Mathematical Modelling of Traffic Flow on Lagos-Ibadan Expressway Using Fluid Dynamics Approach

Traffic congestion on the Lagos-Ibadan Expressway has become a persistent challenge with significant economic and social consequences for commuters in the South West geopolitical zone of Nigeria. This study applies fluid dynamics principles, specifically the Lighthill-Whitham-Richards model, to simulate vehicular flow patterns along the 127-kilometre corridor. The research collects empirical traffic count data at five major interchanges over a twelve-week period, capturing peak and off-peak periods across weekdays and weekends. Using density-flow-speed relationships, the model identifies critical congestion thresholds and predicts bottleneck formation under varying traffic demand scenarios. The study further examines how incidents such as tanker accidents and construction activities influence shock wave propagation along the route. Results indicate that maximum flow capacity is consistently exceeded during morning peak hours between 6:30 and 9:00 am, with queue lengths extending beyond measurable bounds at Sagamu interchange. The model achieves a mean absolute percentage error of 8.3 percent when validated against observed field data, confirming its predictive reliability. The study recommends adaptive signal control strategies and staggered work-hour policies as cost-effective interventions. These findings provide a mathematical foundation for evidence-based transport planning in high-density Nigerian corridors and contribute to the growing body of applied mathematics research addressing urban mobility challenges. Keywords: traffic flow, fluid dynamics, LWR model, Lagos-Ibadan Expressway, congestion modelling.