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This paper analyzes various algorithms for scheduling low priority disk drive tasks. The derived closed form solution is applicable to class of greedy algorithms that include a variety of background disk scanning applications. By paying close attention to many characteristics of modern disk drives, the analytical solutions achieve very high accuracy---the difference between the predicted response times and the measurements on two different disks is only 3% for all but one examined workload. This paper also proves a theorem which shows that background tasks implemented by greedy algorithms can be accomplished with very little seek penalty. Using greedy algorithm gives a 10% shorter response time for the foreground application requests and up to a 20% decrease in total background task run time compared to results from previously published techniques.