Exact(31)
: represents the arrival time of task τ i. : represents the arrival time of task τ j.
D i =P i : the deadline of task τ i (message streams S i ) is equal to its period.
recordtime(τ i ) is the starting time of the sliding window of task τ i, which initializes to be 1.
UER′(τ i, t) is the maximal speed of task τ i starting from time t, while it is not blocked.
From lines 11 to 13, we see that every sliding window of task τ i can have capacity(τ i ) instances at most.
Every arrival task is an instance of its corresponding task, and the jth instance of task τ i is denoted as τ i,j.
Similar(29)
For a given task τ i, the busy period calculation is performed, considering the execution of tasks τ j (j
In addition, let N cs (τ i ) be the number of critical sections for τ i, and the total amount of computation for τ i under all non-critical sections be c ns (τ i ), then the amount of computation for task τ i is {c}_i={c}_{ns}left {tau}_iright)+{displaystyle sum_{j=1}^{N_{cs}left {tau}_iright)}{c}_{cs}left {z}_{i,j}right)}.
Length is the number of instructions (computational cost) of the task τ k.
It is possible to verify this because concerning any time instant t, between the interval (k i P i ) of a task τ i (j
We use U i to denote the time/utility function of the task τ i, and thus, U i is the time/utility function of any instance of τ i.
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