基于Stackelberg博弈的时变双层交通分配模型
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摘要
提出一个时变双层交通分配模型,其中上层网络管理者设立了一个路段的最大排队长度,其目标是使由网络流和排队长度定义的总出行时间最小.目标函数在离散时段内以路段流量和排队长度作为决策变量,同时考虑不同类型的信号交叉口延误的影响.下层网络用户的反应依赖于上层管理者的决策,其选择是使自身感知阻抗最小的路径,服从一个基于成对组合Logit的路径选择模型,构成一个成对组合Logit的均衡分配问题.结合了交通分配和流传播方法,将其表示为一个均衡约束下的双层数学规划问题,形成了一个Stackelberg非合作博弈.使用遗传算法求解该双层规划问题,并采用实证分析来表现模型的特征和算法的计算表现.结果表明路径重叠、路段流量、路段排队长度等因素对网络均衡流分布均有显著影响.
A time varying bi-level transportation assignment model is proposed in which the upper level network administrator establishes the maximum queue of a link to minimum total travel time defined by network flow and length of queue.The objective function uses the link flow and queue length as decision variables in discrete time,taking into account the influence of different types of signalized intersection delays.The response of users from the lower level network depends on the decision of the upper level manager.They choose a route that minimizes their own perceived impedance and follow a paired combinatorial legit-based route choice model and constitutes a paired combinatorial legit equilibrium assignment problem.The formula combines the methods of traffic assignment and flow propagation and presents a bi-level mathematical programming problem under equilibrium constraints,forming a Stackelberg non-cooperative game.A genetic algorithm is used to solve the bi-level problem and an positive analysis is performed to express the characteristics of the model and the computational performance of the algorithm.The results show that the overlap of routes,the traffic volume of the link and the queue length of the link all have significant effects on the distribution of network equilibrium flows.
A time varying bi-level transportation assignment model is proposed in which the upper level network administrator establishes the maximum queue of a link to minimum total travel time defined by network flow and length of queue.The objective function uses the link flow and queue length as decision variables in discrete time,taking into account the influence of different types of signalized intersection delays.The response of users from the lower level network depends on the decision of the upper level manager.They choose a route that minimizes their own perceived impedance and follow a paired combinatorial legit-based route choice model and constitutes a paired combinatorial legit equilibrium assignment problem.The formula combines the methods of traffic assignment and flow propagation and presents a bi-level mathematical programming problem under equilibrium constraints,forming a Stackelberg non-cooperative game.A genetic algorithm is used to solve the bi-level problem and an positive analysis is performed to express the characteristics of the model and the computational performance of the algorithm.The results show that the overlap of routes,the traffic volume of the link and the queue length of the link all have significant effects on the distribution of network equilibrium flows.
引文
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[10]陆化普,蔚欣欣,卞长志.发生吸引量不确定的离散交通网络设计模型[J].统计与决策,2011(6):8-12.
[2]史峰,李志纯.网络扩容和拥挤道路使用收费的组合模型及求解算法[J].中国公路学报,2003,16(2):90-94.
[3]赵泽斌,安实,王健.基于道路扩容的道路拥挤定价收入再分配研究[J].中国管理科学,2007,15(1):81-85.
[4]李志瑶,隽志才,宗芳.居民出行时间选择及拥挤收费政策[J].交通运输工程学报,2005,5(3):105-110.
[5]张华歆,周溪召.多模式交通网络的拥挤道路收费双层规划模型[J].系统工程理论方法应用,2005,14(6):546-551.
[6]徐建闽,首艳芳,卢凯.基于双层规划模型的交通信号区域协调控制[J].华南理工大学学报(自然科学版),2011,39(3):95-100.
[7]安梅,高自友.模式间相互影响时估计O-D需求的双层规划模型及求解算法[J].系统工程理论与实践,2001,21(4):36-42.
[8]许项东,程琳.城市道路单行系统布局优化的双层规划模型和混合算法[J].系统工程理论与实践,2009,29(10):180-187.
[9]田晟,马美娜,许凯.随机均衡配流下的连续性交通网络设计[J].华南理工大学学报:自然科学版,2017,45(11):23-29.
[10]陆化普,蔚欣欣,卞长志.发生吸引量不确定的离散交通网络设计模型[J].统计与决策,2011(6):8-12.