frame theory

For several decades, finding the optimal location of counting sensors in a traffic network to obtain the best estimates of the O-D matrix has attracted a growing amount of attention. The availability and the accuracy of a priori data in a network such as O-D matrix and route choice probabilities on one hand, and the complexity of the mathematical operations for solving the location problem even in not a large network, on the other hand, are two main concerns of the presented methods. This paper aims to propose a method that identifies optimum locations for counting sensors without utilizing any a priori data. Relying on the network topological characteristics and link travel times as the representation of the network’s pattern of trips is the core concept of this study. By taking benefit of the frame theory algebraic operations, needless of any pre-given a priori data, the location set vector with higher coverage on the network route vectors is identified as the optimal location set of the sensor-equipped network links based on its representation in the route-vectors frame. The most probable used paths are identified utilizing an efficient path algorithm. Additionally, by taking advantage of the matrix operations, the novel method obviates the calculations required in methods using linear or non-linear programming solutions. The presented method is applied on a test network and the results show that in comparison to the non-linear programming method, the proposed method finds a better solution.