# Exploring the Direct and Indirect Use of ICT Measurements in DODME (Dynamic OD Matrix Estimation) +
## 9 Conclusions  
The origin-to-destination (OD) estimation problem is an underdetermined problem that, depending on the used seed OD matrix, could lead to the resulting OD matrices fitting traffic counts but losing the OD trip pattern from available historical matrices. We focused on reducing such underdetermination using new ICT traffic measurements and improving the quality of the estimated matrices. The knowledge that was acquired can be summarized in two ideas: first, the stochastic approaches that were based in SPSA (stochastic perturbation stochastic approximation) showed slow convergence and a high computation time. They failed to preserve the structural similarity of the resulting matrix compared with a reliable origin-to-destination (OD) historical matrix and they were incapable of increasing the total number of trips. As a benefit, they allowed for adding as many traffic measurements as desired into the objective function. Second, analytical approaches rely on a dynamic assignment matrix estimation and they become extremely complex when they include additional traffic measurements to the traffic counts. In another work [19], we addressed the estimation of the dynamic assignment matrix from GPS data, and the DODME problem was reformulated, leading to a DDAF method. The quality of the estimated origin-to-destination (OD) matrices was better at preserving the structural similarity of the OD matrix relative to a reliable OD historical matrix, where the number of trips was increased/decreased when needed and fast convergence was obtained. The main contribution of this article relied on the comparison of simulation optimization and the new analytical method using an experimental design that was based on synthetic data. The experimental framework allows for optionally adding information from GPS tracking to traffic count measures and a distance term to a reliable origin-to-destination (OD) historical matrix. Well-known goodness-of-fit indicators (\(R^{2}\), RMSE, and number of trips) and a revised proposal as a structural similarity index were collected for the SPSA (stochastic perturbation stochastic approximation) and DDAF approaches when the stopping criteria were modified. The primary conclusion supports the use of a modified stopping criterion that was based on the variation of structural similarity that limited the number of iterations relative to classical stopping criteria. This new criterion was shown to provide remarkably good results in terms of structural similarity in the DDAF approach. As a secondary conclusion, the DDAF approach that was proposed by the authors is the only method that has been shown to be capable of improving the total number of trips as needed. The number of trips of the estimated matrix has been rarely taken into account as a goodness-of-fit indicator. The best results were obtained for the DDAF approach when a distance term to a reliable historical origin-to-destination (OD) was considered. Figure 7: Relative changes of the MSSIM according to Equations (19) and (20) for the data-driven results when \(w_{2}=1\). The performed band used \(\epsilon=10^{-3}\). Lastly, but not least, adding a distance term to a reliable origin-to-destination (OD) historical matrix in the SPSA studied approaches and travel time data that were derived from GPS traces were shown to benefit the quality of the estimated OD matrix, although never reaching the remarkable results obtained with the DDAF approach. The results for the SPSA (stochastic perturbation stochastic approximation) approaches indicated an excellent fit to traffic counts and travel times at the expense of structural similarity and slow progress on the number of trips fitting to the ground truth value. Conceptualization, X.R.-R., L.M. and J.B.; methodology, [PERSON]-R., L.M. and J.B.; software, [PERSON]-R., L.M. and J.B.; validation, X.R.-R., L.M. and J.B.; formal analysis, [PERSON]-R., L.M. and J.B.; investigation, [PERSON]-R., L.M. and J.B.; resources, [PERSON]-R., L.M. and J.B.; data curation, [PERSON]-R., L.M.