Having trouble proving relation is not necessary for RMS real-time scheduling to be true.
I can see how to solve the right side of the equation but when not knowing what C and T are how can I prove it is not necessary and confirm it is sufficient?
I thought about changing the C/T to a variable such as x and starting from N = 1 and solving for x at each step until the RHS is not >= to the LHS. Is this a correct way to go about this?
As the questions stated the bound you provided n(2^(1/n)-1) is sufficient in the sense that if it is true then the set of tasks is schedulable but it is not complete, it will reject task sets that are still schedulable under RMS. A simple example is a harmonic task set. A harmonic task set is one where each period is is an exact multiple of all the tasks with small periods. A trivial example is the task set of two tasks each with a capacity of 1 and a period of 2. It has 100% utilization and is schedulable under RMS but its utilization is greater than the percentage 0.828 listed in the chart for N=2.
In general, to determine if a task set is schedulable under RMS the follow recurrence relationship is solved for each task i:
If this value is less than T_i for each task assuming implicit deadlines) than the task set is schedulable.
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