 Workload Chernoff bound for independent increments

For independent identically distributed traffic increments and constant service $C$, let $a(s)=\mathbb{E}[e^{s(X-C)}]$. If $a(s)<1$, apply the Chernoff bound at each candidate workload window and sum a geometric series. This bounds the stationary random-walk supremum. It explains the effective bandwidth criterion $\alpha (s)<C$ and distinguishes a queue's infinite-horizon overflow event from a single-window traffic event.