Lyapunov-Based Stability and Delay Bounds for IEEE 802.1Qbv in Imperfectly Synchronized TSN

IEEE 802.1Qbv Time-Aware Shaper (TAS) is a cornerstone of Time-Sensitive Networking (TSN), offering bounded latency and near-zero jitter for critical traffic (CT). However, prior scheduling algorithms either rely on ideal clock synchronization or resource reservation, sacrificing bandwidth efficiency. In this paper, we present a unified framework for the analysis of stability for queueing process and delay bounds in TAS, in which clock drift, gate-switching jitter, and sync-message loss are modeled as a stochastic service-loss process in TAS scheduling. Then, a Lyapunov-drift analysis is used to derive both deterministic worst-case delay bounds under maximal service loss and probabilistic stability conditions when the average service rate exceeds the arrival rate. Finally, based on the theoretical analysis, the guard-band sizing and slot-provisioning guidelines are proposed for practical TSN deployment under non-ideal synchronization. Extensive simulations have been conducted to validate the tightness of our delay bounds, and the simulation results demonstrate that the proposed configuration rules can guarantee bounded latency and queue stability.