Traffic signal control (TSC) is a challenging problem within intelligent transportation systems and has been tackled using multi-agent reinforcement learning (MARL). While centralized approaches are often infeasible for large-scale TSC problems, decentralized approaches provide scalability but introduce new challenges, such as partial observability. Communication plays a critical role in decentralized MARL, as agents must learn to exchange information using messages to better understand the system and achieve effective coordination. Deep MARL has been used to enable inter-agent communication by learning communication protocols in a differentiable manner. However, many deep MARL communication frameworks proposed for TSC allow agents to communicate with all other agents at all times, which can add to the existing noise in the system and degrade overall performance. In this study, we propose a communication-based MARL framework for large-scale TSC. Our framework allows each agent to learn a communication policy that dictates "which" part of the message is sent "to whom". In essence, our framework enables agents to selectively choose the recipients of their messages and exchange variable length messages with them. This results in a decentralized and flexible communication mechanism in which agents can effectively use the communication channel only when necessary. We designed two networks, a synthetic $4 \times 4$ grid network and a real-world network based on the Pasubio neighborhood in Bologna. Our framework achieved the lowest network congestion compared to related methods, with agents utilizing $\sim 47-65 \%$ of the communication channel. Ablation studies further demonstrated the effectiveness of the communication policies learned within our framework.

Reinforcement Learning (RL) is currently one of the most commonly used techniques for traffic signal control (TSC), which can adaptively adjusted traffic signal phase and duration according to real-time traffic data. However, a fully centralized RL approach is beset with difficulties in a multi-network scenario because of exponential growth in state-action space with increasing intersections. Multi-agent reinforcement learning (MARL) can overcome the high-dimension problem by employing the global control of each local RL agent, but it also brings new challenges, such as the failure of convergence caused by the non-stationary Markov Decision Process (MDP). In this paper, we introduce an off-policy nash deep Q-Network (OPNDQN) algorithm, which mitigates the weakness of both fully centralized and MARL approaches. The OPNDQN algorithm solves the problem that traditional algorithms cannot be used in large state-action space traffic models by utilizing a fictitious game approach at each iteration to find the nash equilibrium among neighboring intersections, from which no intersection has incentive to unilaterally deviate. One of main advantages of OPNDQN is to mitigate the non-stationarity of multi-agent Markov process because it considers the mutual influence among neighboring intersections by sharing their actions. On the other hand, for training a large traffic network, the convergence rate of OPNDQN is higher than that of existing MARL approaches because it does not incorporate all state information of each agent. We conduct an extensive experiments by using Simulation of Urban MObility simulator (SUMO), and show the dominant superiority of OPNDQN over several existing MARL approaches in terms of average queue length, episode training reward and average waiting time.