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The conflicts between pedestrians and vehicles at unsignalized intersections are rather dangerous. Besides the motion features, pedestrians and vehicle drivers also have behavioral features, so modelling the crossing behaviors of pedestrians and vehicles from the sociological aspect is necessary. Through an in-depth analysis of the interference mechanism between pedestrians and vehicles at unsignalized intersections, in this paper, a dirty faces game to analyze the crossing behaviors of pedestrians and vehicles as “rational man” is proposed. The formation process of common knowledge, the producing mechanism of dominant strategy and the kinetic process of dirty faces game are analyzed. Under the assumption of probability of the dominant strategy and distribution of crossing times, theoretical derivations of the benefits gained by pedestrians and vehicles as well as the conflict probability are given. Results show that a collision is more likely to occur when the theoretical time of pedestrian passing through is closer to that of the vehicle driver, and this is consistent with the actual situation. Furthermore, the influences of vehicle type, waiting time and heterogeneity of pedestrians on the conflict probability are also considered.
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Keywords:
- pedestrian crossing /
- unsignalized intersection /
- dirty faces game /
- common knowledge
[1] Lighthill M J, Whitham G B 1955 Proc. Roy. Soc. A 229 317
[2] Richards P I 1956 Oper. Res. 4 42
[3] Payne H J 1971 Math. Mod. Pub. Sys. 1 51
[4] Paveri-Fontana S L 1975 Trans. Res. 9 225
[5] Helbing D 1996 Physica A 233 253
[6] Pipes L A 1953 J. Appl. Phys. 24 274
[7] Cremer M, Ludwig J 1986 Math. Comp. Simul. 28 297
[8] Sun Z, Jia B, Li X G 2012 Acta Phys. Sin. 61 100508 (in Chinese) [孙泽, 贾斌, 李新刚 2012 61 100508]
[9] Wu Z X, Rong Z H, Wang W X 2008 Adv. Mech. 38 794 (in Chinese) [吴枝喜, 荣智海, 王文旭 2008 力学进展 38 794]
[10] Bell M G H 2000 Transp. Res. Part B 34 53
[11] Perc M 2007 New J. Phys. 9 1
[12] Alvarez I, Poznyak A 2010 International Conference on Control, Automation and System Gyeonggi-do, Korea, October 27-30, 2010 p2164
[13] Nakata M, Yamauchi A, Tanimoto J, Hagishima A 2010 Physica A 389 5353
[14] Xie J J, Xue Y 2012 Acta Phys. Sin. 61 194502 (in Chinese) [谢积鉴, 薛郁 2012 61 194502]
[15] Sun X Y, Wang B H 2012 J. Shanghai Univ. Sci. Technol. 34 14 (in Chinese) [孙晓燕, 汪秉宏 2012 上海理工大学学报 34 14]
[16] Sun X Y, Jiang R, Hao Q Y, Wang B H 2010 Eur. Phys. Lett. 92 18003
[17] Tang J J 2010 M. S. Dissertation (Beijing: Beijing Jiaotong University) (in Chinese) [唐勍勍 2010 硕士学位论文 (北京: 北京交通大学)]
[18] Li P 2011 M. S. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [李平 2011 硕士学位论文 (哈尔滨: 哈尔滨工业大学)]
[19] Pan W, Xue Y, Zhao R, Lu W Z 2014 Chin. Phys. B 23 058902
[20] Schelling T C (translated by Xie J, Deng Z L, Li T Y) 2005 Micromotives and Macrobehavior (Beijing: China Renmin University Press) p1 (in Chinese)[谢林 T C 著 (谢静, 邓子梁, 李天有 译) 2005 微观动机与宏观行为 (北京: 中国人民大学出版社) 第1页]
[21] Littlewood J E 1953 A Mathematician’s Miscellany (London: Methuen Publishing) p4
[22] Alberucci L, Jäger G 2005 Ann. Pure Appl. Log. 133 73
[23] Xiao R J, Kong L J, Liu M R 2007 Acta Phys. Sin. 56 740 (in Chinese) [肖瑞杰, 孔令江, 刘慕仁 2007 56 740]
[24] Wang J, Tang Z H, Lu H P 2004 China Civil Eng. J. 37 97 (in Chinese) [王进, 唐忠华, 陆化普 2004 土木工程学报 37 97]
[25] Rouphail N, Hummer J, Milazzo II J, Allen P 1998 Capacity Analysis of Pedestrian and Bicycle Facilities: Recommended Procedures for the “Signalized Intersections” Chapter of the Highway Capacity Manual (Washington: Federal Highway Administration) p30
[26] Lu S F, Wang H R, Liu X M 2009 J. Transp. Inform. Safety 5 69 (in Chinese) [卢守峰, 王红茹, 刘喜敏 2009 交通信息与安全 5 69]
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[1] Lighthill M J, Whitham G B 1955 Proc. Roy. Soc. A 229 317
[2] Richards P I 1956 Oper. Res. 4 42
[3] Payne H J 1971 Math. Mod. Pub. Sys. 1 51
[4] Paveri-Fontana S L 1975 Trans. Res. 9 225
[5] Helbing D 1996 Physica A 233 253
[6] Pipes L A 1953 J. Appl. Phys. 24 274
[7] Cremer M, Ludwig J 1986 Math. Comp. Simul. 28 297
[8] Sun Z, Jia B, Li X G 2012 Acta Phys. Sin. 61 100508 (in Chinese) [孙泽, 贾斌, 李新刚 2012 61 100508]
[9] Wu Z X, Rong Z H, Wang W X 2008 Adv. Mech. 38 794 (in Chinese) [吴枝喜, 荣智海, 王文旭 2008 力学进展 38 794]
[10] Bell M G H 2000 Transp. Res. Part B 34 53
[11] Perc M 2007 New J. Phys. 9 1
[12] Alvarez I, Poznyak A 2010 International Conference on Control, Automation and System Gyeonggi-do, Korea, October 27-30, 2010 p2164
[13] Nakata M, Yamauchi A, Tanimoto J, Hagishima A 2010 Physica A 389 5353
[14] Xie J J, Xue Y 2012 Acta Phys. Sin. 61 194502 (in Chinese) [谢积鉴, 薛郁 2012 61 194502]
[15] Sun X Y, Wang B H 2012 J. Shanghai Univ. Sci. Technol. 34 14 (in Chinese) [孙晓燕, 汪秉宏 2012 上海理工大学学报 34 14]
[16] Sun X Y, Jiang R, Hao Q Y, Wang B H 2010 Eur. Phys. Lett. 92 18003
[17] Tang J J 2010 M. S. Dissertation (Beijing: Beijing Jiaotong University) (in Chinese) [唐勍勍 2010 硕士学位论文 (北京: 北京交通大学)]
[18] Li P 2011 M. S. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [李平 2011 硕士学位论文 (哈尔滨: 哈尔滨工业大学)]
[19] Pan W, Xue Y, Zhao R, Lu W Z 2014 Chin. Phys. B 23 058902
[20] Schelling T C (translated by Xie J, Deng Z L, Li T Y) 2005 Micromotives and Macrobehavior (Beijing: China Renmin University Press) p1 (in Chinese)[谢林 T C 著 (谢静, 邓子梁, 李天有 译) 2005 微观动机与宏观行为 (北京: 中国人民大学出版社) 第1页]
[21] Littlewood J E 1953 A Mathematician’s Miscellany (London: Methuen Publishing) p4
[22] Alberucci L, Jäger G 2005 Ann. Pure Appl. Log. 133 73
[23] Xiao R J, Kong L J, Liu M R 2007 Acta Phys. Sin. 56 740 (in Chinese) [肖瑞杰, 孔令江, 刘慕仁 2007 56 740]
[24] Wang J, Tang Z H, Lu H P 2004 China Civil Eng. J. 37 97 (in Chinese) [王进, 唐忠华, 陆化普 2004 土木工程学报 37 97]
[25] Rouphail N, Hummer J, Milazzo II J, Allen P 1998 Capacity Analysis of Pedestrian and Bicycle Facilities: Recommended Procedures for the “Signalized Intersections” Chapter of the Highway Capacity Manual (Washington: Federal Highway Administration) p30
[26] Lu S F, Wang H R, Liu X M 2009 J. Transp. Inform. Safety 5 69 (in Chinese) [卢守峰, 王红茹, 刘喜敏 2009 交通信息与安全 5 69]
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