# 4. Fixed-Priority Scheduling

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4 Timeline for task set C Task a b c Critique of utilization-based tests They are not exact They are not general But they are Ω(N) Which makes them interesting for a large class of users The test is said to be sufficient but not necessary and as such falls in the class of schedulability tests Time 2011/12 UniPD / T. Vardanega Real-Time Systems 166 of /12 UniPD / T. Vardanega Real-Time Systems 167 of 352 Response time analysis 1 Calculating R The worst-case response time of task is first calculated and then checked (trivially) with its deadline R i D i Within, each higher priority task will execute a times The ceiling function gives the smallest integer greater than the fractional number on which it acts E.g., the ceiling of 1/3 is 1, of 6/5 is 2, and of 6/3 is 2 The total interference suffered by from in Where I is the interference from higher priority tasks is given by 2011/12 UniPD / T. Vardanega Real-Time Systems 168 of /12 UniPD / T. Vardanega Real-Time Systems 169 of 352 4

5 Response time equation Response time algorithm for i in 1..N loop -- for each task in turn n := 0 Where is the set of tasks with priority higher than task Solved by forming a recurrence relationship The set of values is monotonically non-decreasing When the solution to the equation has been found must not be greater than (e.g. 0 or ) loop calculate new if then exit value found end if if then exit value not found end if n := n + 1 end loop end loop If the recurrence does not converge before T i we can still set a termination condition that attempts to determine how long past T i job i completes 2011/12 UniPD / T. Vardanega Real-Time Systems 170 of /12 UniPD / T. Vardanega Real-Time Systems 171 of 352 Example: task set D Example (cont d) Task Period Computation Time Priority Utilization T C P U a (high) b c (low) /12 UniPD / T. Vardanega Real-Time Systems 172 of /12 UniPD / T. Vardanega Real-Time Systems 173 of 352 5

11 Summary A simple (periodic) workload model Delving into fixed-priority scheduling A (rapid) survey of schedulability tests Some extensions to the workload model Priority assignment techniques 2011/12 UniPD / T. Vardanega Real-Time Systems 194 of

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