## 3 Results and Discussion
### Results and Discussion of Experiment 3
From period 200, in S1, it takes 4 periods for the network to empty, in S2 it takes 5 periods, and in S3 it takes 37 periods (an indicator that congestion happened). The critical density is reached in S3 at 0.021582 veh/m (beyond this point, as density increases, flow decreases), which corresponds with a maximum flow of 0.123737 veh/s. The congestion occurs from approximately period 92 to period 202, then after period 81 (from this period and until period 200, the input flow is 0.16666 veh/s per entrance) it takes 0.3 h for the congestion to appears. Concerning the periods range [92, 202], Figure 14 shows that S3 frequently presents higher densities than S1 and S2, and Figure 15 shows that S3 frequently presents a lower flow than S1 and S2. This is a consequence of the poor procedure used to estimate the links' travel times when selecting routes in S3. Therefore, in Figure 16, the DS pattern of S3 is extended to the right in comparison with the DS patterns of S1 and S2; in S1, the density range is [0.0063, 0.0240] and the corresponding speed range is [11.8664, 6.0352]; in S2, the density range is [0.0063, 0.0226] and the corresponding speed range is [10.7580, 5.9230]; in S3 the density range is [0.0040, 0.0259] and the corresponding speed range is [12.1548, 6.2501]. Figures 22-24 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 \(\rm{D}_{\rm{speed}}^{\rm{S1S2}}=0.0446\) m/s; between simulation 2 and simulation 3 (green crosses), it is \(\rm{D}_{\rm{speed}}^{\rm{S2S3}}=0.0298\) m/s; and between S1 and S3, it is \(\rm{D}_{\rm{speed}}^{\rm{S1S3}}=0.024\) 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. \(\rm{D}_{\rm{flow}}^{\rm{S1S2}}=|0.13424-0.13556|=0.00132\) veh/s, \(\rm{D}_{\rm{flow}}^{\rm{S2S3}}=|0.13556-0.12923|=0.00633\) veh/s, and \(\rm{D}_{\rm{flow}}^{\rm{S1S3}}|0.13424-0.12923|=0.005009\) veh/s, hence the capacities of S1 and S2 are similar, the capacities of S2 and S3 are similar, and the capacities of S1 and S3 are similar. Figure 19: Period index vs. network speed: experiment 4. Figure 20: Period index vs. network density: experiment 4. \(\mathrm{D}_{\mathrm{density}}^{\mathrm{S1S2}}=|0.020203-0.022451|=0.002248\)\(\mathrm{veh}/\mathrm{m}\), \(\mathrm{D}_{\mathrm{density}}^{\mathrm{S2S3}}=|0.022451-0.026724|=0.004273\)\(\mathrm{veh}/\mathrm{m}\), and \(\mathrm{D}_{\mathrm{density}}^{\mathrm{S1S3}}|0.020203-0.026724|=0.006521\)\(\mathrm{veh}/\mathrm{m}\), hence the critical densities of S1 and S2 are dissimilar, the critical densities of S2 and S3 are dissimilar, and the critical densities of S1 and S3 are dissimilar. The results presented above are summarized in Table 7. According to these results, the procedures we use to generate the OD table cannot affect the MFD. Figure 14:0 Period index vs. network flow: experiment 4. Figure 14:1 Network density vs. network speed: experiment 4. In Table 8, the mean and standard deviation of the network speed, network density, and network flow for simulations S1, S2, and S3 in experiment 4 are presented across three phases. Figure 14:2 Network speed vs. network flow: experiment 4. Figure 14:3 Network density vs. network flow: experiment 4. The DSs patterns between any possible pair (S1 and S2, S2 and S3, and S1 and S3) are similar, as can be visually corroborated in Figure 14:4 In this Figure, it is observed that from period 3, the network densities and the corresponding network speeds of S1, S2, and S3 share similar values.