AFDX is the de facto communication standard in avionics domain. It is primarily used for the transmission of critical avionic flows. The mandatory certification process requires to upper bound the end-to-end transmission delay for each critical flow. Therefore, worst-case traversal time analysis has been implemented. However, it leads to a very lightly loaded network (up to 10%) as it considers very rare worst-case situations. Introducing a QoS mechanism is often a good solution to improve network utilisation since it allows differentiating critical flows based on their constraints as well as the transmission of less/non-critical flows with bounded impact on critical ones. Deficit Round Robin is such a mechanism and it is envisioned for future avionic networks. Using this mechanism, we propose to share the bandwidth between n − 1 classes for critical flows and one class for non-critical ones. Therefore the contributions of this paper are (1) to propose a quantum assignment that ensures that critical flows always respect their deadlines and maximises the bandwidth for non-critical ones and (2) to propose a heuristic for the distribution of the flows among different classes.