Algebraic Method of Coordination Design for Bi-directional Red and Green Waves of Saturated Intersection

doi:10.12141/j.issn.1000-565X.210809

Abstract

Abstract:

When there is a saturated intersection on the arterial road, it is necessary to intercept and regulate the traffic flow in the entry direction of the saturated intersection, so as to avoid the overflow of the section queue, and to conduct green wave dredging in the exit direction of the saturated intersection to facilitate the rapid departure of traffic flow. According to the coordination control requirements in different directions of saturated intersection, this paper proposed an algebraic method of coordination design for bi-directional red and green waves on arterial roads. Firstly, the general formula for calculating the ideal intersection distance was derived by using the time-space diagram, and the calculation method of bias-split for the coordinated phase was given. Secondly, for different common signal cycles, the bias-split for the coordinated phase under different signal phase modes of each intersection was calculated respectively. The signal phase mode corresponding to the bias-split with the smallest absolute value was taken as the preferred phase of each intersection. Then, the max difference of bias-split corresponding to the preferred phase under different common signal cycles was compared, and the common signal cycle with the minimum of the max difference of bias-split was selected as the best common signal cycle. Finally, based on the characteristics of red and green waves, the optimization method of fine-tuning signal offsets was given to minimize the bias-split of the green wave direction, so as to ensure that the arterial road can obtain bi-directional red and green wave bandwidth as wider as possible. The case analysis shows that, compared with the scheme of bi-directional green wave coordinated control, the bi-directional red and green waves coordinated control scheme designed by this method can significantly increase the green wave bandwidth in the direction of leaving the saturated intersection while ensuring that there is a maximum red wave bandwidth in the direction of entering the saturated intersection. The VISSIM simulation experiment shows that the scheme designed by this method can not only shorten the maximum queue length by 23.1% and the average queue length by 33.8%, and delay the time of vehicles queuing to overflow to the upstream intersection, but also reduce the travel time and the number of stops of the vehicles leaving at the saturated intersection in the downstream section by 17.5% and 76.3%, respectively. It can realize the overflow prevention and green wave dredging of the saturated intersection.

Key words: traffic engineering, coordination control, bi-directional red and green waves, algebraic method, saturated intersection, ideal position

CLC Number:

U491.4

LU Kai, ZHAO Shijie, WU Huan, et al. Algebraic Method of Coordination Design for Bi-directional Red and Green Waves of Saturated Intersection[J]. Journal of South China University of Technology(Natural Science Edition), 2022, 50(9): 1-11.

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交叉口编号	信号周期变化范围/s	绿信比
交叉口编号	信号周期变化范围/s	南进口	北进口	东进口	西进口
1	［95，125］	0.38	0.34	0.13	0.15
2	［90，125］	0.37	0.39	0.13	0.11
3	［90，135］	0.37	0.36	0.14	0.13
4	［100，130］	0.26	0.27	0.24	0.23
5	［95，130］	0.36	0.39	0.12	0.13
6	［85，120］	0.35	0.38	0.13	0.14
7	［95，125］	0.38	0.36	0.14	0.12
8	［100，135］	0.36	0.35	0.15	0.14

公共信号周期/s	理想间距/m				中心偏移率				优选相位
公共信号周期/s	北南东西	南东北西	南西北东	南北东西	北南东西	南东北西	南西北东	南北东西	优选相位
100	180.0	262.5	277.5	360.0	0.320	0.210	0.190	0.080	南北东西
102	183.6	267.8	283.1	367.2	0.309	0.199	0.179	0.069	南北东西
104	187.2	273.0	288.6	374.4	0.298	0.188	0.168	0.058	南北东西
106	190.8	278.3	294.2	381.6	0.288	0.178	0.158	0.048	南北东西
108	194.4	283.5	299.7	388.8	0.279	0.169	0.149	0.039	南北东西
110	198.0	288.8	305.3	396.0	0.269	0.159	0.139	0.029	南北东西
112	201.6	294.0	310.8	403.2	0.260	0.150	0.130	0.020	南北东西
114	205.2	299.3	316.4	410.4	0.251	0.141	0.121	0.011	南北东西
116	208.8	304.5	321.9	417.6	0.243	0.133	0.113	0.003	南北东西
118	212.4	309.8	327.5	424.8	0.235	0.125	0.105	-0.005	南北东西
120	216.0	315.0	333.0	432.0	0.227	0.117	0.097	-0.013	南北东西

交叉口1~8的最佳相位组合		公共信号周期/s	最大中心偏移率之差
1	北南东西，北南东西，北南东西，南东北西，北南东西，南西北东，南北东西，南西北东	100	0.165
2	南东北西，南西北东，南东北西，南东北西，北南东西，南西北东，南北东西，南西北东	106	0.095
3	南西北东，南西北东，南东北西，南东北西，北南东西，南西北东，南北东西，南西北东	104	0.109
4	南北东西，南北东西，南北东西，南西北东，北南东西，南西北东，南北东西，南西北东	110	0.114

交叉口	信号相位	理想间距/m	中心偏移率	区间行驶速度/（m?s^-1）	相位差调整率	绝对相位差/s
1	南东北西	0	0.000	15	0.000	-20.1
2	南西北东	397.5	0.028	15	-0.014	58.4
3	南东北西	783.1	-0.016	15	-0.008	33.4
4	南东北西	1 180.6	-0.026	15	-0.013	13.3
5	北南东西	1 482.7	-0.041	15	-0.006	27.3
6	南西北东	1 975.6	-0.057	15	-0.003	59.9
7	南北东西	2 480.4	0.037	15	0.045	96.9
8	南西北东	2 778.5	0.002	15	0.027	10.0

行驶方向	交叉口编号	直行相位绿信比	中心偏移率	绿信比		绿波带宽/%
行驶方向	交叉口编号	直行相位绿信比	中心偏移率	中心线上方	中心线下方	绿波带宽/%
上行方向	4	0.260	0	0.130	0.130	26.0
	5	0.360	0	0.180	0.180
	6	0.350	0	0.175	0.175
	7	0.380	0	0.190	0.190
	8	0.360	0	0.180	0.180
下行方向	4	0.270	0	0.135	0.135	27.0
	3	0.360	0	0.180	0.180
	2	0.390	0	0.195	0.195
	1	0.340	0	0.170	0.170