We investigate on-line algorithms that schedule preemptive tasks on single processor machines when the arrival time of a task is not known in advance and the length of a task is unknown until its termination. The goal is to minimize the sum of the waiting times over all tasks. We formulate an on-line algorithm, RR, which is an ideal version of so-called Round Robin algorithm. It is known that, if all tasks arrive at one time, RR is 2-competitive [W]. We prove that, when tasks may arrive at different times, the competitve ratio of RR is between 2(k–1)/H _k –1 and 2(k–1), where k is the maximal number of tasks that can exist at any given time. Our analysis also yields bounds on the sum of response times, and through several criteria we demonstrate the effectiveness of Round Robin algorithm.