A PDE-ODE Model for a Junction with Ramp Buffer
Abstract
We consider the Lighthill--Whitham--Richards traffic flow model on a junction composed by
one mainline, an onramp, and an offramp, which are connected by a node. The onramp
dynamics is modeled using an ordinary differential equation describing the evolution of the
queue length. The definition of the solution of the Riemann problem at the junction is based
on an optimization problem and the use of a right-of-way parameter. The numerical
approximation is carried out using a Godunov scheme, modified to take into account the
effects of the onramp buffer. We present the result of some simulations and numerically
check the convergence of the method.
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