# Hybrid Model-Based Traffic Network Control Using Population Games
###### Abstract  
Modern traffic management requires sophisticated approaches to address the complexities of urban road networks, which continue to grow in complexity due to increasing urbanization and vehicle usage. Traditional methods often fall short in mitigating congestion and optimizing traffic flow, inducing the exploration of innovative traffic control strategies based on advanced theoretical frameworks. In this sense, we explore different game theory-based control strategies in an eight-intersection traffic network modeled by means of hybrid systems and graph theory, using a software simulator that combines the multi-modal traffic simulation software VISSIM and MATLAB to integrate traffic network parameters and population game criteria. Across five distinct network scenarios with varying saturation conditions, we explore a fixed-time scheme of signaling by means of fictitious play dynamics and adaptive schemes, using dynamics such as Smith, replicator, Logit and Brown-Von Neumann-Nash (BNN). Results show better performance for Smith and replicator dynamics in terms of traffic parameters both for fixed and variable signaling times, with an interesting outcome of fictitious play over BNN and Logit. population dynamics; hybrid system; traffic network; game theory; graph theory 2  
about the green times in intersections considering street lengths, input and output flows, and street capacity to store vehicles, among other traffic parameters. Often, researchers focus their work on traffic signal timing (TST) and traffic signal control (TSC) optimization to develop mechanisms that assure the right of way (ROW) for multiple road users in two different strategy types, one based on _fixed_ time, whose scheme defines the traffic lights plan according to historical data, and other that follows an _adaptive_ schedule considering the traffic variability to assign dynamic times for traffic lights [4]. Fixed-time strategies [5], in spite of their limited applicability in environments with high traffic variability, continue to be widely employed in situations where technological infrastructure upgrades are not feasible. However, modern techniques have emerged to address this challenge, including nonlinear combinatorial programming models for pedestrian and vehicular signal plans [6], and the implementation of platoon size control based on lane dimensions for connected and automated vehicles (CAVs) [7]. Recently, fixed-time strategies have primarily served as benchmarks for comparing performance with novel adaptive approaches. These approaches leverage machine learning algorithms, IoT-based traffic control focused on CAVs [8], semi-actuated networks [8], and multi-agent methods [9; 10], as well as many game theory-based controllers that consider not only vehicles but also pedestrian dynamics [11]. In terms of adaptive strategies, multiple solutions have been proposed to integrate multi-agent and game theory concepts [12; 13; 14; 15; 16; 17]. These strategies aim to improve real-time control over green light cycles and tackle vehicular congestion challenges in contexts involving conventional car drivers, pedestrians, and autonomous vehicles (AV). In this regard, in [18], authors propose a game theory based multi-agent algorithm called GAMEPLAN that determines the optimal action for each agent based on their driving style (passive or aggressive), considering AV and drivers as agents with hidden intentions. In [19], a mixed traffic environment including CAVs and human-driven vehicles (HDVs) is studied using a model involving adaptive dynamic programming (ADP) techniques, alongside quadratic zero-sum games to minimize external disturbances that cause stop and go waves in vehicular platoons. Another mixed study, this time involving pedestrians and vehicles, is proposed in [16]. In this analysis, authors employ a Nash bargaining solution to determine the optimal green time that reduces pedestrian and vehicle delays.