Stochastic Network Calculus is a probabilistic method to compute performance bounds in networks, such as end-to-end delays. It relies on the analysis of stochastic processes using formalism of (Deterministic) Network Calculus. However, unlike the deterministic theory, the computed bounds are usually very loose compared to the simulation. This is mainly due to the intensive use of the Boole's inequality. On the other hand, analyses based on martingales can achieve tight bounds, but until now, they have not been applied to sequences of servers. In this paper, we improve the accuracy of Stochastic Network Calculus by combining this martingale analysis with a recent Stochastic Network Calculus results based on the Pay-Multiplexing-Only-Once property, well-known from the Deterministic Network calculus. We exhibit a non-trivial class of networks that can benefit from this analysis and compare our bounds with simulation.

翻译：随机网络演算是一种用于计算网络中性能界限（如端到端延迟）的概率方法，它基于（确定性）网络演算的形式体系对随机过程进行分析。然而，与确定性理论不同，其计算的界限通常远宽于仿真结果，这主要源于布尔不等式的过度使用。另一方面，基于鞅的分析虽能获得紧致界限，但迄今尚未应用于服务器序列。本文通过将鞅分析与近期基于确定性网络演算中著名的“单次复用付费”性质的随机网络演算成果相结合，改进了随机网络演算的精度。我们展示了一类可从该分析中获益的非平凡网络，并将所得界限与仿真结果进行了比较。