# Hybrid Model-Based Traffic Network Control Using Population Games
###### Abstract
Bargaining games, supported by predictive control techniques, have also been employed in [20] to establish an operating agreement among vehicles within a platoon, demonstrating acceptable performance in vehicular network coordination. In general, game theory and multi-agent systems have provided approaches for vehicular time delay reduction [17; 21; 22; 23], space allocation control in vehicular platoons [24], AV driving strategies based on velocity control considering road networks' structure [25], and traffic signal time modeling in intersections, where cooperating players or agents represent phase sequences as in [26], or agents, which model intersections, work in non-cooperative schemes based on reinforcement learning, or in a cooperative way using Pareto optimal strategy [27]. From the perspective of traffic system modeling, simulation tools offer relevant capabilities for analyzing a wide range of traffic conditions. These tools allow to set control parameters, such as cycle time, phase sequence, and cycle length, enabling detailed examination of various scenarios. Traditionally, simulation tools have been classified based on the level of detail that they consider regarding to the traffic actors in three types: microscopic, macroscopic and mesoscopic. Microscopic models delve into individual interactions between drivers and pedestrians. Between the most popular platforms of this type of models are AIMSUN, CORSIM, MATSim, Paramics, SUMO and VISSIM, with the latter being the most widely accepted in the research community [4]. Macroscopic models, exemplified in platforms such as VISUM, TRANSYT-7F, and FREFLO, among others, provide a general view of the entire traffic network. A Mesoscopic model, on the other hand, combines the above mentioned approaches. Most of the mentioned modeling approaches are focused on traffic parameters for vehicular and pedestrian congestion control without the incorporation of additional and novel techniques, such as game theory, which is of primary interest in this work. Additionally, none of these works, which are heavily focused on techniques related to game theory and multi-agent algorithms, have modeled the traffic system as a hybrid system that represents vehicle storage as a continuous system and the transitions between network modes caused by traffic light changes as a discrete system. Furthermore, these studies have primarily focused on analyzing delay times, without considering other important factors of the traffic network, such as the number of stops, total travel time, average speed, and total distance traveled, among others, which are crucial for determining the relevance of an algorithm. In this sense, the main contributions of this work, which, to the best of our knowledge, have not been considered in previous research, are described below. * First, we implement a traffic simulator that integrates the microscopic simulation tool VISSIM with MATLAB to evaluate the dynamics of various evolutionary game-theoretic techniques within a traffic network. This network employs a **hybrid signaling system**, combining **continuous dynamics**--modeling vehicular storage changes--with **discrete dynamics**--representing transitions between network modes driven by traffic light changes. This hybrid approach, combined with control strategies based on evolutionary game theory that consider queue lengths and traffic light times as utility functions both in fixed-time and adaptive traffic control schemes, allows for a more realistic representation of traffic behavior, which, to the best of our knowledge, has not been addressed in the literature. * Second, beyond traditional metrics like delay, we comprehensively analyze a range of **performance parameters** that are often overlooked in prior studies involving game theory and multi-agent algorithms, such as the number of stops, the total travel time, average speed, total distance traveled, and average stop time per vehicle.