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Networks in many safety-critical systems like avionics, automotive, and industrial plants have strict end-to-end delay requirements to be met for correct system operation. Existing software-defined real-time networks do not support data plane programmability provided by recent protocol-independent switch architectures such as P4. Our research enables time-aware flow forwarding in P4-enabled software-defined time-critical networks. In this paper, we introduce time-aware flow scheduling for P4-enabled SDN architectures. We study two scheduling policies: the first one prioritizes flows based on slack (i.e., how much time is left to reach the destination), and the second one uses finish time as a priority metric, which is determined from its data rate requirements. Both approaches were implemented and tested in the P4 software stack. We find that the slack-based forwarding scheme performs better in retaining real-time requirements. Our publicly released scheduler implementations will assist network engineers in adapting programmable switches to safety-critical applications that demand precise timing guarantees.