Queuing and convergence properties of a dynamic assignment model for congested networks

The growing congestion problems demand a new generation of traffic models that are applicable in the planning and management of infrastructure. The aim of this thesis is the development of a traffic model able to predict congestions and their influence on traffic operation. This model is meant for three areas of applications: research into travellers' reaction to congestion; the planning of scarce infrastructure and the optimisation of the use of scarce road capacity. This thesis has been restricted to traffic operation on motorways. It is assumed that all travellers show the same behaviour. The literature review resulted in the conclusion that the so called dynamic traffic assignment models are able to detect a shortcoming of supply of infrastructure and to give insight in time dependent effects of congestion. Two different groups of traffic models can be distinguished, the traffic assignment models that assign traffic sequential per OD pair and the simulation models that calculate traffic operation on individual vehicle level. The traffic assignment models were chosen for fiirther development because these are expected to be useful both for planning and management, due to the ability to restrain the costs of use of these models by an appropriate choice of the required level of detail. Basis of the model is a dynamic traffic assignment model developed at Delft University of Technology. This model can be seen as an extended version of the existing static assignment models. Time dependent traffic operation in a network is modelled by using sequential time periods. Capacity restraints are introduced by the use of a speed/density relation instead of a speed/flow relation that is customary in static assignment models. An adequate mathematical definition of the model is missing. It is concluded that the original model without the use of a queuing algorithm does not converge in congested situations. A newly developed queuing algorithm gives a realistic representation of congested roadways, especially in those cases where spillback effects appear to upstream bottleneck links. This representation is achieved by the determination of the speed effects on upstream bottleneck links. The speed reducing effects depend on the level of oversaturation of the involved bottleneck. The newly developed queuing algorithm resulted in a better convergence behaviour than the original model (and queuing algorithm). This is shown several elementary test cases that have been investigated with software developed for this purpose. The new developed queuing algorithm resulted also in better solutions. The calculated results match better with the expected results based on traffic flow theory. The applicability of the model remains restrained to situations where spill back effects do not have substanially impact on the route choices and where a restricted level of detail of the results is sufficient for the considered application. Application in the field of traffic management requires more practical research. An approach with simulation models should not be dismissed.