Книга: Real-Time Concepts for Embedded Systems

14.4.1 Basic RMA Schedulability Test

14.4.1 Basic RMA Schedulability Test

Equation 14.1 is used to perform the basic RMA schedulability test on a system.


Ci = worst-case execution time associated with periodic task I

Ti= period associated with task i

n = number of tasks

U(n) is the utilization factor. The right side of the equation is the theoretical processor utilization bound. If the processor utilization for a given set of tasks is less than the theoretical utilization bound, this set of tasks is schedulable. The value of U decreases as n increases and eventually converges to 69% when n becomes infinite.

Let's look at a sample problem and see how the formula is implemented. Table 14.3 summarizes the properties of three tasks that are scheduled using the RMS.

Table 14.3: Properties of tasks.

Periodic Task Execution Time Period (milliseconds)
Task 1 20 100
Task 2 30 150
Task 3 50 300

Using Equation 14.1, the processor utilization for this sample problem is calculated as follows


Total utilization for the sample problem is at 57%, which is below the theoretical bound of 77%. This system of three tasks is schedulable, i.e., every task can meet its deadline.

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