高速路网不停车收费车道优化布设方法

Optimal Deployment of Electronic Toll Collection Lanes for Freeway Network

合理设置高速公路收费站ETC(Electronic Toll Collection)车道数量,对高速公路通行效率至关重要。针对目前路网中ETC与MTC(Manual Toll Collection)车辆混行的情况,考虑ETC的普及率,结合多用户路网均衡模型和排队论方法,建立基于双层规划模型的高速路网ETC车道优化布设方法。上层模型以车辆总通行时间最小为目标,优化设置进出收费站的ETC车道数量;下层模型为多用户路网均衡模型,反映ETC和MTC车辆的路径和收费车道选择行为。下层模型通过设计收费站的等价拓扑结构,表征收费站的车道使用规则及车辆的收费车道选择行为,并采用排队论方法估计ETC和MTC车道的收费排队时间。根据模型的特点设计了基于主动集的启发式算法,利用参数二进制与拉格朗日函数法确定迭代下降方向,解决了下降方向与步长难以计算的问题;通过内嵌优化函数的方式,保证在主动集转化过程中上层约束均不会失效,且避免了迭代过程中的模型解退化问题。基于上海市绕城高速进行实证分析,结果表明:随着ETC普及率的提升,收费排队时长按照负指数趋势下降;与按比例布设ETC车道的方法相比,所提方法最高可降低57.4%的收费排队时间,且该方法可以避免ETC车道布设过多对于MTC车道通行能力挤压造成的负面效果。研究成果可以有效指导高速路网ETC车道的布设,提高路网通行效率。

Appropriate allocation of the required number of electronic toll collection(ETC)lanes at toll stations is crucial for achieving optimal operation efficiency of a freeway network.Accordingly,this study explored the current situation of mixed ETC and manual toll collection(MTC)vehicles in the road network,considering the installation rate of ETC vehicles,and developed a bi-level programming model to optimize the deployment of ETC lanes based on the multi-class network equilibrium model and queuing theory.The upper-level model optimized the number of ETC lanes at the entry and exit toll stations to minimize the total vehicle travel time.The lower-level model was a multi-class network equilibrium model that reflected the path and toll lane selection behavior of ETC and MTC vehicles.In the lower-level model,an equivalent topological structure was proposed to represent a toll station to describe the rules for usage of the toll lanes and the behavior of vehicles in selecting toll lanes.In addition,the queuing times of the ETC and MTC lanes were estimated using queuing theory.A heuristic algorithm based on an active set was designed according to the characteristics of the proposed model.The algorithm used the parameter binary method and Lagrangian function to determine the iterative descent direction,whereby the problem concerning calculation of the descent step and direction was solved.The embedded optimization function ensured that the upper constraints would not be invalid during the conversion of the active set,and the degradation problem of the model solutions in the iterative process was avoided.The developed methodology was evaluated on a ring freeway in Shanghai.The results show that with an increase in the ETC penetration rate,the queuing time decreases according to the negative exponent rule.When compared with the method of proportionally allocating the ETC lanes,the method proposed in this paper afforded a reduction in queuing time by up to 57.4%,whereby the negative effects of excessive ETC lanes on the capacity of MTC lanes can be avoided.Overall,this research provides guidelines for the layout of the ETC lanes in freeway networks and could improve their operational efficiency.