 Finite-buffer workload map

With lookback net input $z(s)=a(-s,0]-Cs$, the stable finite-buffer workload is ${\sup }_{t\ge 0}\min ({\sup }_{0\le s\le t}z(s),B+{\inf }_{0\le s\le t}z(s))$. Since $z(0)=0$, it lies between zero and B, and is at most the infinite-buffer supremum $q(a)={\sup }_{s\ge 0}z(s)$. For a constant-rate burst which builds exactly x work from an empty queue, no upper reflection occurs when $x\le B$ and both workloads equal x.