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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (12): 2386-2394    DOI: 10.3785/j.issn.1008-973X.2020.12.013
    
Improved numerical method for two-way arterial signal coordinate control
Jia-qi ZENG(),Dian-hai WANG*()
College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
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Abstract  

A new improved numerical method was proposed aiming at the problem that the original numerical method cannot ensure the optimal solution. First, the range and mode of the movement of the ideal signal position were defined, and the concept of the initial ideal signal position was put forward. Then, a new definition of offset green ratio was proposed. The offset green ratio relative to the front and back initial ideal signal position were called the front and back projected green ratio, respectively. Finally, by finding the relationship between the green wave bandwidth and the front/back projected green ratio, it was proved that the change times of green wave bandwidth is equal to the number of intersections during the ideal signal movement. By pre-calculating the forward and back projected green ratio, redundant calculation of the loss green ratio was avoided after each movement of the ideal signal position. The results demonstrate that, the proposed method can obtain the maximum green wave bandwidth compared with the existing numerical method, and reduce the calculation amount when the results are the same.

Key words： traffic engineering      arterial signal coordination      numerical method      green wave bandwidth      signal offset     
Received: 18 October 2019      Published: 31 December 2020
CLC:  U 491.2  
Corresponding Authors: Dian-hai WANG     E-mail: zengjiaqi@zju.edu.cn;wangdianhai@zju.edu.cn
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Cite this article:

Jia-qi ZENG,Dian-hai WANG. Improved numerical method for two-way arterial signal coordinate control. Journal of ZheJiang University (Engineering Science), 2020, 54(12): 2386-2394.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2020.12.013     OR     http://www.zjujournals.com/eng/Y2020/V54/I12/2386


双向干线协调控制的改进数解算法

针对经典数解法不能确保得到最优解的问题，提出新的改进数解算法. 明确理想信号位置的移动范围和移动方式，提出初始理想信号位置的概念；提出偏移绿信比的新定义，将信号相对于前、后方初始理想信号位置的偏移绿信比分别称为前、后投影绿信比；通过寻找绿波带宽度与前、后投影绿信比的关系，证明在理想信号移动的过程中绿波带宽度的变化次数等于干线交叉口的数量. 预先计算前、后投影绿信比，避免在移动理想信号位置时对绿时损失的重复计算. 研究结果表明，改进后的数解算法相比经典数解法，可以得到最大绿波带宽，并且在结果相同的情况下计算量更小.


关键词： 交通工程,  干线协调控制,  数解算法,  绿波带宽度,  相位差 
Fig.1 Arrangement of ideal signal position
Fig.2 Layout for the arterial road in example 1
信号 Di/m 邻项差/m
S1 0 ?
S4 40 40
S3 60 20
S2 300 240
S5 320 20
S1 380 60
Tab.1 Neighbor difference of Di calculation
Fig.3 Ideal signal placement of example 1 using original numerical method
a/m b/m （b∶a）/% dmax/m
　　注：“▲”为最优解标记符号.
360 200 56 80
370 220 59 75
380 240 63 70▲
390 240 62 75
400 220 55 90
410 170 41 120
420 140 33 140
430 180 42 125
440 220 50 110
450 210 47 120
460 180 39 140
470 150 32 160
480 180 38 150
490 230 47 130
500 280 56 110
510 330 65 90
520 360▲ 69▲ 80
530 350 66 90
540 340 63 100
550 330 60 110
Tab.2 Relationship of ideal signal spacing and matching degree indicators for example 1
信号
编号 		最近理想
信号编号 		相位
差/% 		实际信号所处方位 λ /% λloss /% λe /% B /%
S1 ① 0 前 45 2.63 42.37 26.85/2+
31.58/2=
29.21
S2 ③ 0 后 50 18.42 31.58
S3 ④ 50 前 60 18.42 41.58
S4 ⑤ 0 前 40 13.15 26.85
S5 ⑦ 0 后 55 13.15 41.85
Tab.3 Signal offset calculation of example 1 when a=380 m
Fig.4 Schematic diagram of offset green ratio
Fig.5 Offset green ratio and projected green ratio diagram
信号 Λi λi ${ { {\lambda _i} } }/{2} + {\varLambda _i}$ ${ { {\lambda _i} } }/{2} - {\varLambda _i}$
${S'_2}$ $\dfrac{{{{D'}_2}}}{{2a}} - \dfrac{1}{2}$ ${\lambda '_2} $ ${\lambda '_2}/ 2 + {\varLambda _2}$ ${\lambda '_2}/ 2 - {\varLambda _2}$
${S'_3}$ $\dfrac{{{{D'}_3}}}{{2a}} - \dfrac{1}{2}$ ${\lambda '_3} $ ${\lambda '_3}/ 2 + {\varLambda _3}$ ${\lambda '_3}/ 2 - {\varLambda _3}$
$ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $
${S'_n}$ $\dfrac{{{{D'}_n}}}{{2a}} - \dfrac{1}{2}$ ${\lambda '_n} $ ${\lambda '_n}/ 2+ {\varLambda _n}$ ${\lambda '_n}/ 2 - {\varLambda _n}$
${S'_1}$ $\dfrac{{{{D'}_1}}}{{2a}}$ ${\lambda '_1} $ ${\lambda '_1}/ 2 + {\varLambda _1}$ ${\lambda '_1}/ 2 - {\varLambda _1}$
${S'_2}$ $\dfrac{{{{D'}_2}}}{{2a}}$ ${\lambda '_2} $ ${\lambda '_2}/ 2 + {\varLambda _2}$ ${\lambda '_2}/ 2 - {\varLambda _2}$
$ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $
${S'_n}$ $\dfrac{{{{D'}_n}}}{{2a}}$ ${\lambda '_n} $ ${\lambda '_n}/ 2 + {\varLambda _n}$ ${\lambda '_n}/ 2 - {\varLambda _n}$
Tab.4 Green wave bandwidth calculation table of improved numerical method
a/m B/% a/m B/% a/m B/%
　　注：“▲”为最优解标记符号.
360 7.78 430 13.43 500 18.00
370 11.08 440 14.77 510 16.28
380 14.21 450 11.95 520 14.62
390 17.18 460 9.89 530 13.02
400 20.00 470 13.83 540 11.48
410 20.42▲ 480 16.66 550 10.00
420 14.28 490 18.11
Tab.5 Relationship of ideal signal spacing and green wave bandwidth for example 2
信号 Λi λi ${ { {\lambda _i} } }/{2} + {\varLambda _i}$ ${ { {\lambda _i} } }/{2} - {\varLambda _i}$
S5 ?29.27 55 ?1.77 56.77
S2 ?17.08 30 ?2.08 32.08
S4 ?9.76 30 5.25 24.76
S3 ?3.66 60 26.34 33.66
S1 0 45 22.50 22.50
S5 20.73 55 48.23 6.77
S2 32.93 30 47.93 ?17.93
S4 40.25 30 55.25 ?25.25
S3 46.34 60 76.34 ?16.34
Tab.6 Green wave bandwidth calculation table of improved numerical method when a=410 m in example 2
理想信号位置 $\min \;\left\{ {{ { {\lambda _i} } }/{2} + {\varLambda _i} } \right\}/{\text{%}}$ $\min\; \left\{ { { { {\lambda _i} } }/{2} - {\varLambda _i} } \right\}/{\text{%} }$ B /%
　　注：“▲”为各方法最优解标记符号
l1，cr<l≤l5，cr ?2.08 22.5 20.42▲
l5，cr<l≤l2，cr ?2.08 6.77 4.69
l2，cr<l≤l4，cr 5.24 ?17.92 ?12.68
l4，cr<l≤l3，cr 22.5 ?25.24 ?2.74
l3，cr<l≤l1，cr+a 22.5 ?25.24 ?2.74
Tab.7 Green wave bandwidth at each ideal signal position when a=410 m in example 2
Fig.6 Ideal signal placement of example 2 using improved numerical method
Fig.7 Ideal signal position and time-space diagram of example 2
信号编号 最近理想信号编号 相位差/%
S1 ① 0
S2 ③ 0
S3 ④ 50
S4 ⑤ 0
S5 ⑦ 0
Tab.8 Signal offset calculation of example 1 when a=410 m
a/m b/m ba?1/% dmax/m B/%
　　注： “▲”为各方法最优解标记符号.
340 140 29.4 100▲ 33.1
350 130 31.4 110 33.6▲
360 90 37.5 135 30.0
370 100 36.5 135 24.3
380 110 35.5 135 22.0
390 110 35.9 140 21.6
400 120 35.0 140 22.5
410 130 34.1 140 23.4
420 140 33.3 140 24.2
430 130 34.9 150 24.9
440 120 29.4 100▲ 23.2
450 110 37.8 170 22.5
460 120 37.0 170 20.9
470 150 34.0 160 22.7
480 180 31.2 150 23.3
490 210 28.6 140 23.9
500 220▲ 28.0▲ 140 24.5
510 200 30.4 155 25.1
520 170 33.7 175 25.6
530 140 36.8 195 24.8
540 150 36.1 195 24.2
Tab.9 Relationship of ideal signal spacing and matching degree indicators for example 3
a /m b /m ba?1 /% dmax /m B/%
　　注：“▲”为各方法最优解标记符号.
460 120 26.1 170 20.9
470 150 31.9 160 22.7
480 180 37.5 150 23.3
490 210 42.9 140▲ 23.9
500 220 44.0▲ 140▲ 24.5
510 200 39.2 155 25.1
520 170 32.7 175 25.6
530 140 26.4 195 24.8
540 150 27.8 195 24.2
550 190 34.5 180 24.8
560 210 37.5 175 27.5
570 220 38.6 175 27.9▲
580 190 32.8 195 26.5
590 160 27.1 215 26.2
600 150 25.0 225 25.0
610 140 23.0 235 22.3
620 130 21.0 245 20.5
630 160 25.4 235 22.7
640 190 29.7 225 24.4
650 220 33.8 215 24.0
660 250▲ 37.9 205 23.7
Tab.10 Relationship of ideal signal spacing and matching degree indicators for example 4
n T1（n） T2（n） T3（n） T4（n） T4（n）/T1（n）
6 745 1985 2481 135 18.1%
8 1313 10497 3281 213 16.2%
10 2041 52225 4081 307 15.0%
12 2929 249857 4881 417 14.2%
Tab.11 Number of operations of each method under different n
[1]   杨佩昆, 吴兵. 交通管理与控制[M]. 北京: 人民交通出版社, 2003: 122-131.
[2]   MORGAN J T, LITTLE J D C Synchronizing traffic signals for maximal bandwidth[J]. Operations Research, 1964, 12 (6): 896- 912
doi: 10.1287/opre.12.6.896
[3]   LITTLE J D C, KELSON M D, GARTNER N H MAXBAND: a versatile program for setting signals on arteries and triangular networks[J]. Transportation Researeh Record, 1981, 795: 40- 46
[4]   GARTNER N H, ASSMAN S F, LASAGA F, et al A multi-band approach to arterial traffic signal optimization[J]. Transportation Research Part B: Methodological, 1991, 25 (1): 55- 74
[5]   中国公路学会《交通工程手册》编委会. 交通工程手册[M]. 北京: 人民交通出版社, 1998: 1192-1208.
[6]   陈垚, 刘莎莎, 李玲利, 等 基于Synchro的相位差优化方法研究——以长安街交叉口为例[J]. 交通信息与安全, 2012, 30 (6): 115- 117
CHEN Yao, LIU Sha-sha, LI Ling-li, et al Synchro-based offset optimization method: a case study of intersection in Chang’an Avenue[J]. Journal of Transport Information and Safety, 2012, 30 (6): 115- 117
doi: 10.3963/j.issn1674-4861.2012.06.024
[7]   裴玉龙, 孙明哲, 董向辉 城市主干路交叉口信号协调控制系统设计研究[J]. 交通运输工程与信息学报, 2004, (2): 41- 46
PEI Yu-long, SUN Ming-zhe, DONG Xiang-hui Research on the design of signal coordination control system in intersections of urban main roads[J]. Journal of Transportation Engineering and Information, 2004, (2): 41- 46
doi: 10.3969/j.issn.1672-4747.2004.02.005
[8]   邹成伟, 李志海, 于冬意 哈尔滨市红旗大街线控制系统设计[J]. 应用科技, 2002, (5): 30- 33
ZOU Cheng-wei, LI Zhi-hai, YU Dong-yi Design of linear control system in Hongqi Street in Harbin[J]. Applied Science and Technology, 2002, (5): 30- 33
doi: 10.3969/j.issn.1009-671X.2002.05.011
[9]   栗红强. 城市交通控制信号配时参数优化方法研究[D]. 长春: 吉林大学, 2004.
LI Hong-qiang. Study on the optimization methods of signal timing parameters of urban traffic control [D]. Changchun: Jilin University, 2004.
[10]   卢凯, 徐建闽, 叶瑞敏 经典干道协调控制信号配时数解算法的改进[J]. 公路交通科技, 2009, 26 (1): 120- 124
LU Kai, XU Jian-min, YE Rui-min Improvement of classical algebraic method of signal timing for arterial road coordinate control[J]. Journal of Highway and Transportation Research and Development, 2009, 26 (1): 120- 124
doi: 10.3969/j.issn.1002-0268.2009.01.022
[11]   卢凯, 刘永洋, 吴焕, 等 非对称通行条件下的双向绿波协调控制数解算法[J]. 中国公路学报, 2015, 28 (6): 95- 103
LU Kai, LIU Yong-yang, WU Huan, et al Algebraic method of bidirectional green wave coordinated control under asymmetric traffic conditions[J]. China Journal of Highway and Transport, 2015, 28 (6): 95- 103
doi: 10.3969/j.issn.1001-7372.2015.06.013
[12]   王殿海, 杨希锐, 宋现敏 交通信号干线协调控制经典数值计算法的改进[J]. 吉林大学学报: 工学版, 2011, 41 (1): 29- 34
WANG Dian-hai, YANG Xi-rui, SONG Xian-min Improvement of classical numerical method for arterial road signal coordinate control[J]. Journal of Jilin University: Engineering and Technology Edition, 2011, 41 (1): 29- 34
[13]   荆彬彬, 鄢小文, 吴焕, 等 基于双向最大绿波带宽的通用干道协调控制数解算法[J]. 交通运输系统工程与信息, 2017, 17 (2): 76- 82
JING Bin-bin, YAN Xiao-wen, WU Huan, et al General algebraic algorithm for arterial coordination control based on maximum bidirectional progression bandwidth[J]. Journal of Transportation Systems Engineering and Information Technology, 2017, 17 (2): 76- 82
[14]   叶晓飞, 羊钊, 包哲宁, 等 考虑行车延误的干线协调控制信号配时数解算法[J]. 长安大学学报: 自然科学版, 2015, 35 (Suppl.1): 115- 119
YE Xiao-fei, YANG Zhao, BAO Zhe-ning, et al Improvement of classical algebraic method of signal timing for arterial road coordinate control considering traffic delay[J]. Journal of Chang'an University: Natural Science Edition, 2015, 35 (Suppl.1): 115- 119
[15]   李小会, 闫冬 进口单独放行条件的双向绿波数解法改进研究[J]. 交通科技与经济, 2019, 21 (6): 9- 18
LI Xiao-hui, YAN Dong Research on an improved algebraic method of two-way green wave based on one-phase-one-approach[J]. Technology and Economy in Areas of Communications, 2019, 21 (6): 9- 18
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