## 7 Conclusions  
In this paper, vehicle CO2 emission models based on equilibrium velocity and density were developed through regressive techniques using data acquired with the help of engine onboard diagnostic units from vehicles moving on the road. The emissions regression models were integrated with [PERSON]'s model, and a new macroscopic traffic model that included traffic emissions was proposed. The traffic speed and density predicted by the proposed model could provide the details of vehicle emissions. The spatial and temporal evolutions of the suggested model were compared with those of [PERSON]'s model at various time steps. The analysis of the results considered the worst traffic scenario on a circular 300 m road. Simulation results showed that [PERSON]'s model failed to remain within the predefined maximum 9 m/s and minimum 0 m/s velocity. The proposed model's velocity and density, which were based on traffic emissions, remained within the prescribed limits. In addition, the proposed model could predict emissions based on traffic velocity and could be optimized for pollution mitigation. The unrealistic traffic behavior of [PERSON]'s model was due to inadequate traffic characterization. [PERSON]'s model considered the traffic's spatial and temporal evolution based on the changes in velocity, while the proposed model obtained practical data from the roadside and could therefore more accurately characterize the precise traffic behavior. That is, the proposed model considered the changes in density based on directly obtained emissions data. The maximum emissions occurred at lower velocities and were lower at higher velocities, as predicted by the proposed model. Further, the integration of traffic emissions and driver presumptions in the proposed model was established on the basis of physical traffic parameters.  
The proposed model could manage traffic control, congestion, and pollution, while [PERSON]'s model was inadequate for these purposes.  
Conceptualization, T.Q., A.B.A., K.S.K. and Z.H.K.; methodology, T.Q., A.B.A., F.A.K. and K.S.K.; software, A.B.A., M.A. and A.A.; validation, T.Q., Z.H.K., K.S.K., F.A.K. and A.A.; formal analysis, T.Q., Z.H.K. and K.S.K.; investigation, T.Q., A.B.A., F.A.K. and W.K.; resources, Z.H.K., A.B.A., K.S.K. and F.A.K.; data curation, K.S.K., Z.H.K., A.B.A. and M.A.; writing--original draft preparation, T.Q. and A.B.A.; writing, T.Q., A.B.A., Z.H.K., K.S.K. and M.A., review and editing, Z.H.K., T.Q., A.B.A., M.A. and W.K.; visualization, T.Q., M.A., A.A. and A.B.A.; supervision, Z.H.K. and F.A.K.; project administration, F.A.K., K.S.K. and A.B.A.; funding acquisition, A.B.A., Z.H.K., M.A., A.A. and W.K. All authors have read and agreed to the published version of the manuscript.  
This research has been funded by Scientific Research Deanship at University of Ha'il--Saudi Arabia through project number RG-22 020.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**S. No**} & \multirow{2}{*}{**Distance Step (Ax) and Time Step (\(\Delta\)t = 10)**} & \multicolumn{2}{c}{**Proposed Model**} \\ \cline{3-5}  & & **Velocity (m/s)** & **Velocity (m/s)** & **Emissions (kg CO2/km)** \\ \hline
1 & \(\Delta\)x = 50 & 8.10 & 8.32 & 8.60 \\ \hline
2 & \(\Delta\)x = 100 & 0.18 & 8.10 & 8.70 \\ \hline
3 & \(\Delta\)x = 150 & 4.01 & 3.50 & 11.10 \\ \hline
4 & \(\Delta\)x = 200 & 6.40 & 3.70 & 11.00 \\ \hline
5 & \(\Delta\)x = 250 & 9.10 & 8.00 & 8.70 \\ \hline
6 & \(\Delta\)x = 300 & 6.70 & 8.10 & 8.70 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of the CO2 emissions based on the velocity estimated by [PERSON]’s model and the proposed model.