Graph-Based Deep Learning for Fast and Tight Network Calculus Analyses

Network Calculus (NC) computes end-to-end delay bounds for individual data flows in networks of aggregate schedulers. It searches for the best model bounding resource contention between these flows at each scheduler. The literature proposes different analyses to consider realistic behavior of networked system such as multiplexing, and contention between flows in consecutive queues even though there is no knowledge on the multiplexing discipline employed by the crossed systems (arbitrary multiplexing property). Bounding delays in entire feed-forward networks needs to keep track of such behavior. Moreover, not a single of the existing fast NC heuristics that are based on an algebraic analysis is strictly best. An exhaustive search for the best combination of analyses, i.e., contention modeling, was proposed with the Tandem Matching Analysis (TMA). Additional measures made it scale best among the NC analyses, yet bounding delays may still require several hours of computation time. In this paper, we demonstrate the ability to couple graph-based neural networks with NC by extending TMA with a prediction mechanism replacing the exhaustive search. We propose a framework that learns from NC's TMA, predicts best contention models, and feeds them back to TMA where the according NC computations are executed. We achieve provably valid bounds that are very competitive with the exhaustive TMA. We observe a maximum relative error to TMA below 12%, while execution times remain nearly constant, and outperform TMA in differently sized networks by several orders of magnitude.