Junction Conditions for Hamilton–Jacobi Equations for Solving Real-Time Traffic Flow Problems

In this paper, we propose junction conditions for discontinuities due to local perturbation, diverging, merging, and multi-in-multi-out junctions. Traffic flows on junctions can be described by a system of coupled Hamilton-Jacobi equations. At their connection points, it is necessary to propose appropriate junction conditions to close the system. Then, we provide an effective numerical method to compute approximate solutions to these Hamilton-Jacobi equations on junctions. The numerical boundary conditions to close the Hamilton-Jacobi system are also proposed. Numerical tests demonstrate the effectiveness of both the proposed junction conditions and the numerical method.