In this paper, we first assess the most relevant existing solutions enabling mixed-criticality on the AFDX and select the most adequate one. Afterwards, the specification of an extended AFDX, based on the Burst-Limiting Shaper (BLS), is detailed to fulfill the main avionics requirements and challenges. Finally, the preliminary evaluation of such a proposal is conducted through simulations. Results show its ability to guarantee the highest criticality traffic constraints, while limiting its impact on the current AFDX traffic