A Developed generalized mathematical traffic flow model for a single intersection
Efficient traffic management at urban intersections remains a major challenge due to increasing demand and complex network interactions. This paper presents a generalized mathematical traffic flow model for a signalized intersection that dynamically communicates with four neighbouring intersections (ahead, behind, left, and right). The model integrates a state-space representation to capture queue dynamics, arrival rates, and interconnection effects within a unified framework. A demand-driven signal control strategy is developed to allocate green time based on real-time vehicle demand, eliminating wasted signal phases. The framework further incorporates Internet of Things (IoT)-based sensing for real-time data acquisition and inter-intersection communication, alongside an Artificial Intelligence (AI)-based optimization layer for adaptive decision-making. A Petri Net supervisory control mechanism is introduced to manage signal transitions and enable emergency vehicle pre-emption. These results were obtained through MATLAB-SUMO co-simulation across multiple traffic scenarios. Results demonstrate significant improvements, including reduced queue length and delay, increased throughput, and enhanced congestion management compared to conventional methods. The proposed model provides a scalable and intelligent solution for modern smart city traffic systems.