Inefficient road usage in a traffic network context – i.e. over-saturation on one route, where other roads are still available – is an important problem. It appears often and in different types of situations. We concentrate on congestion caused by predicted temporary road blockades, such as open bridges. This research aims to reduce such congestion by focussing on solving a routing problem that accounts for these road blockades.

More specifically, we consider traffic that is to be guided through a network with a number of different routes, where bridges function as temporary blockades when they are opened. A river that is used by freight transport runs through this network, in which road traffic uses bridges to cross the river. These bridges would open to let the freight ships pass. In such a situation, open bridges are a predictable temporary blockade for the vehicles on the road, a disturbance on the traffic flow.

We propose a model predictive controller that routes the vehicles efficiently to their destinations, making a trade-off between waiting in front of bridges and taking a detour. Model predictive control has been selected because it can handle these predicted disturbances that the bridges pose. Furthermore, it can be tuned to make a trade-off between a computationally fast and an accurate solution. A traffic split determines which part of the incoming traffic flow on a road interchange is sent towards which emanating road. These traffic splits represent the actuator variables of the controller. The total time spent by all vehicles in the network is the cost function to be minimised.

We describe a motorway network with METANET, a macroscopic traffic model. We do not use the full model, but a piecewise-affine approximation, in order to simplify the optimisation calculations significantly. We discuss two ways of modelling this approximation: an existing Mixed Logical Dynamical (MLD) formulation and a novel Linear Programming (LP) formulation. An analysis of the novel LP model in an N-step-ahead simulation is performed. We show that this problem cannot be written in a single LP problem, but that it is actually a linear multilevel programming problem (where N LP problems have to be solved consecutively).
As a means to model predicted disturbances, a novel store-and-forward bridge element is added to the nonlinear and the MLD model. A case study is performed to evaluate the effectiveness of this new bridge element. The results of this case study were satisfactory. Moreover, the results obtained with the MLD model provided an acceptable approximation of the results obtained with the nonlinear model.