# Hybrid Model-Based Traffic Network Control Using Population Games
## 7 Discussion  
The implemented control strategies based on the population dynamics described in Section 4.1 were used on each one of the scenarios described in Table 2, during a simulation time of 3600s, with sample intervals \(\delta=5s\), cycle time \(C_{p}=60s\) and idle time \(L_{p}=10s\). The performance of each control strategy is evaluated according to the parameters shown in Table 3 and compared in Table 4, with the current fixed-time strategy used by the traffic controller company of Barranquilla city. Observe how most of the proposed control strategies outperform the current one, achieving reductions in the number of stops (NS) up to 90% and increasing the average speed (AS) up to 79% and 80% in scenario 4 with RD and Smith dynamics, respectively. There is not a notable improvement for scenario 1 due to the low and constant flow of vehicles. However, it is noticeable that under saturation and variable conditions, the proposed strategies enhance the results for the evaluated parameters, except the total distance traveled (TDT), which has increased up to 17% in scenario 4 in almost all the proposed strategies. This can be attributed to the change of routes inherent to the dynamics of the strategies. Another important comparison provided by Table 4 encompasses game theory-based control strategies. In general, both Smith and replicator dynamics demonstrate superior performance in saturated and non-saturated scenarios due to their decentralized mechanisms. In replicator dynamics (RD), agents adjust their strategies based on pairwise fitness \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Scenario** & **Name** & **Description** \\ \hline
1 & _No saturation condition 1_ & The input flow of vehicles is constant and equal to \(1000\frac{\mathrm{p}\mathrm{e}\mathrm{i}\mathrm{d}}{\hbar}\) during the simulation. \\ \hline
2 & _No saturation condition 2_ & Input flow increased to \(1600\frac{\mathrm{p}\mathrm{e}\mathrm{i}\mathrm{d}}{\hbar}\) during the simulation. \\ \hline
3 1 & _Saturation condition 1_ & Horizontal links (Streets 82 and 84) are saturated with input flows of \(2400\frac{\mathrm{p}\mathrm{e}\mathrm{i}\mathrm{d}}{\hbar}\). Additionally, vertical links have flows of \(1400\frac{\mathrm{p}\mathrm{e}\mathrm{i}\mathrm{d}}{\hbar}\). These values are constant during the simulation time. \\ \hline
4 & _Saturation condition 2_ & Vertical links (Kras. 50 to 52) are saturated with input flows of \(2000\frac{\mathrm{p}\mathrm{e}\mathrm{i}\mathrm{d}}{\hbar}\). Additionally, streets (horizontal links) have flows of \(1000\frac{\mathrm{p}\mathrm{i}\mathrm{d}}{\hbar}\). These values are constant during the simulation time. \\ \hline
5 & _Variable conditions_ & Flows for horizontal and vertical links change during the simulation time \\ \hline \end{tabular}  
* The saturation flow rate of 2400 vehicles/hour is a parameter that has been reported in multiple works related to traffic analysis, mostly using a passenger car as a standard unit [31; 32; 33].  
\end{table} 
Table 2: Simulation scenarios. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline
**Parameter** & **Description** \\ \hline NS & Number of Stops \\ TTT & Total Travel Time \\ TDT & Total Distance Traveled \\ AS & Average Speed \\ TST & Total Stop Time \\ ASTV & Average Stop Time per Vehicle \\ \hline \end{tabular}
\end{table} 
Table 3: Performance parameters. comparisons, whereas in Smith dynamics, they compare the expected payoffs of different strategies. This localized decision-making approach eliminates the need for complete information--unlike BNN or Logit dynamics--enhancing adaptability to unpredictable environments and, consequently, traffic volatility. In this case, the control strategy with better performance was Smith dynamics. As shown in Table 4, all parameters show the most favorable values in comparison with the other controllers.