A practical approach to assignment-free Dynamic Origin–Destination Matrix Estimation problem

Dynamic traffic models require dynamic inputs, one of the main ones being the Dynamic Origin–Destinations (OD) matrices describing the variability over time of the trip patterns across the network. The Dynamic OD Matrix Estimation (DODME) is a challenging problem since no direct observations are available, and therefore one should resort to indirect estimation approaches. Among the most efficient approaches, the one that formulates the problem in terms of a bi-level optimization problem has been widely used. This formulation solves at the upper level a nonlinear optimization problem that minimizes some distance measures between observed and estimated link flow counts at certain counting stations located in a subset of links in the network, and at the lower level a traffic assignment that estimates these link flow counts assigning the current estimated matrix. The variants of this formulation differ in the analytical approaches that estimate the link flows in terms of the traffic assignment and their time dependencies. Since these estimations are based on a traffic assignment at the lower level, these analytical approaches, although numerically efficient, imply a high computational cost. The advent of ICT applications has made available new sets of traffic-related measurements enabling new approaches; under certain conditions, the data collected allows to estimate the most likely used paths, from which a de facto assignment matrix can be computed. This allows extracting empirically similar information to that provided by the dynamic traffic assignment that is used in the analytical approaches. This paper explores how to extract such information from the recorded commercial data, proposes a new constrained non-linear optimization model to solve the DODME problem, with a reduced number of variables linearly depending on network size instead of quadratically. Moreover, the bilevel iterative process and the traffic assignment need are avoided. Validation and computational results on its performance are presented.