The accurate and effective prediction of the traffic flow of vehicles plays a significant role in the construction and planning of signalized road intersections. The application of artificially intelligent predictive models in the prediction of the performance of traffic flow has yielded positive results. However, much uncertainty still exists in the determination of which artificial intelligence methods effectively resolve traffic congestion issues, especially from the perspective of the traffic flow of vehicles at a four-way signalized road intersection. A hybrid algorithm, an artificial neural network trained by a particle swarm optimization model (ANN-PSO), and a heuristic Artificial Neural Network model (ANN) were compared in the prediction of the flow of traffic of vehicles using the South Africa transportation system as a case study. Two hundred and fifty-nine (259) traffic datasets were obtained from the South African road network using inductive loop detectors, video cameras, and GPS-controlled equipment. For the ANN and ANN-PSO training and testing, 219 traffic data were used for the training, and 40 were used for the testing of the ANN-PSO model, while training (160), testing (40), and validation (59) was used for the ANN. The ANN result presented a logistic sigmoid transfer function with a 13–6–1 model and a testing R2 of 0.99169 compared to the ANN-PSO result, which showed a testing performance of R2 0.99710. This result shows that the ANN-PSO model is more efficient and effective than the ANN model in the prediction of the traffic flow of vehicles at a four-way signalized road intersection. Furthermore, the ANN and ANN-PSO models are robust enough to predict traffic flow due to their better testing performance. The modelling approaches proposed in this study will assist transportation engineers and urban planners in designing a traffic control system for traffic lights at four-way signalized road intersections. Finally, the results of this research will assist transportation engineers and traffic controllers in providing traffic flow information and travel guidance for motorists and pedestrians in the optimization of their travel time decision-making.