SUMMARYThe solution methods for optimal control problems with coupled partial differential equations as constraints are computationally costly and memory intensive; in particular for problems stated on networks, this prevents the methods from being relevant. We present instantaneous control problems for the optimization of traffic flow problems on road networks. We derive the optimality conditions, investigate the relation to the full optimal control problem and prove that certain properties of the optimal control problem carry over to the instantaneous one. We propose a solution algorithm and compare quality of the computed controls and run-times.

Abstract. We consider a multi-class (resp. source-destination) model for traffic flow as introduced in [10]. We propose a reformulation and discuss the extension of this model to road networks by proposing criteria for solving Riemann problems at a road intersection. We present some numerical simulations for the derived conditions.

Abstract. We consider a supply network where the flow of parts can be controlled at the vertices of the network. Based on a coarse grid discretization provided in [6] we derive discrete adjoint equations which are subsequently validated by the continuous adjoint calculus. Moreover, we present numerical results concerning the quality of approximations and computing times of the presented approaches.

In this paper, we discuss the multicommodity flow for vehicular traffic on road networks. To model the traffic, we use the "Aw-Rascle" multiclass macroscopic model [3]. We describe a solution to the Riemann problem at junctions with a criterion of maximization of the total flux, taking into account the destination path of the vehicles. At such a junction, the actual distribution depends on the demands and the supplies on the incoming and outgoing roads, respectively. Furthermore, this new distribution scheme captures efficiently key merging characteristics of the traffic and in contrast to [M.

Abstract. We show how the Aw-Rascle model, a hyperbolic system of PDEs modeling traffic flow, can be derived from a simplified Fokker-Planck type kinetic equation.