Optimization of Scanning and Counting Sensor Layout for Full Route Observability with a Bi-Level Programming Model

Utilizing the data obtained from both scanning and counting sensors is critical for efficiently managing traffic flow on roadways. Past studies mainly focused on the optimal layout of one type of sensor, and how to optimize the arrangement of more than one type of sensor has not been fully researched. This paper develops a methodology that optimizes the deployment of different types of sensors to solve the well-recognized network sensors location problem (NSLP). To answer the questions of how many, where and what types of sensors should be deployed on each particular link of the network, a novel bi-level programming model for full route observability is presented to strategically locate scanning and counting sensors in a network. The methodology works in two steps. First, a mathematical program is formulated to determine the minimum number of scanning sensors. To solve this program, a new 'differentiating matrix' is introduced and the corresponding greedy algorithm of 'differentiating first' is put forward. In the second step, a scanning map and an incidence matrix are incorporated into the program, which extends the theoretical model for multiple sensors' deployment and provides the replacement method to reduce total cost of sensors without loss of observability. The algorithm developed at the second step involved in two coefficient matrixes from scanning map and incidence parameter enumerate all possibilities of replacement schemes so that cost of different combination schemes can be compared. Finally, the proposed approach is demonstrated by comparison of Nguyen-Dupuis network and real network, which indicates the proposed method is capable to evaluate the trade-off between cost and all routes observability.