智能网联公交车出站强制换道的演化博弈机制

doi:10.13229/j.cnki.jdxbgxb.20220207

摘要/Abstract

摘要：

为缓解智能网联公交车出站强制换道时与社会车辆之间的冲突，分析了智能网联公交车与社会车辆行为决策的演化博弈机制。考虑社会车辆为人工驾驶社会车辆和智能网联社会车辆两种场景，从安全效用、时间效用和节能效用角度构建演化博弈效用函数，并以此建立演化博弈的复制动态方程。根据动态博弈系统的雅克比矩阵的行列式和迹，分析不同情况下博弈的均衡点及其稳定性，并探讨动态博弈系统对合作策略与非合作策略差值的灵敏度。结果表明，动态博弈系统可能的演化方向包括“智能网联公交车换道、社会车辆让路”，“智能网联公交车不换道、社会车辆不让路”和“智能网联公交车不换道、社会车辆让路”。从整体最优的角度看，调整社会车辆安全效用和时间效用的相关变量，能够保证更多车辆在智能网联公交车出站强制换道过程中的安全和效率。节能效用对（换道，让路）策略组合有促进作用，对（不换道，不让路）策略组合有抑制作用。

关键词: 交通工程, 智能网联公交车, 强制换道, 演化博弈, 行为决策

Abstract:

To relieve the conflicts between the intelligent connected bus and the social vehicle in the mandatory lane changing for bus exiting， the evolutionary game mechanisms for their behavioral decision-makings are analyzed. Two scenarios where the social vehicles are human-driven and intelligent connected are considered. The utility functions in different strategy profiles of the evolutionary game are formulated from the perspectives of safety utility， time utility and energy-saving utility. On this basis， the replicator dynamics equations for the two scenarios are constructed. According to the determinant and trace of Jacobi matrix in the dynamic game system， the equilibrium points and their stability in different situations are analyzed deeply. The sensitivity of evolutionary results to the difference between the cooperative and non-cooperative strategies is explored. The results reveal that： the possible evolutionary directions in the dynamic game system involve “intelligent connected buses changing lanes， and social vehicles giving way”， “intelligent connected buses not changing lanes， and social vehicles not giving way”， and “intelligent connected buses not changing lanes， and social vehicles giving way”. From the perspective of overall optimization， adjusting the relevant variables of the safety and time utility of social vehicles can ensure the safety and efficiency of more vehicles in the process of mandatory lane changing of intelligent connected bus. The energy-saving utility promotes the strategy profile of changing lanes and giving way， and inhibits the strategy profile of not changing lanes and not giving way.

Key words: traffic engineering, intelligent connected bus, mandatory lane changing, evolutionary game, behavioral decision-making

中图分类号:

U121

杜筱婧,姚荣涵. 智能网联公交车出站强制换道的演化博弈机制[J]. 吉林大学学报(工学版), 2024, 54(1): 124-135.

Xiao-jing DU,Rong-han YAO. Evolutionary game mechanism of mandatory lane changing for exiting for intelligent connected bus[J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(1): 124-135.

图/表 13

图1

图2

表1

场景1中博弈的效用矩阵"

策略	让路	不让路
换道	$u B T - 11 +$ ， $u V S - 11 +$	$u B S - 12 -$ ， $u V S - 12 -$
不换道	$u B S - 21 + + u B T - 21 -$ ， $u V S - 21 + + u V T - 21 -$	$u B S - 22 +$ ， $u V T - 22 +$

表1

表2

场景2中博弈的效用矩阵"

策略	让路	不让路
换道	$u B T - 11 +$ ， $u V S - 11 + + u V E - 11 +$	$u B S - 12 -$ ， $u V S - 12 -$
不换道	$u B S - 21 + + u B T - 21 -$ ， $u V S - 21 + + u V T - 21 - + u V E - 21 +$	$u B S - 22 +$ ， $u V T - 22 +$

表2

表3

各均衡点对应的雅克比矩阵的行列式和迹"

均衡点	行列式	迹
（0，0）	$- Δ B 2 ? Δ S 2$	$- Δ B 2 + Δ S 2$
（0，1）	$Δ B 1 ? Δ S 2$	$- Δ B 1 - Δ S 2$
（1，0）	$Δ B 2 ? Δ S 1$	$Δ B 2 + Δ S 1$
（1，1）	$- Δ B 1 ? Δ S 1$	$Δ B 1 - Δ S 1$
$Δ S 2 / Δ S 2 - Δ S 1, Δ B 2 / Δ B 2 - Δ B 1$	$Δ B 1 ? Δ B 2 ? Δ S 1 ? Δ S 2 (Δ B 1 - Δ B 2) ? (Δ S 1 - Δ S 2)$	0

表3

表4

均衡点稳定性分析"

均衡点	情形1	情形2	情形3	情形4
（0，0）	鞍点	稳定点	鞍点	稳定点
（0，1）	稳定点	鞍点	鞍点	不稳定点
（1，0）	不稳定点	不稳定点	不稳定点	不稳定点
（1，1）	鞍点	鞍点	稳定点	稳定点
$Δ S 2 / Δ S 2 - Δ S 1, Δ B 2 / Δ B 2 - Δ B 1$	-	-	-	纳什均衡点

表4

表5

不同类型效用的统计结果"

效用	物理量	平均值	最大值	最小值	归一化值
安全效用/（m·s^-2）	$u B S - 12 -$	-1.52	-0.01	-3.08	-0.49
	$u B S - 2 j +$	1.44	3.36	0.02	0.42
	$u V S - i 1 +$	0.61	1.91	0.01	0.32
	$u V S - 12 -$	-0.82	-0.01	-3.53	-0.23
时间效用/s	$u B T - 11 +$	664.75	1190.00	234.50	0.45
	$u B T - 21 -$	-778.10	-448.90	-1504.80	-0.31
	$u V T - 21 -$	-4.07	-2.30	-9.70	-0.24
	$u V T - 22 +$	3.42	7.10	1.50	0.34
节能收益/［kg·（100 km）^-1］	$u V E - i 1 +$	7.44	93.00	4.70	0.03

表5

图3

图4

图5

图6

图7

图8

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