On Computing Bounds on Average Backlogs and Delays with Network Calculus

The stochastic network calculus is an analytical tool which was mainly developed to compute tail bounds on backlogs and delays. From these, bounds on average backlogs and delays are derived in the literature by integration. This paper improves such bounds on average backlogs by using Jensen's inequality; improved bounds on average delays follow immediately from Little's Law. The gain factor can be substantial especially at high utilizations, e.g., of order ${\Omega}\left(\frac{1}{1-\rho}\right)$ when $\rho\rightarrow 1$. This gain is further numerically illustrated for Markov-modulated On-Off arrival processes. Moreover, the paper shows how to improve standard stochastic network calculus performance bounds by suitably using FIFO service curves.