Control of heterogeneous network flow via multimarginal optimal transport

A strong trend in today´s society is the emergence of large scale systems where each subststem also is a system.

As the systems becomes larger, more complex, and more important in the society, there is an increasing need for understanding and controlling the macroscopic behaviour of such systems of systems.

For these systems the available control is typically local and must also take into account the constraints and the utility functions of the individual subsystems.

An example is the road traffic system where each vehicle has a given destination, but where a greedy routing approach may lead to traffic congestion with increasing travel time for everyone in addition to negative external effects such as pollution.

Thus it is important to design methodsthat can guide all the vehicles to their destinations without causing conjection.In this project we will develop theory and computational methods for controlling such systems of systems by leveraging recent computational breakthroughs in the area of optimal transport.

In particular, we propose a new formulation of the optimal transport problem on a graph. This allows for modelling of several important problems in traffic control and operations research.

For these formulations we will be able to formulate efficient solution methods which makes this a suitable framework for real time control of large dynamic network problems.