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In computer operating systems where background jobs must occasionally be preempted in order to run high priority jobs, it is generally the case that efficient operation and rapid response to the high priority jobs are conflicting objectives. In this short paper a preemption scheme in which a delay is introduced is shown to provide the designer with the ability to trade off these two performance measures to any desired degree. A mathematical model is developed and results are derived for the mean high priority waiting time and a measure of operating efficiency. The paper concludes with a discussion of examples designed to illustrate how the above performance measures interact as a function of system parameters.