Motivated by the desire to explore future traffic flows that will consist of a mixture of classical vehicles and vehicles equipped with advanced driver assistance systems, new mathematical theories and models are developed. The basis for this theory was borrowed from the kinetic description of gas flows, where we replaced the behaviour of the molecules by typical human driving behaviour. From a methodological point of view, this 'human-kinetic' traffic flow theory provides two major improvements with respect to existing theory. Firstly, the model builds exclusively on a mathematical description of individual driver behaviour, whereas traditionally field measurements of traffic flow variables like flow rate and average speed of the flow are needed. This is of major importance for the exploration of future traffic flows with vehicles and equipment that are not yet on the market, and for which at best individual test results from driving simulator experiments or small scale field trials are available. Secondly, the model accounts for the more refined aspects of individual driver behaviour by considering the 'internal' state of the driver (active/passive, aware/unaware,...) and the variations of driving strategy that occur during driving. This is important when the ambition is to capture refined congestion patterns like the occurrence of stop-and-go waves, oscillating congestion and long jams, where the driving strategy may depend for instance on the motivation of the driver to follow closely. This new theory links together the worlds of traffic engineers and behavioural scientists. As such, it is a promising tool that increases the insight in the human behaviour as a basis of various dynamic congestion patterns, and it facilitates the design and evaluation of electronic systems in the vehicle that assist the driver to behave safer, more comfortable and more efficient in busy traffic flows. Herewith, the results of this research are relevant, both for the theoretical interest of the TRAIL research school, and for the more practically oriented work of TNO, who provided financing for this research in the joint T3 research program.
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