In this article we focus on instantaneous traffic fl ow optimization on a roundabout using a macroscopic approach. The roundabout is modeled as a concatenation of 2x2 junctions with one main lane and secondary incoming and outgoing roads. We consider a cost functional that measures the total travel time spent by drivers on the roundabout and compute its gradient with respect to the priority parameters at junctions. Then, through numerical simulations, the traffic behavior is studied on the whole roundabout. The numerical approximations compare the performance of a roundabout for instantaneous optimization of the priority parameters and fixed constant parameters.