## 3 Results and Discussion
### Results and Discussion of Experiment 3  
Figures 13-15 present the period index vs. network speed, period index vs. network density, and period index vs. network flow, respectively. Figures 16-18 show the network density vs. network speed, network speed vs. network flow, and network density vs. network flow, respectively. The distance between the network density vs. network speed pattern of simulation 1 (green dots) and the pattern of simulation 2 (green circles) is \(\mathrm{D}_{\mathrm{speed}}^{\mathrm{S1S2}}=0.0348\) m/s, between simulation 2 and simulation 3 (green crosses) is \(\mathrm{D}_{\mathrm{speed}}^{\mathrm{S2S3}}=0.3265\) m/s, and between S1 and S3 is \(\mathrm{D}_{\mathrm{speed}}^{\mathrm{S1S3}}=0.3663\) m/s. Therefore, the DS patterns of S1 and S2 are similar, the DS patterns of S2 and S3 are similar, and the DS patterns of S1 and S3 are similar. \(\mathrm{D}_{\mathrm{flow}}^{\mathrm{S1S2}}=[0.13424-0.13352]=0.000719\) veh/s, \(\mathrm{D}_{\mathrm{flow}}^{\mathrm{S2S3}}=[0.13352-0.12374]=0.009779\) veh/s,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  
and \(\text{D}_{\text{flow}}^{\text{S1S3}}|0.13424-0.12374|=0.01049\) veh/s, hence the capacities of S1 and S2 are similar, the capacities of S2 and S3 are similar, the capacities of S1 and S3 are similar, the capacities of S1 and S3 are dissimilar. \(\text{D}_{\text{density}}^{\text{S1S2}}=|0.020203-0.020109|=9.4\times 10^{-5}\) veh/m, \(\text{D}_{\text{density}}^{\text{S2S3}}=|0.020109-0.021582|=0.001473\) veh/m, and \(\text{D}_{\text{density}}^{\text{S1S3}}|0.020203-0.021582|=0.001379\) veh/m, hence the critical densities of S1 and S2 are similar, the critical densities of S2 and S3 are similar, and the critical densities of S1 and S3 are similar. The results presented above are summarized in Table 5. According to these results, the procedures we presented for route selection do not affect the MFD. Figure 14: Period index vs. network density: experiment 3. Figure 13: Period index vs. network speed: experiment 3. In Table 6, the mean and standard deviation of the network speed, network density, and network flow for simulations S1, S2, and S3 in experiment 3 are presented across three phases. The DS patterns of S1 and S2 are similar, as shown by \(\rm D_{speed}^{S1S2}=0.0348\) m/s. In both simulations, similar procedures were used to forecast the travel times for selecting routes; in S3, the routes were selected based on fixed travel times (calculated based on the links lengths and a constant speed). This explains \(\rm D_{speed}^{S1S2}<D_{Speed}^{S1S3}\) and \(\rm D_{Speed}^{S1S2}<D_{Speed}^{S2S3}\); as the DS patterns of S1 and S2 are so close (see Figure 16), it follows that \(\rm D_{speed}^{S1S2}\) and \(\rm D_{Speed}^{S2S3}\) are close values. Figure 16: Network density vs. network speed: experiment 3. Figure 15: Period index vs. network flow: experiment 3. Figure 13 shows that in S3, most of the speed observations greater than 9 m/s occurred in the periods in which the links were filling up with cars (periods 1 and 2) and emptying of cars (period 203 and above). Figure 16 shows that in the density range [0.01, 0.015], the modeled DS pattern of S3 is slightly higher than the modeled DS patterns of S1 and S2 (meaning that in this density range, choosing routes with links that add shorter distances is favorable in terms of a greater speed than the procedures used to select the routes chosen in S1 and S2). Nevertheless, S3 achieved higher density values (from 0.0227 veh/m and above) that were not reached in S1 and S2. Despite this, in Figure 16, the modeled DS pattern of S3 looks promising compared to those exhibited by S1 and S2, in S3 is reached (and exceeded) the critical density (congestion appears, queues are formed at the network's  
Figure 17: Network speed vs. network flow: experiment 3. Figure 18: Network density vs. network flow: experiment 3.  
entrances and network flow drops), so in S3, since the input flow at the network entrances is zero, more time is required for the network to empty than in S1 or S2.