The Traffic Flow Control Algorithm Based on Graph Theory together with the Maximum Flow: A Case Study on Consecutive Road at Pattani Hospital and City Hall

Abstract

This study proposes a traffic signal control algorithm for consecutive intersections surrounding Pattani Hospital and City Hall based on graph theory and maximum flow analysis. The traffic system is formulated as a flow network in which arc weights represent road capacities, and the Ford–Fulkerson algorithm is employed to determine the maximum feasible traffic flow. Optimal green signal durations for inbound approaches are subsequently derived from the resulting flow distribution to improve traffic performance. Furthermore, the study investigates the relationship between green signal duration and the maximum traffic clearance capacity of an intersection during a signal phase. Signal timing optimization is conducted with the objective of reducing vehicle delay and enhancing overall traffic efficiency. The analytical framework integrates effective road length with estimated traffic flow capacity derived from vehicle registration statistics in Pattani Province, while intersection traffic volumes are computed using fundamental kinematic principles. Numerical results indicate that while the proposed model successfully discharges all queued vehicles within a single green phase at certain intersections, residual queues still remain at highly congested nodes. However, by actively accounting for the receiving capacity of downstream intersections and the available roadway storage capacity, the algorithm ensures that all segments can accommodate the remaining queued vehicles. Consequently, although temporary queue accumulation occurs, the system effectively prevents complete traffic blockage or cascading gridlock across the network. Ultimately, a comparative evaluation demonstrates that the proposed approach provides superior traffic clearance performance and more efficient signal utilization compared to the Averaged-Time (AT) model.