Logical and mathematical interpretation of intelligent traffic light management strategies in the city

Introduction. This article examines the application of explainable reinforcement learning (XRL) methods to intelligent traffic light control in an urban environment, using Vladikavkaz as an example. Purpose of the research. The primary objective of the study is to develop an adaptive, efficient, and interpretable traffic flow management system that overcomes the shortcomings of traditional fixed - cycle schemes. Materials and Methods. The proposed model is based on a deep neural network (DQN), which optimizes traffic light phases based on current traffic parameters - queue length, flow intensity, and the time since the start of the current phase. To improve the transparency of decisions, a formal logical interpretation of agent behavior is applied using linear temporal logic (LTL) and epistemic logic (EL). This enables verification of safety (absence of conflicting phases) and viability (guaranteed queue service) properties. Results. A computational experiment showed that the trained DQN agent significantly outperforms the traditional round - robin approach, with average delay reduced by 25.7 % and maximum queue length by 51.4 %. Importantly, the system demonstrates a balanced distribution of priorities between directions and prevents excessive queue accumulation. Unlike most studies, where traffic lights are controlled in isolation, your method models the knowledge of agents ("traffic light X knows that Y has a long queue"), ensures consistency of decisions between adjacent intersections, and introduces the concept of "bounded knowledge," which corresponds to reality (the agent only sees its own intersection but can reason about others). This enables the construction of scalable and cooperative systems for entire intersection networks, not just for individual objects. A key result of the work is the derivation of interpretable logical rules reflecting the agent's strategy, which eliminates the "black box effect" and makes the system's behavior understandable to operators. Resume. Thus, the approach ensures not only adaptability but also formal verifiability, security, and trust in decisions, which is especially important for implementation in real urban conditions. The research results may be useful for the modernization of urban traffic management systems, for substantiating decisions made by municipal and regional transport authorities, as well as for integrating intelligent traffic light controllers with existing traffic monitoring systems

Intelligent transportation system · Queue · Scalability · Traffic signal · Traffic control and management · Traffic Prediction and Management Techniques · Transportation Systems and Logistics