# Hybrid Model-Based Traffic Network Control Using Population Games
## 8 Conclusions  
In this work, we implemented a traffic simulator that combines the micro-simulation platforms VISSIM and MATLAB in order to include population game-based control strategies to define green times in an eight-intersection traffic network. Due to its determinant role in network congestion, the queue length of links is an important parameter for fitness and payoff functions' definitions, both in the fixed case, which is modeled using fictitious play dynamics, and for the adaptive case, modeled using the control strategies based on RD, BNN, Logit and Smith dynamics. Within the traffic simulator, we included a hybrid system to model both the continuous and discrete behavior of the network in order to involve both the vehicular storing change in links and the transitions between modes caused by the traffic light changes in nodes. The results, obtained in five different traffic scenarios, demonstrated acceptable performance for the fixed-time scheme modeled with fictitious play in a traffic network without saturation conditions. In conditions considering saturation and variability in traffic flows, fictitious play exhibited good performance in many of the analyzed parameters, specifically in NS, TTT, AS, TST and ASTV, in which it outperformed BNN and Logit dynamics. On the other hand, Smith dynamics emerged as the most effective control strategy across all studied scenarios, consistently outperforming the others, particularly in situations where increased congestion led to a decline in fitness values. Replicator dynamics also demonstrated strong performance, though slightly behind Smith dynamics. This superior performance can be attributed to the decentralized nature of Smith dynamics and RD. In the case of RD, agents adjust their strategies based on pairwise comparisons of fitness values, while in Smith dynamics, agents compare the expected payoffs of different strategies. This localized decision-making process enhances their adaptability in unpredictable environments, such as traffic conditions, as they do not rely on a complete information scheme, which is a requirement that other dynamics, such as BNN or Logit, depend on. The proposed model, unlike other related works, considers five distinct levels of saturation or traffic characteristics, ranging from constant flows to variable flows in both vertical and horizontal links. Under these scenarios, the performance of various control strategies based on game theory was evaluated across multiple parameters, including the number of stops (NS), total travel time (TTT), total distance traveled (TDT), average speed (AS), total stop time (TST), and average stop time per vehicle (ASTV). Although the density of traffic flows can be adjusted to further validate the results, this study demonstrates that certain control strategies outperform others across most performance metrics, particularly under high saturation levels. The findings provide clear evidence of which game theory-based control strategies are best-suited for fixed or adaptive schemes. Furthermore, the traffic network is modeled as a hybrid system, a novel approach not explored in previous studies. This hybrid modeling provides a more realistic representation of traffic behavior, capturing both the continuous and discrete dynamics inherent in real-world traffic systems. Limitations and Future DirectionsAlthough VISSIM and MATLAB are widely used for traffic analysis, the proposed combination operates in a simulated environment that accounts for various congestion conditions and performance metrics. However, it does not incorporate real-world data, which would enhance the accuracy and practical applicability of the results. Therefore, future research should focus on implementing this approach using actual traffic datasets and more complex traffic networks. Additionally, it is important to consider how the proposed control strategies could improve the performance in terms of the TDT parameter, which was the only one presenting negative behavior in saturated scenarios. Formal analysis, S.P.A., P.A.N.