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Figure 1: Traffic waves generated by human driving increase the energy consumption of traffic flow. A small fraction of wellcontrolled automated vehicles can smooth the flow and the reduce energy consumption.

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In this article, we study the problem of stabilizing the traffic flow on a ring road to a uniform steady-state using autonomous vehicles (AV). Traffic is represented at microscopic level via a Bando-Follow-the-Leader model capable of reproducing phantom jams. For the single-lane case, a single AV can stabilize an arbitrary large ring road with an arbitrary large number of cars. Moreover, this stabilization is exponentially quick with a decay rate independent of the number of cars and control gain also independent of the number of cars. On the other side, the stabilization domain and stabilization time depend on the number of cars. Two types of controller algorithms are proposed: a proportional control and a proportional-integral control. In both cases, the measurements used by the controller only depend on the local data around the AV, enabling an easy implementation. After numerical tests of the single-lane case, a multi-lane model is described using safety-incentive mechanism for lane change. Numerical simulations for the multi-lane ring road suggest that the control strategy is also very efficient in such setting, even with a single AV.