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Macroscopic models describing lane-free movement of automated vehicles

Titakis Georgios

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Summary

Recent advances in technology have revolutionized vehicle automation with different kinds of driver support systems. In the era of connected automated vehicles (CAVs), new perspectives and principles have been suggested, where the vehicles can move on the two-dimensional surface of lane-free roads without abiding to lane discipline, something that may improve traffic flow and increase capacity of highways. Therefore, there is a need for cruise controllers that can operate in a lane-free environment. The cruise controllers under consideration are performed in microscopic models, i.e. models that consist of Ordinary Differential Equations (ODEs) and describe the dynamics of each individual vehicle.Although several aspects of the cruise controllers, such as safety and passenger convenience, may be investigated at the microscopic level, it is also important to study their implications for the emerging traffic flow. To this end, macroscopic traffic flow models have been formally derived for the description of the traffic flow of CAVs under the effect of cruise controllers. The derived macroscopic models consist of two Partial Differential Equations (PDEs) (i.e a continuity equation and a speed equation) and they are similar to the equations of a viscous compressible fluid. The obtained macroscopic models have been formally derived using particle methods, in which the vehicles are considered as "self-driven" particles of a fluid ("the traffic fluid"). The particle methods provide the link between the macroscopic models and the cruise controllers, since certain relations between the microscopic quantities and the "traffic fluid" physical properties hold. Consequently, by changing the microscopic quantities of the cruise controllers we can determine the physical properties of the emerging traffic flow. Based on that, a specific selection for the functions included in the cruise controllers enabled a model reduction, which is completely analogous to the human-driven vehicles case, where the Aw-Rascle-Zhang (ARZ) model reduces to the well-known Lighthill-Whitham-Richards (LWR) model. Moreover, in contrast to conventional traffic, the proposed macroscopic models are isotropic since the vehicles react to both upstream and downstream vehicles. Isotropy, as well as the presence of "fluid-like" characteristics in the derived macroscopic models follow from the fact that lane-free movement and nudging are allowed by the cruise controllers. In this thesis, numerical studies of the proposed macroscopic traffic flow models for CAVs are performed, where numerical experiments are conducted to study their properties and evaluate the performance of several numerical methods that are used to approximate their solutions. Moreover, the present work provides evidence that the proposed macroscopic models are successful for the description of the traffic flow in real complex traffic environments. More specifically, by considering traffic scenarios for which macroscopic traffic data are collected from microscopic simulations using the respective cruise controllers, it is shown that after calibrating one of the proposed macroscopic models for CAVs, all the traffic conditions that appear in the collected macroscopic traffic data are reproduced with high accuracy.

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