A Formal Link Between Response Time Analysis and Network Calculus

Classical Response Time Analysis (RTA) and Network Calculus (NC) are two major formalisms used for the verification of real-time properties. We offer mathematical links between these two different theories. Based on these links, we then prove the equivalence of various key notions in both frameworks. This enables specialists of both formalisms to get increase confidence on their models, or even, like the authors, to discover errors in theorems by investigating apparent discrepancies between some notions expected to be equivalent. The presented mathematical results are all mechanically checked with the interactive theorem prover Coq, building on existing formalizations of RTA and NC. Establishing such a link between NC and RTA paves the way for improved real-time analyses obtained by combining both theories to enjoy their respective strengths (e.g., multicore analyses for RTA or clock drifts for NC)