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c-user/rate_monotonic_manager.rst: Use Latex math for utilization formulas

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Joel Sherrill 2017-03-10 15:26:35 -06:00
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c-user/rate_monotonic_manager.rst
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@ -266,22 +266,21 @@ Processor Utilization Rule
.. index:: RMS Processor Utilization Rule .. index:: RMS Processor Utilization Rule
The Processor Utilization Rule requires that processor utilization be The Processor Utilization Rule requires that processor utilization be
calculated based upon the period and execution time of each task. The fraction calculated based upon the period and execution time of each task.
of processor time spent executing task index is ``Time(index) / The fraction of processor time spent executing task index is ``Time(i)
Period(index)``. The processor utilization can be calculated as follows: / Period(i)``. The processor utilization can be calculated as follows
where n is the number of tasks in the set being analyzed:
.. code-block:: c .. math::
Utilization = 0 Utilization = \sum_{i=1}^{n} Time_i/Period_i
for index = 1 to maximum_tasks
Utilization = Utilization + (Time(index)/Period(index))
To ensure schedulability even under transient overload, the processor To ensure schedulability even under transient overload, the processor
utilization must adhere to the following rule: utilization must adhere to the following rule:
.. code-block:: c .. math::
Utilization = maximum_tasks * (2**(1/maximum_tasks) - 1) maximumUtilization = n * (2^{\frac{1}{n}} - 1)
As the number of tasks increases, the above formula approaches ln(2) for a As the number of tasks increases, the above formula approaches ln(2) for a
worst-case utilization factor of approximately 0.693. Many tasks sets can be worst-case utilization factor of approximately 0.693. Many tasks sets can be