## 4 Numerical Results
### Real-Scale Urban Network  
The real-scale urban test network is the network of Benevento, a town in the south of Italy with about 61,000 inhabitants. The network, as represented in Figure 4, has 1577 oriented links, comprising about 216 km of roads, 678 nodes and 80 centroids (66 internal and 14 external). The peak-hour OD matrix was made available by studies carried out while drawing up the Urban Traffic Plan. The route choice model is Multinomial Logit with an implicit enumeration of paths according to the algorithm proposed in Reference [27].  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{8}{c}{**Percentage Variations with Respect to MSA**} \\ \hline
**Matrix** & **0.6**\(d\) & **0.8**\(d\) & **1.0**\(d\) & **1.2**\(d\) & **1.4**\(d\) & **1.6**\(d\) & **1.8**\(d\) & **2.0**\(d\) \\ \hline \(\eta=1\)(MSA) & - & - & - & - & - & - & - \\ \(\eta=0.9\) & \(-14\%\) & \(\mathbf{-13\%}\) & \(-11\%\) & \(-17\%\) & \(-13\%\) & \(-17\%\) & \(-18\%\) \\ \(\eta=0.8\) & \(-14\%\) & \(0\%\) & \(-24\%\) & \(-26\%\) & \(-25\%\) & \(-30\%\) & \(-31\%\) & \(-32\%\) \\ \(\eta=0.7\) & \(-29\%\) & \(38\%\) & \(-33\%\) & \(-34\%\) & \(-36\%\) & \(-41\%\) & \(-43\%\) \\ \(\eta=0.6\) & \(-29\%\) & \(75\%\) & \(-36\%\) & \(-44\%\) & \(-45\%\) & \(-50\%\) & \(-50\%\) & \(-52\%\) \\ \(\eta=0.5\) & \(\mathbf{-43\%}\) & \(88\%\) & \(-40\%\) & \(-50\%\) & \(-52\%\) & \(-56\%\) & \(-57\%\) & \(-58\%\) \\ \(\eta=0.4\) & \(\mathbf{-43\%}\) & \(63\%\) & \(\mathbf{-49\%}\) & \(\mathbf{-55\%}\) & \(\mathbf{-57\%}\) & \(\mathbf{-61\%}\) & \(\mathbf{-59\%}\) \\ \(\eta=0.3\) & \(-29\%\) & \(38\%\) & \(-47\%\) & \(-52\%\) & \(-52\%\) & \(-54\%\) & \(-51\%\) & \(-47\%\) \\ \(\eta=0.2\) & \(-14\%\) & \(88\%\) & \(-24\%\) & \(-31\%\) & \(-30\%\) & \(-32\%\) & \(-28\%\) & \(-21\%\) \\ \(\eta=0.1\) & \(14\%\) & \(225\%\) & \(36\%\) & \(28\%\) & \(32\%\) & \(30\%\) & \(40\%\) & \(53\%\) \\ \(\eta=0.05\) & \(71\%\) & \(463\%\) & \(149\%\) & \(143\%\) & \(155\%\) & \(153\%\) & - & - \\ \(\eta=0.01\) & \(343\%\) & \(2175\%\) & \(1020\%\) & - & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: _Cont._  
Figure 4: Urban real-scale network.  
In order to test the proposed algorithms under several network congestion levels, over the available OD matrix, seven other matrices were generated, multiplying all cells of the OD matrix by the following factors: 0.6, 0.8, 1.2, 1.4, 1.6, 1.8, and 2.0. The corresponding average saturation degrees are summarised in Table 5.  
On this network, we tested the proposed algorithm with the same values of parameter \(\eta\) as those adopted for the small test network; we tested the algorithm with two different values of the coefficient of variation (standard deviation to mean ratio), \(C_{v}\), equal to 0.10 and 0.05. Moreover, in these cases, the proposed algorithm was able to reduce the iterations for convergence with some values of \(\eta\) lower than 1 (MSA). In this case, the best performances were obtained with values between 0.4 and 0.6 (see Table 6) for \(C_{v}\) = 0.10 and between 0.3 and 0.6 (see Table 7) for \(C_{v}\) = 0.05; the reductions in the number of iterations reached -76% (\(C_{v}\) = 0.10) and -79% (\(C_{v}\) = 0.05) with respect to the traditional version of the MSA algorithm. In Figures 5 and 6, the results of Tables 6 and 7 are illustrated. Moreover, in this case, the utility of the proposed algorithm is more significant for medium-high demand levels.  
In bold are reported the best results.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Iterations Needed for Convergence**} \\ \hline
**Matrix** & **0.6** \(d\) & **0.8** \(d\) & **1.0** \(d\) & **1.2** \(d\) & **1.4** \(d\) & **1.6** \(d\) & **1.8** \(d\) & **2.0** \(d\) \\ \hline \(\eta\) = 1(MSA) & 5 & 8 & 17 & 32 & 50 &