## 2 Materials and Methods
### Emissions Model Simulation  
In this part of the study, the simulation was carried out in Stella 9.0.3, which allows for dynamic modeling and presents estimation processes and graphic results. The designed model uses this software to estimate the emissions generated by each type of vehicle. The basic structure of this computer program is a graphical interface with icons that represent variables and processes. In Figure 5, stocks contain the iterative results for each time-differential (TD); arrow connectors indicate relationships between variables; flows represent input and output data for stocks, and converters contain the algorithms. This program has prebuilt functions to define the algorithms, verifying them in order to make sure that their syntax is correct.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Dependent Variable** & **Formula/Data** \\ \hline Vehicles in operation on BLC (V) & 40,748,850 \\ Length (L) & L (every segments from A to J) \\ Travels (T) & T = V \(\times\) L \\ Performance (Pf) & 7.53 Km/L \\ Fuel (F) & F = T/Pf \\ Emissions (E) & E = EF \(\times\) AD \\ \hline \hline \end{tabular}
\end{table}
Table 1: Equations associated with Transport and GHG Emissions model variables.  
Figure 5: Emissions Model in Stella 9.0.3. (“Stocks” are represented by rectangles, “converters” by circles, and “flows” by valves). Abbreviated symbols Fuel (F), Performance (PF), Vehicle Weighted Average (P VEH), Emission Factor (EF).  
The dynamic of the model was structured based on the order that the variables carry within their respective algorithms. Thus, vehicle behavior was measured first and expressed as a weighted vehicle rate based on the by-point segmentation of the urban road length and contrasted with the number of vehicles circulating on each section to obtain BLC travel. Performance (Pf) was measured next, expressed as a performance rate calculated using historical data and the current performance to obtain fuel consumption. Finally, the amounts of emissions were quantified together with the emissions factor.  
For the simulation stage, the Stella software, whose version is 9.0.3, provides three numerical methods to solve equation systems: Euler, Runge-Kutta, and second-order Runge-Kutta. The chosen method depends on the type and behavior of the model, for example, the software's authors recommend Euler for models with discrete variables and Runge-Kutta for discrete behavior or oscillatory systems. The Euler method [37] was selected for the present study.  
An important aspect of the simulation process is the time-differential (TD), which represents a fraction of the time unit (TU) in which the simulation will be carried out; to refine the results, Stella performs calculations in periods shorter than the TU. This variable can take values from zero to one; the lower the TD value the more time required by the model to perform the calculations [37].  
The simulation process consisted of two stages: initialization, where a list of equations was created, the order for their evaluation was established, and the initial state variables or cumulative variables (stock) were calculated; the second stage corresponded to the iteration process, in which the change values corresponding to each TD are estimated and new stocks totals were obtained. With these data, the values in the flows (where the storage variables increase or decrease and their characteristic equations must be described) and converters (element of the model where the equation is described and the calculation is performed) are recalculated (Figure 5). This process is repeated for each TD until the requested simulation period ends [38].