On Stochastic Network Calculus

This research is to develop a new form of stochastic network calculus for queuing system performance guarantees by making use of the Legendre transform at the sample-path level. A symmetrical formulation is resulted in through separate modeling of traffic flows and service capacities. Performance measures at single nodes and the service capacities of tandem systems are explicitly bounded at the sample-path level which consequently leads to bounds of the corresponding tail probabilities. Comparison and contrast to existing (deterministic and stochastic) network calculus formulations and to the theory of large deviations are performed. The applicability of the proposed approach is demonstrated by recovering the “bottleneck” phenomenon studied in large deviations under more general settings and by the improvement of scaling factors known to network calculus. Finally, perspectives on future research directions for tightening performance bounds are provided.