A PDE-ODE model for a junction with ramp buffer

Maria Laura Delle Monache (1) , Samitha Samaranayake (2) , Jack Reilly (2) , Walid Krichene (2) , Paola Goatin (1) , Alexandre Bayen (2)

1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
2 CEE - Department of Civil and Environmental Engineering [Berkeley]

We consider the Lighthill-Witham-Richards traffic flow model on a junction com- posed 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 Godunov scheme, modified to take into account the effects of the onramp buffer. We present the result of some simulations and check numerically the convergence of the method.

Domaines: Equations aux dérivées partielles [math.AP]

Maria Laura Delle Monache, Samitha Samaranayake, Jack Reilly, Walid Krichene, Paola Goatin, et al.. A PDE-ODE model for a junction with ramp buffer . SIAM Journal on Applied Mathematics, 2014, 74 (1), pp.22-39. ⟨hal-00786002⟩