Optimizing Quantum Assignment for DRR in TSN: A Network Calculus-Based Method

Time-sensitive networking (TSN) is an evolving set of Ethernet standards designed to ensure deterministic communication. Several schedulers can be applied in TSN to support the transmission of mixed time-critical traffic, among which deficit round robin (DRR) is a potential candidate since it can achieve fair queuing with very low complexity. The real-time quality of service (QoS) performance of DRR is determined by the quantum assigned to each queue, yet obtaining configurations with QoS guarantess at the network level is challenging due to the complex interactions of traffic flows. Conventional configuration methods typically adopt the framework based on ex-post schedulability verification, using heuristic algorithms to search for feasible configurations. However, these methods incur significant time overhead during the solution searching and performance verification stage and often lead to bandwidth wastage. This paper proposes an innovative DRR quantum assignment method that maximizes bandwidth utilization while providing prior realtime QoS guarantees. We use network calculus (NC) to build the optimization model and develop a numerical approximation approach based on local analytic solutions to solve for the optimal solution, making our method efficient and scalable. The correctness and optimality of our method are formally proven. Through experiments with network cases of various scales, we comprehensively evaluate the performance of our method. The results show that our method exhibits significant advantages over the conventional methods in terms of both bandwidth utilization and time complexity. In industrial-sized cases, our method saves around 31% of transmission bandwidth compared to the state-of-the-art with a runtime within milliseconds, which is several orders of magnitude faster.