An extended second-order macroscopic traffic flow model is presented that describes multi-lane traffic dynamics and also incorporates the effects of adaptive cruise control (ACC) or cooperative ACC (CACC). The extended model equations stem from a recently proposed multi-lane gas-kinetic traffic flow (GKT) model that can simulate lane changes due to vehicle interactions as well as spontaneous ones. The proposed extension that models the effects of ACC/CACC satisfies the time-gap principle of such systems on each lane and allows for consideration of mixed traffic comprising both manual and ACC/CACC vehicles. Numerical simulations are performed for a particular three-lane motorway stretch in the United Kingdom, where recurrent traffic congestion is observed during the morning peak hours, so as to compare the effects of ACC/CACC in the traffic flow conditions with those resulting from manual driving.
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