Our goal is to design an IEEE 802.11e/AFDX (WiFi with QoS/Avionics Full DupleX switched Ethernet) hybrid network. More precisely the aim is to guarantee the QoS requirements of AFDX traffics transmitted on an IEEE 802.11e wireless network, for on-ground maintenance applications. The AFDX requirements are related to the temporal constraints (latency and jitter). The use of IEEE 802.11e induces several constraints due to the wireless communication medium (QoS, non-deterministic access method, high packet loss rate, transmission errors). In this paper, we present a HCCA (HCF Controlled Channel Access) scheduling algorithm named AWS (AFDX Wireless Scheduler) which improves the performance of the HCCA Reference Scheduler (RS) in order to convey AFDX traffics on an IEEE 802.11e wireless network. AWS is based on the classification of flows, on the retransmission management of frames and on the guarantee of deadline and maximum jitter of frames. We also present, in this paper, an optimized version of AWS (OAWS) which uses the available bandwidth of TXOP periods for transmitting frames near of their deadline and frames in retransmission. Performance evaluation results show that a very large reduction of dropped packets and a better throughput are obtained with AWS compared to RS. The performance of the optimized version of AWS (OAWS) are better than those of AWS.