We investigate the problem of on-line scheduling jobs on m identical p
arallel machines where preemption is allowed. The goal is to minimize
the makespan. We derive an approximation algorithm with worst-case gua
rantee m(m)/(m(m) - (m - 1)(m)) for every m greater than or equal to 2
, which increasingly tends to e/(e - 1) approximate to 1.58 as m --> i
nfinity. Moreover, we prove that for no m greater than or equal to 2 t
here does exist any approximation algorithm with a better worst-case g
uarantee.