Before revision:  We can take this advantage even more, precisely we can achieve a CR } of 2+R{3} if the number of requests in each stage is at most Rk, where R is a constant and 1 \le R \le 2. Both ratios are tight. Our algorithm can also accommodate the original kS2L-F without changing its basic structure .
After revision:  We can take this advantage even more, precisely we can achieve a CR } of 2+R{3} if the number of requests in each stage is at most Rk, where R is a constant and 1 \le R \le 2, where we do not have to know the value of R in advance. Finally we demonstrate that randomization also helps to get (slightly) better CR's .