An efficient algorithm for real-time estimation and prediction of dynamic origin–destination tables

The problem of estimating and predicting Origin–Destination (OD) tables is known to be important and difficult. In the specific context of Intelligent Transportation Systems (ITS), the dynamic nature of the problem and the real-time requirements make it even more intricate. We consider here a least-squares modeling approach for solving the OD estimation and prediction problem, which seems to offer convenient and flexible algorithms. The dynamic nature of the problem is represented by an autoregressive process, capturing the serial correlations of the state variables. Our formulation is inspired from Cascetta et al. and Ashok and Ben-Akiva. We compare the Kalman filter algorithm to LSQR, an iterative algorithm proposed by Paige and Saunders for the solution of large-scale least-squares problems. LSQR explicitly exploits matrix sparsity, allowing to consider larger problems likely to occur in real applications. We show that the LSQR algorithm significantly decreases the computation effort needed by the Kalman filter approach for large-scale problems. We also provide a theoretical number of flops for both algorithms to predict which algorithm will perform better on a specific instance of the problem.