A parametric scheme for online uniform-machine scheduling to minimize the makespan

In this paper, we consider the Online Uniform Machine Scheduling problem in the case when speed $s_i=1$ for $i=n-k+1,\dots,n$ and $S_i=s$, $1\leq s\leq2$ for $i=1,\dots,k$, where $k$ is a constant, and we propose a parametric scheme with an asymptotic worst-case behavior (when $m$ tends to infinity).