Model-based assessment of the impact of driver-assist vehicles using kinetic theory
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Zeitschrift f¨ ur angewandte Mathematik und Physik ZAMP
Model-based assessment of the impact of driver-assist vehicles using kinetic theory Benedetto Piccoli, Andrea Tosin
and Mattia Zanella
Abstract. In this paper, we consider a kinetic description of follow-the-leader traffic models, which we use to study the effect of vehicle-wise driver-assist control strategies at various scales, from that of the local traffic up to that of the macroscopic stream of vehicles. We provide theoretical evidence of the fact that some typical control strategies, such as the alignment of the speeds and the optimisation of the time headways, impact on the local traffic features (for instance, the speed and headway dispersion responsible for local traffic instabilities) but have virtually no effect on the observable macroscopic traffic trends (for instance, the flux/throughput of vehicles). This unobvious conclusion, which is in very nice agreement with recent field studies on autonomous vehicles, suggests that the kinetic approach may be a valid tool for an organic multiscale investigation and possibly the design of driver-assist algorithms. Mathematics Subject Classification. 35Q20, 35Q84, 35Q93, 90B20. Keywords. Follow-the-leader models, Boltzmann-type equation, Fokker–Planck asymptotics, Hydrodynamic limit.
1. Introduction The last decade has been characterised by an increasing level of automation in decision processes, thanks to a deep technological development and algorithmic sensing. Nowadays, the coexistence of human and computer-based assistance is one of the main goals in the context of smart cities and vehicular dynamics, due to its potential ability to mitigate dangerous practices and to dissipate congestions created by the behavioural responses of the drivers, see e.g. [32,45]. As an example, we mention the advanced driverassistance systems (ADAS), which constitute a real interface between human drivers and machine-based decision making. Since motor vehicles are commonly durable goods, decisions by policy makers in this market are expected to impact over a time horizon of several years. On the other hand, a full penetration of the new technologies is unrealistic in the near future, even in those markets with high consumer demand, see e.g. [46]. Therefore, it is of interest to study transient regimes, in which the penetration rate of driverassist vehicles is quite small, say in the benchmark range 5–10%. Remarkably enough, field experiments recently confirmed the enhancement produced by suitable ADAS-type protocols in the regularisation of the stream of vehicles, even for small penetration rates. At the same time, virtually no observable effect was measured at the level of vehicle flux (throughput in the engineering literature), which seems to remain unchanged also after the activation of automatic control procedures, see [49]. In order to get a deeper understanding and mastery of these issues, it is fundamental to complement the experimental observations with theoretical insights into the links between the elementary vehiclewise dynamics
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