Traffic control and traveller’s behaviour are two processes that influence each other. The two processes have different ‘actors’ who can have different goals. The road manager will try to achieve a network optimum and will try to control traffic in such a way that this optimum is reached. Tools for controlling traffic control are for example traffic signals, traffic information, ramp metering, etc. The optimum can be a system optimum or a preferential treatment for certain user groups, eg public transport or pedestrians. The road users will search for their own optimum, eg the fastest or cheapest way to travel from A to B. Decisions taken by the road manager in controlling traffic in a certain way have an influence on the possibilities for travellers to choose their preferred mode, route and time of departure, and vice versa. A change in traffic control may have the impact that traffic volumes change. If for example traffic control is modified such that congestion on a certain route disappears and delays on intersections decrease, traffic might be attracted from other links where congestion still exists or which are part of a longer route. This might have the consequence that queues, which originally disappeared, return. Delays may come back on the original levels. The question is then whether there still is a net profit for the traffic system as a whole. Another example is that public transport gets priority in intersection control. The delay for other road users may increase and thus force these road users to search for other routes, departure times or even transport modes in the network. If it is assumed that a modification in traffic control gives a change in travel behaviour, it is necessary to anticipate this change. If delays are optimised, it should be done for the traffic volumes that will be present after the introduction of the optimised traffic control and not for the traffic volumes which existed before the implementation. Of course, it is possible to follow an interactive approach, where after each shift in traffic volumes the control scheme is adjusted until equilibrium has been reached, or one may use self-adjusting traffic control. However, it can be shown, for certain examples, that the process of the adjustment of traffic control, followed by a shift in traffic volumes, does not necessarily lead to a system optimum. It is even possible that the system oscillates between two or more states. This arises from the fact that the system optimum is not necessarily the same as the user optimum. The system optimum is good for the network as a whole, but can be disadvantageous for a part of the travellers in the network. The control problem is therefore to optimise traffic control in such a way that the system is at a certain, prescribed optimum, taking into account the reaction of travellers. This is called the combined traffic assignment and control problem.

In one classifies the available literature, a distinction can be made between three different approaches to solve the combined assignment and control problem. The first is the iterative approach, which solves both problems separately and uses the outcome of one problem to serve as the input for the other problem. Hopefully, in an iterative process the combined problem converges to a solution. The second approach is the global optimisation approach. This approach solves both problems simultaneously and aims at a control policy that optimises globally, taking into account users’ behaviour (mostly route choice). The third approach is not really a different one, but is a specific global optimisation approach and uses game theory to solve the combined problem. Game theory provides a framework for modelling a decision process with multiple decision makers. In this …