Stochastic Network Calculus for Rate-Constrained Traffic Based on Markov Service Models

Time-Triggered Ethernet (TTEthernet) is an integrated avionics interconnection solution that supports distributed clock synchronization and Time-Triggered (TT) traffic communication. When the exact TT schedule is unavailable, it becomes challenging to use Deterministic Network Calculus (DNC) to derive the delay bound of RC traffic under the blocking effects of high-priority TT traffic. To address this issue, this paper proposes a method that constructs a Markov service model based solely on the statistical characteristics of TT traffic. By leveraging the moment-generating functions of the arrival and service processes, Stochastic Network Calculus (SNC) is applied to perform a probabilistic delay bound analysis for RC traffic. A simplified approach abstracts the service process of RC traffic at a node as an ON/OFF process, where stochastic network calculus is performed based on service rates and the transition probabilities between the two states, yielding results comparable to deterministic analysis. Furthermore, by incorporating the Hurst parameter and one-step correlation parameter, the service process of RC traffic is modeled as a Markov Modulated Poisson Process (MMPP), which represents a superposition of multiple ON/OFF processes and captures higher-order statistical properties. Case studies show that, for probabilistic delay bounds, the MMPP model alleviates the pessimism inherent in the ON/OFF process model, yielding tighter delay bounds.