# Exploring the Direct and Indirect Use of ICT Measurements in DODME (Dynamic OD Matrix Estimation) +
## 8 Computational Results
Figure 5: Number of trips and the MSSIM evolution during the optimization procedure. Figure 6 shows the simulated and real traffic measurements that were related to the objective function in the case of \(w_{2}=1\). Table 1 summarizes the \(R^{2}\) adjustment and the _MSSIM_ between the measurements. Regarding the traffic counts, the inclusion of the travel times in the objective function decreased the \(R^{2}\). On the other hand, the two variants of the SPSA (stochastic perturbation stochastic approximation) with travel times adjusted the paths travel times relative to the real measurements well, but the SPSA with travel times showed greater \(R^{2}\) values. In Figure 6, a remarkable group of outliers is shown for the traffic counts measurements. All these points belonged to the same detector in the outer limits of the study area and appeared for all methods, indicating that the traffic counts could not be satisfied without perturbing the global fit. A general trend can be highlighted: the SPSA (stochastic perturbation stochastic approximation) without travel times method had a greater \(R^{2}\) because the estimation procedure behaved as a metamodel that modified the output matrix in such a way that traffic counts were forced. Nevertheless, as travel times were included, a compromise between the traffic counts and travel times had to be met and a joint enhancement required relaxing the traffic counts fit to obtain a global benefit in the estimation of the output matrix. The obtained results when the historical matrix term was included in the objective function were generally beneficial in terms of the structural similarity and \(R^{2}\) for counts and travel times (if included). These results were consistent with the common practice that considered historical matrices as reliable reference matrices. Obsolete matrices that are available in some practical applications should not be included in the objective function for an origin-to-destination (OD) matrix adjustment. In the left panel of Figure 7, the evolution of the MSSIM indicator, calculated as a comparative index relative to the historical matrix in one of the approaches (DDAF), is shown. Wide oscillations were present in the first few iterations; nevertheless, smooth behavior was found as the optimization progressed, indicating structural similarity pattern convergence to the historical matrix. In the right panel of Figure 7, even a weaker oscillation of the MSSIM indicator (Equation (20)) was obtained when comparing two consecutive \begin{table}
\begin{tabular}{l l c c c c c} \hline \hline  & & \multicolumn{2}{c}{**SPSA**} & \multicolumn{2}{c}{**Hybrid SPSA**} & \multicolumn{2}{c}{**Data-Driven**} \\ \hline  & & **No tt** & **tt** & **No tt** & **tt** & **tt** \\ \hline \multirow{2}{*}{Traffic Counts \((y_{lt})\)} & \(w_{2}=0\) & 0.8297 & 0.7614 & 0.7598 & 0.6485 & 0.6187 \\  & \(w_{2}=1\) & 0.8319 & 0.7488 & 0.7684 & 0.7243 & 0.6620 \\ \hline \multirow{2}{*}{Travel Times \((tt_{k})\)} & \(w_{2}=0\) & - & 0.8312 & - & 0.8371 & - \\  & \(w_{2}=1\) & - & 0.8426 & - & 0.8297 & - \\ \hline \multirow{2}{*}{MSSIM} & \(w_{2}=0\) & 0.9189 & 0.9282 & 0.9371 & 0.9283 & 0.9703 \\  & \(w_{2}=1\) & 0.9207 & 0.9318 & 0.9371 & 0.9278 & 0.9706 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(R^{2}\) adjustments and _MSSIM_ between measurements. Figure 6: Traffic count and travel time linear regressions when \(w_{2}=1\). iterations of the matrix estimates; in terms of structural similarity, this behavior indicated that the proposed DDAF formulation smoothly converged to the resulting matrix.