A key element in transportation planning is the origin–destination matrix. Observing the origin–destination matrix is achievable through data gathered from traffic sensors. This paper introduces a new mixed-integer nonlinear mathematical programming model to determine the optimal number and location of active sensors required for observing the origin–destination matrix. The model structure is such that it can incorporate additional equations obtained from network characteristics and planning assumptions. The user equilibrium assumption was considered in the sensor location model as a specific case. The user equilibrium state, known as Wardrop’s first principle, can enhance the solution of the model in two ways: it limits the number of paths used between each origin–destination pair and incorporates additional equations into the model. A genetic-based algorithm was developed to solve this model for real-world networks. Numerical examples demonstrated that, depending on the network topology, the number of sensors required to observe the origin–destination matrix was decreased by 10% to 50% when considering the user equilibrium additional equations.
Beygi et al. (Mon,) studied this question.