The document discusses scheduling mixed-criticality applications in time-sensitive networks. It proposes using time-aware shapers and schedulers defined in the Time-Sensitive Networking standards to support both time-triggered and audio-video traffic on a single network infrastructure. The problem of determining schedules for the time-triggered traffic queues at each network node to ensure all traffic deadlines are met is formulated. A metaheuristic optimization approach called GRASP is developed to solve this scheduling problem. Preliminary results suggest the approach can find schedules for example test cases that meet the timing requirements of both critical and non-critical traffic.