Constant-rate burst path ($t=x/(v-C),v>C$)

Use arrival rate v during the last t time units and the normal stable rate mu before that, where $\mu <C$. The lookback net input increases from zero to x over the burst, then decreases because the earlier net drift is negative. Its infinite-buffer workload is x, as is the finite-buffer workload map for capacity at least x. For a local convex path cost with density g and $g(\mu )=0$, its cost is $tg(v)=xg(v)/(v-C)$. These paths realize or approximate the optimal workload cost even if an optimizing duration is not attained.