A network sensor location problem for link flow observability and estimation

Effective traffic sensor systems can collect precise and reliable real-time traffic information to improve the performance of traffic guidance and traffic flow control. In particular, link flow data are among the most intuitive sources of information for reflecting road congestion and can be further used to estimate origin-destination (OD) and path demands. To efficiently obtain link flow information, much effort has been devoted to the network sensor location problem for link flow observability and estimation. The objective of the observability problem is to minimize the number of installed sensors while ensuring full link observability, whereas the objective of the link flow estimation problem is to maximize the information gain or minimize the estimation deviations given a limited number of sensors. To the best of our knowledge, our study is the first to integrate link flow observability, flow estimation and the impact of prior link flow uncertainty into the sensor location problem. Accordingly, we propose two new models. In detail, we first present a new mixed-integer optimization model to achieve full link flow observability. Since only topological information is used, this is a generalized version of the existing models as well as a basic representation of other models for the flow estimation problem in our study. The second model integrates linear regression into the traffic sensor location problem. The results of this model provide both location selection and estimation methods for the decision maker. Furthermore, to address the problems of data loss and low computational efficiency in large-scale networks, we exploit the concepts of ambiguity sets and linear decision rules in robust optimization to generate a tractable approximate counterpart to the above sample-based link estimation model. Sample information is further integrated into this tractable approximate model to enhance the simulation performance without incurring a loss in computational efficiency. Numerical experiments are conducted for networks of different sizes. The results show significant improvement in surveillance performance, with a significant reduction in the number of required sensors and good estimation performance. Our work also verifies that when the number of samples is small, compared with the sample-based model, our enhanced tractable approximate model has several advantages, including (i) better out-of-sample performance, (ii) a similar noninferred link distribution, (iii) less dependence on sample size, and (iv) lower computation time requirements for large-scale problems.