Optimization Model of Bus Priority Control Considering Carbon Emissions with Stochastic Characteristics

doi:10.12141/j.issn.1000-565X.230178

Abstract

Abstract:

In the context of the construction of a country with a strong transportation network, vigorously developing urban public transportation and promoting sustainable urban development has become an inevitable requirement for urban transportation development. Transit signal priority control, as an active priority strategy, can effectively reduce the carbon emissions and delays generated by buses at signal intersections, and improve the quality of bus service. A bus speed probability density function was introduced to study the effect of bus priority control strategy on traffic carbon emission, based on the speed stochastic characteristics of intersection. The effect of main parameters such as delay, stopping times, and speed on traffic carbon emission was analyzed. A bi-level optimization model of single-intersection bus priority control was established using the combination strategy of speed guidance and green extension. The model took the optimal carbon emission reduction of buses and cars with different fuel types in the upstream section of the intersection and the intersection control area as the upper-level objective, the optimal total people delay reduction as the lower-level objective, and the guidance speed as well as the compressed green time of the non-bus-priority phases as the decision variables. The Gauss-Seidel iterative algorithm was used to solve the model. Finally, the established model was applied to the calculation cases for analysis, and the results indicated that under the guidance acceleration and green extension strategy, the overall carbon emission and total passenger delay reduction of the intersection could reach 25.63% and 36.27%, respectively. The model effectively reduced carbon emissions and total passenger delays in the upstream sections of the intersection and the intersection control area, and optimized the overall traffic benefit of the intersection while promoting sustainable development.

Key words: urban traffic, carbon emissions, bus priority control, speed guidance, probability density function

CLC Number:

U491.1⁺7

HU Xinghua, CHEN Xinghui, WANG Ran, et al. Optimization Model of Bus Priority Control Considering Carbon Emissions with Stochastic Characteristics[J]. Journal of South China University of Technology(Natural Science Edition), 2023, 51(10): 160-170.

Figures/Tables 14

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Table 1

Solution steps of Gauss-Seidel algorithm"

算法：Gauss-Seidel

步骤1 固定上层模型的决策变量 $v b 1, 1$ 、 $v b 2, 1$ 、 $g e k$ （k=1， …， n），视下层目标函数为f（t₁， …， t_z ），其中，z为决策变量的个数，t₁， …， t_z 分别为 $v b 1, 1$ ， …， $g e k$ 。设第p次外循环迭代后的下层变量 $T p$ =（ $t 1 p$ ， $t 2 p$ ， …， $t j p$ ， …， $t z p$ ），初始化 $T p$ 中的元素序号j为1，外循环迭代次数p为0，预设目标函数初值为0。根据下层变量的约束条件，随机产生初始解 $T 0$ =（ $t 10$ ， $t 20$ ， …， $t j 0$ ， …， $t z 0$ ）。

步骤2 定义 $T t j -$ 为除 $t j$ 外的变量集， $T j -$ =（t₁， t₂， …， $t j$ ， …， t_z ），赋值 $T p + 1$ = $T p$ ，对下层目标函数的决策变量进行对角化迭代。

步骤3 如果 $t j$ ∈｛ $v b 1, 1$ 、 $v b 2, 1$ 、 $g e k$ ｝， j=j+1，暂时固定 $T t j -$ ，得到f（ $t j, T t j -$ ）， $t j$ ∈（ $t j m i n$ ， $t j m a x$ ）， $t j m i n$ 、 $t j m a x$ 分别为 $t j$ 的上、下界。

步骤4 计算满足 $∂ f t j, T t j - ∂ t j$ =0的 $t j$ 值，标识为 $t j ¯$ 。

步骤5 如果 $t j ¯$ ∈（ $t j m i n$ ， $t j m a x$ ），计算 $m a x f t j m i n, T t j m i n -, f t j ¯, T t ¯ j -, f t j m a x, T t j m a x -$ ；否则，计算 $m a x f t j m i n, T t j m i n -, f t j m a x, T t j m a x -$ ，将其对应的 $t j$ 值赋给 $t j k + 1$ ， j=j+1。

步骤6 小循环终止准则为：如果j>z，p=p+1，执行步骤7，否则返回步骤3。

步骤7 优化上层模型决策变量，暂时固定下层模型中的决策变量，对上层模型中的决策变量进行对角化迭代，更新 $v b 1, 1$ 、 $v b 2, 1$ 、 $g e k$ ，得到 $T p$ 。

步骤8 大循环收敛准则为：如果 $f T p + 1 - f T p$ 满足收敛精度，则停止迭代；否则，j=1，转到步骤2。

步骤9 将求得的未知变量 $v b 1, 1$ 、 $v b 2, 1$ 、 $g e k$ （k=1， …， n）代入目标函数 $∆ E$ 和 $∆ D$ 中，得到对应的目标函数值。

Table 1

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Table 2

Table 3

Table 4

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进口道方向		到达率/（辆·s^-1）		饱和流率/（辆·s^-1）
进口道方向		纯电动小汽车	燃油小汽车	饱和流率/（辆·s^-1）
南进口	直行	0.13	0.76	1.30
南进口	左转	0.10	0.25	0.41
北进口	直行	0.15	0.74	1.30
北进口	左转	0.11	0.26	0.41
东进口	直行	0.18	0.58	1.02
东进口	左转	0.13	0.42	0.72
西进口	直行	0.17	0.65	1.02
西进口	左转	0.13	0.40	0.72

工况类型	能耗/（g·s^-1）
工况类型	减速能耗	加速能耗	怠速能耗
纯电动公交车	0.678 4	2.815 4	1.371 0
天然气公交车	4.731 4	19.635 5	9.561 8
纯电动小汽车	0.254 6	1.100 5	0.525 6
燃油小汽车	1.068 4	4.618 2	2.205 7

进口道方向	多项式系数	b₁/10^-6	b₂/10^-3	b₃/10^-3	b₀/10^-2	R²
进口道方向	多项式基函数次数	x³	x²	x	1	R²
南进口道	直行	-7.34	24.30	-168.00	1.73	0.968
南进口道	左转	-12.30	3.38	43.70	-10.10	0.967
北进口道	直行	-43.80	21.90	-25.70	30.30	0.984
北进口道	左转	-13.20	4.46	1.67	-23.40	0.964
东进口道	直行	-7.68	3.57	42.80	2.37	0.958
东进口道	左转	-23.60	1.07	19.30	-38.20	0.972
西进口道	直行	-7.28	2.58	46.70	25.80	0.967
西进口道	左转	-21.60	1.73	24.30	6.37	0.958

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