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How to free a road from vehicle traffic as efficiently as possible and in agiven time, in order to allow for example the passage of emergency vehicles? Weare interested in this question which we reformulate as an optimal controlproblem. We consider a macroscopic road traffic model on networks,semi-discretized in space and decide to give ourselves the possibility tocontrol the flow at junctions. Our target is to smooth the traffic along agiven path within a fixed time. A parsimony constraint is imposed on thecontrols, in order to ensure that the optimal strategies are feasible inpractice. We perform an analysis of the resulting optimal control problem,proving the existence of an optimal control and deriving optimality conditions,which we rewrite as a single functional equation. We then use this formulationto derive a new mixed algorithm interpreting it as a mix between two methods: adescent method combined with a fixed point method allowing globalperturbations. We verify with numerical experiments the efficiency of thismethod on examples of graphs, first simple, then more complex. We highlight theefficiency of our approach by comparing it to standard methods. We propose anopen source code implementing this approach in the Julia language.

Optimal scenario for road evacuation in an urban environment