Formal Timing Analysis of CQF Interference in TSN: A Network Calculus-Based Approach

Cyclic Queuing and Forwarding (CQF) is an increasingly adopted mechanism in Time-Sensitive Networking (TSN) for bounding end-to-end delays through fixed-length cycles with alternating transmission queues. While timing guarantees for CQF flows are well established under both time-triggered (TT) and event-triggered (ET) implementations, the worst-case interference that CQF may impose on other traffic classes in mixed-criticality TSN networks remains an open problem. This challenge is exacerbated by the structured, non-work-conserving behavior of CQF and the complexity of its interaction with heterogeneous TSN scheduling mechanisms such as TAS, CBS, and SP. This paper presents the first formal framework for quantifying the worst-case interference caused by CQF on other schedulers under both TT- and ET-based implementations. We propose a network-calculus-based CQF real-time interface abstraction that models the residual service available to coexisting traffic. We formally derive closed-form upper bounds on CQF-induced interference, explicitly capturing bidirectional interactions between CQF and both higher- and lower-priority traffic classes. These bounds can be modularly and seamlessly integrated into existing schedulability analyses, enabling scalable and compositional timing verification in hybrid TSN architectures. Extensive evaluations on synthetic benchmarks and realistic TSN configurations demonstrate the analytical effectiveness, scalability, and practical applicability of the proposed framework in certifying end-to-end guarantees in mixed-criticality TSN systems.