Density/Flow reconstruction via heterogeneous sources and Optimal Sensor Placement in road networks

• Flow and density reconstruction problem with heterogeneous information sources.
• Calibration of the Fundamental Diagram via gradient descent methods.
• Optimal Sensor Placement problem in the context of flow reconstruction.
• Heuristic strategy for Optimal Sensor Placement via Virtual Variances.
• Implementation in the real world scenario of the Rocade Sud in Grenoble, France.

This paper addresses the two problems of flow and density reconstruction in Road Transportation Networks with heterogeneous information sources and cost effective sensor placement. Following a standard modeling approach, the network is partitioned in cells, whose vehicle densities change dynamically in time according to first order conservation laws. The first problem is to estimate flow and the density of vehicles using as sources of information standard fixed sensors, precise but expensive, and Floating Car Data, less precise due to low penetration rates, but already available on most of main roads. A data fusion algorithm is proposed to merge the two sources of information to estimate the network state. The second problem is to place sensors by trading off between cost and performance. A relaxation of the problem, based on the concept of Virtual Variances, is proposed and solved using convex optimization tools. The efficiency of the designed strategies is shown on a regular grid and in the real world scenario of Rocade Sud in Grenoble, France, a ring road 10.5 km long.