Coupled PDE-ODE systems to model mixed autonomy traffic

Abstract: It is anticipated that in the near future, the penetration rate of vehicles with some autonomous capabilities (e.g., adaptive cruise control, lane following, full automation, etc.) will increase on roadways. This talk will show the potential impact on traffic of these automation systems. In particular, we will focus on the potential to control automated vehicles to stabilize traffic flow and reduce traffic emissions. We present a class of coupled PDE-ODE models describing the interaction of autonomous vehicles (AVs) with the surrounding traffic. The model consists of a scalar conservation law for the main traffic flow, coupled with ordinary differential equations describing the possibly interacting AV trajectories. The coupling is realized through flux constraints at the moving bottleneck positions, inducing the formation of non-classical jump discontinuities in the traffic density. We will show how low penetration rates are sufficient to significantly improve some traffic performances. We will propose some control strategies for the problem and show theoretical and numerical results. This is a joint work with C. Daini, P. Goatin and A. Ferrara.

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