African Pure Mathematics Quarterly (Pure Science) | 16 April 2013
Monte Carlo Estimation Variance Reduction in Dynamical Systems for Traffic Flow Optimization in Senegal
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Abstract
Recent advancements in dynamical systems theory have been applied to improve traffic flow optimization in urban settings, with Senegal as a case study. This review synthesizes existing literature on Monte Carlo methods applied to dynamical systems, focusing specifically on variance reduction strategies tailored for urban traffic management. A key finding is that incorporating importance sampling into traditional Monte Carlo simulations significantly reduced estimation variance by 20% in simulated Senegalese road networks. The reviewed techniques have the potential to enhance real-world traffic flow optimization models, particularly when applied with adaptive importance sampling methods. Further research should explore the integration of machine learning algorithms into Monte Carlo simulations for even more effective variance reduction in urban traffic systems. Monte Carlo Estimation, Variance Reduction, Dynamical Systems, Traffic Flow Optimization, Senegal Model selection is formalised as $\hat{\theta}=argmin_{\theta\in\Theta}\{L(\theta)+\lambda\,\Omega(\theta)\}$ with consistency under mild identifiability assumptions.