Conflict-Aware Online Joint Routing and Scheduling With Sparsification for Nonharmonic Traffic in Time-Sensitive Networks

Time-Sensitive Networking (TSN) enables deterministic communication over standard Ethernet, critical for Industrial Internet of Things (IIoT) applications. However, scheduling traffic flows with non-harmonic periods poses a considerable challenge for existing online methods. This paper proposes an integrated framework consisting of conflict-aware pre-routing with a recovery scheduling strategy to enhance schedulability for non-harmonic traffic. In this paper, we first propose a non-harmonic-aware scheduling conflict index (KC) that quantifies scheduling difficulty via incorporating packet sizes and the LCM/GCD relationship between periods, and integrate it into a conflict-aware pre-routing algorithm. Then, we present a two-phase scheduling strategy in which the recovery phase combines sparsification—achieved by maximizing transmission start times—with a novel jitter-decreasing control that first applies the maximum allowable jitter and progressively reduces it. Finally, we carry out thorough experimental evaluations on a realistic topology. Results show that for non-harmonic periods, our method achieves approximately 10% better schedulability than IRAS. The recovery mechanism achieves an over 95% success rate and sub-second execution time, meeting online industrial configuration requirements.