Industrial automation and control systems are increasingly deployed using wireless networks in master-slave, star-type configurations that employ a slotted timeline schedule. In this paper, the scheduling of (re)transmissions to meet real-time constraints in the presence of non-uniform interference in such networks is considered. As packet losses often occur in correlated bursts, it is often useful to insert gaps before attempting retransmissions. In this paper, a quantum Earliest Deadline First (EDF) scheduling framework entitled ‘Eligible EDF’ is suggested for assigning (re)transmissions to available timeline slots by the master node. A simple but effective server strategy is introduced to reclaim unused channel utilization and replenish failed slave transmissions, a strategy which prevents cascading failures and naturally introduces retransmission gaps. Analysis and examples illustrate the effectiveness of the proposed method. Specifically, the proposed framework gives a timely throughput of 99.81% of the timely throughput that is optimally achievable using a clairvoyant scheduler.