Linear Programming-Based Optimization of Traffic Signal Timing for Reducing Vehicle Delay, Fuel Consumption and Carbon Emissions

Abstract

Urban traffic congestion has become a pervasive challenge in modern metropolitan areas, leading to severe economic losses, prolonged travel delays, and significant environmental degradation. Signalized intersections serve as critical nodes controlling urban traffic flow, yet conventional fixed-time signal control plans frequently fail to adapt to fluctuating demand patterns, resulting in excessive vehicle idling. This study establishes a comprehensive mathematical and computational framework for optimizing traffic signal timings using linear programming (LP). By framing signal timing as a resource allocation problem, the research aims to minimize a multi-objective function encompassing vehicle waiting time, fuel consumption, and carbon dioxide (CO2) emissions. A standardized four-phase intersection model with simulated traffic demand is developed to evaluate the LP framework without relying on unverified real-world measurements. The mathematical formulation defines decision variables representing green-light durations, establishes cycle-time and minimum-green constraints, incorporates linear delay approximations, and characterizes the feasible region as a convex polytope. The optimization model is solved using the Simplex algorithm via Python optimization libraries.