# A Microscopic Traffic Flow Model Characterization for Weather Conditions
## 5 Performance Evaluation
Furthermore, with the proposed model, as \(\alpha\) increases, the distance covered by the 1 st and 6 th vehicles decreases, whereas the distance covered by the 10 th vehicle increases. Figure 5: Time-space vehicle trajectories for the ID and proposed models over an 800 m circular road: (**a**) ID model, \(\delta~{}=~{}1\); (**b**) ID model, \(\delta~{}=~{}4\); (**c**) ID model, \(\delta~{}=~{}20\); (**d**) proposed model, \(\alpha~{}=~{}0\); (**e**) proposed model, \(\alpha~{}=~{}0.3\); (**f**) proposed model, \(\alpha~{}=~{}0.55\); (**g**) proposed model, \(\alpha~{}=~{}0.7\); (**h**) proposed model, \(\alpha~{}=~{}0.8\); (**i**) proposed model, \(\alpha~{}=~{}0.9\). Figure 6 presents the traffic flow evolution for the ID model with \(\delta~{}=~{}1,~{}4,\) and 20 over a circular road of length 800 m. With \(\delta~{}=~{}1,\) the flow increases to 0.31 veh/s at 63.5 s and then decreases to 0.27 veh/s at 74.0 s. It then decreases to 0.25 veh/s at 119.5 s. With \(\delta~{}=~{}4,\) the flow increases to 0.34 veh/s at 54.5 s and then decreases to 0.29 veh/s at 62.5 s. It then increases to 0.37 veh/s at 120 s. With \(\delta~{}=~{}20,\) the flow increases to 0.33 veh/s at 53.0 s and then decreases to 0.27 veh/s at 63.5 s. The flow varies between 0.27 veh/s and 0.33 veh/s from 63.0 s to 101 s. Further, the flow rapidly increases to 2.9 veh/s at 104.5 s and then decreases to 0.054 veh/s at 118.5 s. Figure 6 indicates that variations in the traffic flow are greater with a larger \(\delta\). Figure 7 presents the traffic flow evolution for the proposed model with \(\alpha~{}=~{}0,\)\(0.3,0.55,\)\(0.7,~{}0.8,\) and 0.9 over a circular road of length 800 m. With \(\alpha~{}=~{}0,\) the flow increases to 0.33 veh/s at 53.0 s and then decreases to 0.27 veh/s at 63.0 s. The flow varies between 0.27 veh/s and 0.32 veh/s from 63.0 s to 101 s. It then rapidly increases to 2.7 veh/s at 105 s and then decreases to 0.054 veh/s at 118.5 s. With \(\alpha~{}=~{}0.3,\) the flow increases to 0.33 veh/s at 52.5 s and then decreases to 0.27 veh/s at 64.0 s. It varies between 0.27 veh/s and 0.33 veh/s from 64.0 s to 102 s. Then the flow rapidly increases to 2.5 veh/s at 105.5 s and then decreases to 0.05 veh/s at 118. With \(\alpha~{}=~{}0.55,\) the flow increases to 0.34 veh/s at 54.0 s and then decreases to 0.27 veh/s at 64.5 s. It then increases to 0.41 veh/s at 109.5 s and decreases to 0.32 veh/s at 120 s. With \(\alpha~{}=~{}0.7,\) the flow increases to 0.34 veh/s at 55.0 s and then decreases to 0.27 veh/s at 69.5 s. It then increases to 0.40 veh/s at 114.5 s  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **1 st Vehicle Position** & **6 th Vehicle Position** & **10 th Vehicle Position** \\  & **(m)** & **(m)** & **(m)** \\ \hline \(\delta=1\) & 429.4 & 84.77 & \(-\)34.83 \\ \(\delta=4\) & 522.3 & 116.1 & \(-\)28.58 \\ \(\delta=20\) & 532.5 & 116.5 & \(-\)28.57 \\ \(\alpha~{}=~{}0\) & 532.4 & 116.5 & \(-\)28.57 \\ \(\alpha~{}=~{}0.3 and decreases to 0.38 veh/s at 120 s. With \(\alpha~{}=~{}0.8\), the flow increases to 0.34 veh/s at 56.5 s and then decreases to 0.28 veh/s at 68.0 s. It then increases to 0.39 veh/s at 119.5 s. With \(\alpha~{}=~{}0.9\), the flow increases to 0.32 veh/s at 62.0 s and then decreases to 0.27 veh/s at 76.5 s. It then decreases to 0.26 veh/s at 112.5 s and increases to 0.27 veh/s at 119.5 s. Figure 7 indicates that the variations in traffic flow are smaller during adverse weather than in normal weather. The traffic density behavior of the ID and proposed models is given in Figure 8. This shows that for the ID model with \(\delta~{}=~{}1\), the density between 0 m and 29.97 m at 118 s is 0.014. It then increases to 0.034 at 189.8 m and decreases to 0.015 at 462.8 m, as shown in Figure 8a. The density between 0 s and 35.5 s at \(-\)96.57 m is 0.14, which indicates a traffic queue. After the queue dissipates, the density at 118 s gradually decreases to 0.03 at 189.8 m, as shown in Figure 8a. With \(\delta\) = 4, the density between 0 m and 3.33 m at 119.5 s is 0.014.