Abstract.  We consider the online problem of scheduling jobs with deadlines in a single-processor system that allows preemption. The aim is to maximize the total value of jobs completed by their deadlines. It is known that the competitive ratio for this problem is Θ(k), where k is the ratio of the maximum possible value density to the smallest possible one. Yet, if the online scheduler is given a processor faster (say, two times faster) than the adversary, there exists an algorithm called SLACKER that can achieve an O(1) competitive ratio. In this paper, we show that using only additional unit speed processors is a possible but not a cost effective way to achieve constant competitiveness. Specifically, we found that Θ(log k) unit speed processors are required. On the other hand, we give a better analysis of the competitiveness of SLACKER; this new analysis enables us to show that SLACKER when extended to the multi-processor systems can still guarantee constant competitiveness.