fire in thermally stratified environments [J]. Fire Safety Journal,2007,42:11-24.
[42]Choi H T, Beven K. Multi-period and multi-criteria model conditioning to reduce prediction uncertainty in an application of TOPMODEL within the GLUE framework[J]. Journal of Hydrology 2007; 332:316-336.
[43]Packard N H, Wolfram. Two-Dimensional Cellular Automata [J]. Journal of Statistical Physics,1985,38:901-946.
[44]Kirchner A, Schadschneider A. Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics [J]. Physica A,2002,312:260-276.
[45]Rigo L O, Barbosa V C. Two-dimensional cellular automata and the analysis of correlated time series [J]. Pattern Recognition Letters,2006,27:1353-1360.
[46]Li J, Yang L Z, Zhao D L. Simulation of bi-direction pedestrian movement in corridor [J]. Physica A,2005,354:619-628.
[47]Wang R L, Jiang R, Wu Q S. Synchronized flow and phase separations in single-lane mixed traffic flow [J]. Physica A,2007,378:475-484.
[48]Lum K M, Halim H. A before-and-after study on green signal countdown device installation [J]. Transportation Research Part F,2006,9:29-41.
[49]Shang P, Lu Y B, Kama S. The application of Holder exponent to traffic congestion warning [J]. Physica A,2006,370:769-776.
[50]Lee R S C, Hughes R L. Prediction of human crowd pressures [J].Accident Analysis and Prevention,2006,38:712-722.
[51]Shi Jiangang, Li Yang, Zhao Guanghua, Chen Yanyan. Research on pedestrianmanagement method and simulation evaluation practice in Olympic Games. TheFirst International Conference of Transportation Engineering (ICTE). ChengduChina, July 22-24 2007.
[52]Deinekoa V G, Klinz B, Woegingerc G J. Exact algorithms for the Hamiltonian cycle problem in planar graphs [J]. Operations Research Letters,2006,34:269-274.
[53]Smith B L, Williams B M, Oswald R K. Comparison of parametric and nonparametric models for traffic flow forecasting [J]. Transportation Research Part C:Emerging Technologies,2002, 10:303-321.
[54]Varas A, Cornejo M D, Mainemer D, et al. Cellular automaton model for evacuation process with obstacles [J]. Physica A,2007,382:631-642.
[55]Chen C X, Li Q, Kaneko S, et al. Location optimization algorithm for emergency signs in public facilities and its application to a single-floor supermarket [J]. Fire Safety Journal,2009, 44(1):113-120.
[56]Kirchner A, Klupfel H, Nishinari K, et al. Simulation of competitive egress behavior: comparison with aircraft evacuation data [J]. Physica A,2003,324(3-4):689-697.
[57]Parisi D R, Dorso C O. Microscopic dynamics of pedestrian evacuation [J]. Physica A,2005, 354:606-618.
[58]Izquierdo J, Montalvo I, Perez R, et al. Forecasting pedestrian evacuation times by using swarm intelligence [J]. Physica A,2009,388 (7):1213-1220.
[59]Liu S B, Yang L Z, Fang T Y, et al. Evacuation from a classroom considering the occupant density around exits [J]. Physica A,2009,388 (9):1921-1928.
[60]Yuan W F, Tan K H, An evacuation model using cellular automata [J]. Physica A,2007,384 (2):549-566.
[61]Song W G, Yu Y F, Wang B H, et al. Evacuation behaviors at exit in CA model with force essentials:A comparison with social force model[J]. Physica A,2006,371 (2):658-666.
[62]Yamamoto K, Kokubo S, Nishinari K. Simulation for pedestrian dynamics by real-coded cellular automata (RCA) [J]. Physica A,2007,379 (2):654-660.