Mathematical Modelling and MPC-Based Optimisation of Urban Traffic Flow in the Yaba and Sabo Areas of Lagos Metropolis

Abstract

Traffic jams in Lagos Metropolis are at critical levels, causing annual economic losses estimated in billions of naira and significantly impacting the standard of living. Using Model Predictive Control (MPC), this paper provides a detailed mathematical approach to simulate and enhance metropolitan traffic flow. By adapting the Cell Transmission Model (CTM) to the unique characteristics of Lagos' road networks, we develop a macroscopic traffic flow model. The proposed MPC system integrates real-time traffic data, predictive capabilities, and constraint management to optimise signal timing and traffic routes. The results indicate that the MPC-based method reduces queues by 24%, increases network throughput by 28%, and decreases average travel time by 32%, compared to traditional fixed-time control methods. The model accounts for Yaba and Sabo Areas specific challenges such as mixed traffic composition, informal public transportation networks, and infrastructural constraints.