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c-user/rate_monotonic_manager.rst: Use Latex math for utilization formulas
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@ -266,22 +266,21 @@ Processor Utilization Rule
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.. index:: RMS Processor Utilization Rule
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.. index:: RMS Processor Utilization Rule
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The Processor Utilization Rule requires that processor utilization be
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The Processor Utilization Rule requires that processor utilization be
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calculated based upon the period and execution time of each task. The fraction
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calculated based upon the period and execution time of each task.
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of processor time spent executing task index is ``Time(index) /
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The fraction of processor time spent executing task index is ``Time(i)
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Period(index)``. The processor utilization can be calculated as follows:
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/ Period(i)``. The processor utilization can be calculated as follows
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where n is the number of tasks in the set being analyzed:
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.. code-block:: c
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.. math::
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Utilization = 0
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Utilization = \sum_{i=1}^{n} Time_i/Period_i
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for index = 1 to maximum_tasks
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Utilization = Utilization + (Time(index)/Period(index))
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To ensure schedulability even under transient overload, the processor
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To ensure schedulability even under transient overload, the processor
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utilization must adhere to the following rule:
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utilization must adhere to the following rule:
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.. code-block:: c
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.. math::
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Utilization = maximum_tasks * (2**(1/maximum_tasks) - 1)
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maximumUtilization = n * (2^{\frac{1}{n}} - 1)
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As the number of tasks increases, the above formula approaches ln(2) for a
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As the number of tasks increases, the above formula approaches ln(2) for a
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worst-case utilization factor of approximately 0.693. Many tasks sets can be
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worst-case utilization factor of approximately 0.693. Many tasks sets can be
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