【作者】 吕瑜佩；

【导师】 张鹏；

【作者基本信息】 上海大学 ， 流体力学， 2020， 博士

【摘要】 本文基于交通流LWR(Lighthill-Whitham-Richards)模型,研究在交通路网上满足用户均衡条件但在路段上可以具有激波结构的定常解。针对单OD简单路网,详细讨论了定常解的求解方法。主要内容如下。对连接两个交叉口的多条路段,即所谓的复合路段,讨论了交通流从上游交叉口出发到达下游交叉口的用户均衡条件。据此,得到了无激波定常解的用户均衡曲线和复合路段基本图,从而对给定的复合路段(关于面积的)平均密度,可确定所有路段的密度与总流。还讨论并证明了基本图的一系列数学性质。基于对单OD路网上游和下游复合路段基本图的比较,阐明了当且仅当用户总数介于某一特定区间时,需引入激波以保证解的存在性,此时路网流量受路网外的下游路况限制,或已经达到瓶颈交叉口的最大值。据此,建立了路网上用户总数与定常解之间完整的对应关系,并通过引入激波高密度部分交通流进入下游的优先权系数,解决了解的唯一性问题。这隐含,除非路网不存在瓶颈交叉口,否则,对用户总数在特定区间的取值,不存在经典交通分配理论所预设的无激波结构定常解。构造了LWR模型以收敛于定常解为目标的数值求解格式。基本算法基于模型方程的单调格式和交叉口Riemann解,主要工作是基于定常解的解析性质,即关于用户均衡和优先权系数的信息,配置上游路段进入下游路段的交通流比例,从而得到交通流由交叉口进入下游路段的边界条件。数值模拟分别针对包括一个一进二出和一个二进一出交叉口的单OD简单路网,以及包括两个二进二出交叉口的单OD简单路网,取得了收敛的结果。本文的研究工作改进了经典交通分配理论中将路段上的密度预设为常数的这一明显的缺陷,无疑将推动相关领域新的研究。在智慧交通背景下,将为实施路网的交通流量均衡分配提供核心理论支持和合理的模型和数值模拟方案。更多还原

【Abstract】 The dissertation studies a steady-state solution to the dynamic traffic flow model on a road network,which satisfies the user-equilibrium conditions but may have shock structures on road sections.For a simple road network with just one Origin(O)and one Destination(D),it discusses the method for solving the problem in detail.The main contents are briefly introduced in the following.For a composite roads unit,which is defined as a set of roads connected by an upstream and a downstream junctions,the user-equilibrium conditions are discussed in detail.Accordingly,without shocks we derive the user-equilibrium curves and the fundamental diagram on the roads unit,which respectively help determine the densities on all roads and the total flow,given the average density that is over the area of the unit.Many properties of the fundamental diagram are indicated with strictly mathematical proofs.For the aforementioned one OD road network,we indicate that shock structures have to be introduced to guarantee the existence of solution if and only if total number of vehicles falls into a specific interval,when the flow is limited by road conditions outside in the downstream,or when the flow has already reached the capacity at the bottleneck junction.As a consequence,we are able to completely establish the correlation between the total number of vehicles and the steady-state solution.Moreover,the solution is uniquely determined by introducing priority coefficients for vehicles in higher density region of the shock to enter the downstream road sections.The argument implies that,without shocks the steady-state solution assumed in the classical Transportation Assignment Theory does not exist unless there are no any bottleneck junctions on the road network.A numerical scheme of the LWR(Lighthill-Whitham-Richards)model is designed for evolution of traffic flow into the discussed steady-state solution.Based upon the monotone scheme of the model and the Riemann solver at the junction,the main task for the designing is to determine the percentages of traffic flow at upstream road sections for their entering the downstream road sections,according to the analytical properties of the steady-state solution,i.e.,the user-equilibrium conditions and the information about the priority coefficients.According to the coefficients,we can determine the boundary conditions for traffic flow entering the downstream road sections through the junction.The convergence is observed for numeral simulation on simple one OD road networks with a 1 × 2 and a 2 × 1 junctions and with two 2 × 2junctions,respectively.This research work significantly improves a remarkable shortcoming in classical Transportation Assignment Theory,which assumes that the density is constant in road sections.Therefore,it will surely promote new studies in the related research fields.Moreover,it will provide with key theoretical support and robust modeling and simulation scheme for implementation of equilibrium flow assignments under the background of the smart transportation system.更多还原