Network Calculus Bounds for Time-Sensitive Networks: A Revisit

Abstract

Network calculus (NC), particularly its min-plus branch, has been extensively utilized to construct service models and compute delay bounds for time-sensitive networks (TSNs). This paper provides a revisit to the fundamental results. In particular, counterexamples to the most basic min-plus service models, which have been proposed for TSNs and used for computing delay bounds, indicate that the packetization effect has often been overlooked. To address, the max-plus branch of NC is also considered in this paper, whose models handle packetized traffic more explicitly. It is found that mapping the min-plus models to the max-plus models may bring in an immediate improvement over delay bounds derived from the min-plus analysis. In addition, an integrated analytical approach that combines models from both the min-plus and the max-plus NC branches is introduced. In this approach, the max-plus $g$-server model is extended and the extended model, called $g^{x}$-server, is used together with the min-plus arrival curve traffic model. By applying the integrated NC approach, service and delay bounds are derived for several settings that are fundamental in TSNs.