A Primal-Dual Algorithm for Link Dependent Origin Destination Matrix   Estimation
  Origin-Destination Matrix (ODM) estimation is a classical problem in transport engineering aiming to recover flows from every Origin to every Destination from measured traffic counts and a priori model information. In addition to traffic counts, the present contribution takes advantage of probe trajectories, whose capture is made possible by new measurement technologies. It extends the concept of ODM to that of Link dependent ODM (LODM), keeping the information about the flow distribution on links and containing inherently the ODM assignment. Further, an original formulation of LODM estimation, from traffic counts and probe trajectories is presented as an optimisation problem, where the functional to be minimized consists of five convex functions, each modelling a constraint or property of the transport problem: consistency with traffic counts, consistency with sampled probe trajectories, consistency with traffic conservation (Kirchhoff's law), similarity of flows having close origins and destinations, positivity of traffic flows. A primal-dual algorithm is devised to minimize the designed functional, as the corresponding objective functions are not necessarily differentiable. A case study, on a simulated network and traffic, validates the feasibility of the procedure and details its benefits for the estimation of an LODM matching real-network constraints and observations. 
Gabriel Michau, Nelly Pustelnik, Pierre Borgnat, Patrice Abry, Alfredo   Nantes, Ashish Bhaskar, Edward Chung
math.OC cs.DS