Mathematical Modelling of Traffic Flow on the Lagos-Ibadan Expressway

This study develops and analyses mathematical models of vehicular traffic flow along the Lagos-Ibadan Expressway, one of Nigeria's busiest and most economically strategic road corridors. The expressway, which connects Lagos, South West Nigeria's commercial capital, to Ibadan in Oyo State, experiences chronic congestion that imposes substantial costs on freight logistics and commuter productivity. The study employs the Lighthill-Whitham-Richards continuum model as its primary theoretical framework, supplementing it with a car-following model for microscopic flow analysis at identified bottleneck segments near the Sagamu interchange and the Berger junction. Traffic count data are collected through field surveys conducted over ten days in both peak and off-peak periods, and speed-density relationships are estimated using observed flow measurements. The fundamental diagram of traffic flow is constructed and used to derive critical density and capacity flow values for each segment under study. Simulation results indicate that the current capacity of the expressway is routinely exceeded during morning and evening peak windows, contributing to the formation of persistent shock waves that propagate upstream for several kilometres. The study recommends the implementation of ramp metering controls and dynamic speed limit signage informed by real-time density measurements. It also identifies the ongoing expressway rehabilitation project as an opportunity to incorporate traffic flow modelling into infrastructure planning decisions. Keywords: traffic flow modelling, Lighthill-Whitham-Richards model, Lagos-Ibadan Expressway, congestion, shock waves