Improving Scalability of Delay Bound with Stochastic Network Calculus

Stochastic network calculus is the probabilistic extension of deterministic network calculus for offering stochastic performance guarantee in packet networks. However, it has been shown that the attempts to achieve a scalable stochastic performance bound only have limited success. In this paper, we propose a novel stochastic network calculus approach to perform scalability analysis for the end-to-end delay. With the assumption of independent arrival and services across multiple network nodes, a scalable delay bound is derived in linear way with its moment generating functions. After that, we investigate the tightness of the bound for further improving its scalability using Doob's maximal inequality on a suitable martingale construction. Compared with previous conclusions, numerical results validate that our approach improves the scalability of stochastic delay bound in terms of the linear scaling and tightness. The results help make an important step forward towards improving scalability for delay analysis of realistic SDN.