高速公路网络最小检测器布设新方法  

A new minimum detector layout method to get any section traffic flow of expressway network

作　　者：柳波[1,2] 余红红[1,2] 张生[3] 

机构地区：[1]江苏省城市规划设计研究院宿迁分院 [2]宿迁市城市规划设计研究院有限公司,江苏宿迁223800 [3]长沙理工大学交通运输工程学院,湖南长沙410004

出　　处：《交通科学与工程》2015年第1期74-78,84,共6页Journal of Transport Science and Engineering

基　　金：国家自然科学基金资助项目(51408058);湖南省科技计划项目(2014GK3023)

摘　　要：对节点和路段进行定义,探索节点数目与路段数目之间的数量关系。根据流量守恒原则,建立了一个包含n+1个方程、3n-m个变量的齐次线性方程组。通过对方程组的系数矩阵进行初等行变换,直到找到一个最大无关向量组。将无关组向量对应的变量命名为基变量,其余变量命名为非基变量,所得到的基变量总可用非基变量表示。因变量与路段一一对应,只要在非基变量所对应的路段布设检测器,就可确定整个网络中所有路段的流量。对最小检测器布设数目的存在性和唯一性进行了证明,给出了任意网络检测器布设率的通用公式。应用该方法,设计了贵阳市区部分高速公路网络的最小检测器布设方案。The expressway nodes and sections are defined,and the quantitative relation ship between the node number and the section number is studied.A system of homogeneous linear equations containing n＋1equations and 3n-mvariables are established based on the principle of the flow conservation.By transferring the coefficient matrix of the equations with the elementary row transformation,one of the biggest independent vector group will be found and named,those variables corresponding the vector group are regarded as basic variables and the other variables as nonbasic variables.Therefore,these basic variables are always substituted by the nonbasic variables.Because the relationship of one-to-one correspondence between sections and variables exists,all sections flow can be obtained by setting traffic detectors in those sections corresponding the nonbasic variables.The existence and uniqueness of the minimum detector layout number are also demonstrated and the general formula of the detector setting rate is given.A minimum detector layout scheme is designed in accordance with the method proposed,which is applied in some expressway networks of Guiyang.

关 键 词：高速公路 最小检测器布设 流量守恒 最大向量无关组 

分 类 号：U491.1[交通运输工程—交通运输规划与管理]