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In the HRRN scheduling, priority formula is

P = (W+E)/E , where W: waiting time and E: estimated run time.

CPU finds the job that has highest priority value and does that job.

However, the formula is equivalent to P = 1 + W/E. If we just "minus 1" and make a new formula P' = W/E, the order of jobs does not change.

So the question is, why do we use P = (W+E)/E rather than P' = W/E? Is there any specific reason (like P must be greater than 1)? Or are they just using the original formula since it was made?

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You can use either formula, since as you mention, the resulting algorithms are completely equivalent. The reasoning behind the standard formula $(W+E)/E$ is that it is the ratio between the expected completion time to the expected running time. Presumably when the algorithm was first suggested, the expected completion time was denoted by its own variable.

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