Boundary Conditions Estimation on a Road Network Using Compressed Sensing
Michele Simoni, Ofer Eldad, Andrew Alexander and Christian Claudel, February 2016
This report presents a new boundary condition estimation framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on Hamilton-Jacobi equation, we pose the problem of estimating the boundary conditions of the system on a network, as a Mixed Integer Linear Program (MILP). We show that this framework can handle various types of traffic flow measurements, including floating car data or flow measurements. To regularize the solutions, we propose a compressed sensing approach in which the objective is to minimize the variations over time (in the L1 norm sense) of the boundary flows of the network. We show that this additional requirement can be integrated in the original MILP formulation, and can be solved efficiently for small to medium scale problems.
Keywords: OD Matrix Estimation, Flow Model, Mixed Integer Linear Programming
ENTIRE REPORT (Adobe Acrobat File – 530 KB)