基于转弯比例的检测器布设与流量推算唯一性

Counting Sensor Location Problem Based on Turning Ratios and Uniqueness of Traffic Flow Solution

摘要:

基于交叉口转弯比例列出路网流量守恒的线性方程组，其系数矩阵表示路网中路段间交通流向的逻辑关系，采用“点线变换”的方法给出这种逻辑关系的有向图表示，从而使得流量守恒方程组的系数矩阵同时也是逻辑关系有向图的邻接矩阵。在对逻辑关系有向图进行分析的基础上，采用“回路组”的概念和Taussky定理，得到了系数矩阵的秩与方程数相等的结论，证明了“封闭环”式检测器布设方案可唯一地确定路网内所有路段的流量，并进一步指出检测器布设方案并不唯一。

Abstract:

The system of linear equations can be given to describe the flow conservation in the road network based on the turning ratios at intersection. The coefficient matrix of the system describes the relationship of the flow direction among links. By the point-arc exchanging from the traditional road network topology, a directed graph can be used to represent the flow-direction relationship, with the coefficient matrix of the flow conservation equations as its adjacent matrix. The coefficient matrix describes a directed graph composed by several directed-circle groups. According to the performance of directed-circle group and Taussky’s theorem of nonsingular matrix judgment, the conclusion of the rank of the coefficient matrix is equal to the number of the rows is given. Based on this conclusion, the fact that the close-ring sensor location design can give the unique link flow solution over the network is proven. Finally, the fact that the design of the sensor location based on the turning ratios at intersection is not unique is discussed.