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Butcher, J.C. (1987) The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods. John Wiley & Sons.

has been cited by the following article:

• TITLE: Pontryagin’s Maximum Principle in Penalized Joint Optimization of Vehicle Queue Dynamics for Road Traffic

  AUTHORS: Marc Bigirimana, Fulgence Nahayo, Mounir Haddou, Abraham Niyongere

  KEYWORDS: State Constraint Penalization, Optimal Control Problem, Exterior Penalization, Traffic Fluidity Function, Traffic Queue Optimization, Joint Optimization Problem, Pontryagin Maximum Principle, Symplectic Discretization

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.16 No.7, July 14, 2026

  ABSTRACT: The application of Pontryagin’s Maximum Principle (PMP) to optimize the dynamics of vehicle queues in road traffic systems. We present a mathematical framework that integrates optimal control theory with traffic flow dynamics to enhance the efficiency and performance of road networks. By modeling vehicle behavior and interactions within queues, we identify optimal control strategies that minimize delays and maximize throughput. The proposed methodology includes a comprehensive analysis of system constraints and environmental factors impacting traffic flow. Simulation results demonstrate the effectiveness of the PMP approach in various traffic scenarios, highlighting significant improvements in queue management and overall traffic efficiency. Our findings contribute to the development of advanced traffic management systems and provide valuable insights for future research in transportation optimization.