Mathematical Modeling of Traffic Flow in Lusaka City: A Case Study for Transportation Planning and Optimization

Traffic congestion in Lusaka City has reached critical levels due to rapid urbanization, rising vehicle ownership, and inadequate transport infrastructure. Traditional planning approaches have failed to capture the complex dynamics of traffic flow, highlighting the need for mathematical modeling. This study applies and validates an integrated macro–micro traffic flow model for Lusaka using survey data from 40 drivers, Global Positioning System (GPS) tracking, and traffic volume counts. The model combines macroscopic relationships of flow, speed, and density with microscopic driver behavior representations. Validation against observed data yielded a strong correlation (r=0.759), demonstrating superior predictive performance compared to standalone macroscopic models. Results indicate that congestion is primarily caused by poor road infrastructure, ineffective traffic management, inadequate public transportation, and the high number of vehicles on the road. Policy simulations revealed that 87% of drivers recommended constructing new roads and bridges or expanding existing ones, 5% proposed banning private vehicles, 5% suggested having high levels of car ownership, and 12.5% proposed nonmotorized alternatives. The study's novelty lies in integrating quantitative driver perceptions with advanced traffic modeling tailored to Lusaka's context. Practically, the model serves as a decision-support tool for policymakers to test congestion reduction strategies under real-world constraints.