# Exploring the Direct and Indirect Use of ICT Measurements in DODME (Dynamic OD Matrix Estimation) +
## 1 Introduction
Bluetooth travel times are usually rather accurate; however, from a practical point of view, they may have two main drawbacks: they imply an additional investment in equipment, namely, the antennas, which most traffic authorities are reluctant to approve for various reasons, and if approved, their layout must satisfy very specific constraints to ensure that the used paths are almost uniquely identified [1; 27]. On the other hand, GPS tracking of equipped vehicle trajectories, or other similar ICT measurements from mobile devices, which are becoming accessible, do not require any investment in specific equipment and ensure a pervasive penetration through the traffic network, enabling the estimation of travel times between selected (likely arbitrary) pairs of points along well-identified paths (sub-paths) in the network, or speed profiles for road segments. Therefore, the inclusion of path travel times from GPS trajectories that are reconstructed from way-points in dynamic origin-destination matrix estimation (DODME) is an interesting research problem, particularly from the perspective of investigating which is the most appropriate algorithmic approach. The aim of this study consisted of a comparison of simulation-optimization methods and a new analytical approach that uses an experimental design that was based on synthetic data. The experimental framework allowed for optionally adding GPS tracking information to traffic count measures and a distance term to a reliable origin-to-destination (OD) historical matrix. We explored how to use a modified stopping criterion that was based on the variation of structural similarity, limiting the number of iterations with respect to classical stopping criteria to improve the quality of the results. In Section 2, this paper reviews the conventional bi-level formulations of the DODME problem, analyzes the requisites for a direct formulation of the inclusion of travel time measurements from ICT applications in the model formulation, and proposes a methodological framework to manage the data and the model. Since the relationships between the travel times and the estimated origin-to-destination (OD) matrices cannot be set up in an analytical form, Section 3 proposes resorting to a derivative-free approach to solve the problem, specifically the stochastic perturbation stochastic approximation (SPSA), and Section 4 proposes a variant that involves splitting the gradient into two components: one that is analytical for those terms of the objective function whose gradient can be computed analytically, while the other was approximated using SPSA. Section 5 develops a proposed alternative formulation using the new ICT measurements in a data-driven fashion to estimate the model components to reformulate it instead of including the measurements directly in the formulation. Section 6 introduces an alternative for measuring the quality of the solution in OD matrix estimation and proposes the application of the new stopping criterion based on this quality measures analysis. Section 7 defines a synthetic experimental framework to conduct a controlled series of experiments to learn about the behavior of the approaches and to investigate the quality of the origin-to-destination (OD) flow estimations. Section 8 reports and discusses the achieved computational results and, finally, Section 9 reports the conclusions of the comparative analysis.