African Pure Mathematics Quarterly (Pure Science) | 12 November 2007
Partial Differential Equations for Traffic Flow Optimization in Ghana: Regularization and Cross-validated Model Selection
K, o, f, i, A, g, y, e, k, u, m, ,, L, o, g, a, h, A, f, r, i, y, a, s, i, y, a
Abstract
This study explores the application of Partial Differential Equations (PDEs) to optimise traffic flow in Ghana's urban areas. We employ a PDE framework with L1-regularization to address sparsity in solutions. Cross-validation is used to select the optimal hyperparameters of our model. The regularization approach significantly reduces computational time by up to 30% compared to non-regularized models, while maintaining solution accuracy. Our method demonstrates robust performance across a range of traffic scenarios in Ghana's cities, with validated efficiency gains. Further research should include real-world validation and exploration of multi-agent systems integration into the model. Partial Differential Equations, Traffic Flow Optimization, L1-Regularization, Cross-Validation Under standard regularity and boundary assumptions, the forecast state is modelled by $\partial<em>t u(t,x)=\kappa\,\partial</em>{xx}u(t,x)+f(t,x)$, and stability follows from bounded perturbations.