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

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.