Time Demand Analysis. Real Time System Schedulability of Fixed-Priority Tasks We have identified...
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Transcript of Time Demand Analysis. Real Time System Schedulability of Fixed-Priority Tasks We have identified...
Time Demand Analysis
Real Time System
Schedulability of Fixed-Priority Tasks
• We have identified several simple schedulability tests for fixed priority scheduling:– A system of n independent preemptable periodic tasks with Di = pi can be
feasibly scheduled on one processor using RM if and only if U ≤ n (21/n – 1)⋅– A system of simply periodic independent preemptable tasks with Di ≥ pi is
schedulable on one processor using the RM algorithm if and only if U ≤ 1
– [similar results for DM]
• But: there are algorithms and regions of operation where we don’t have a schedulability test and must resort to exhaustive simulation– Is there a more general schedulability test? Yes, but not as simple as those
we’ve seen so far…
Real Time System
Schedulability Test for Fixed-Priority Tasks
• Fixed priority algorithms are predictable and do not suffer from scheduling anomalies– The worst case execution time of the system occurs with the worst
case execution time of the jobs– Unlike dynamic priority algorithms, which can exhibit anomalous
behaviour• Use this as the basis for a general schedulability test:
1. Find the critical instant when the system is most loaded, and has its worst response time
2. Use time demand analysis to determine if the system is schedulable at that instant
3. Prove that, if a fixed-priority system is schedulable at the critical instant, it is always schedulable
Real Time System
1. Finding the Critical Instant
Finding the Critical Instant
Real Time System
Using the Critical Instant
• Having determined the critical instants, show that for each job Ji,c released at a critical instant, that job and all higher priority tasks complete executing before their relative deadlines
• If so, the entire system be schedulable…
• That is: don’t simulate the entire system, simply show that it has correct characteristics following a critical instant– This process is called time demand analysis
Real Time System
Time-Demand Analysis
Real Time System
Time Demand Analysis
Real Time System
Time Demand Analysis
Real-Time Systems
Time Demand Analysis…calculate
Example:
•
•
•
• Test if is satisfied for • Test if is satisfied for • Test if is satisfied for
)2,7(),2,5(),1,4( 321 TTT
1)( 11 Ctw
14
2)( 11
22
te
p
tCtw
1
1
0for ,)(i
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kii ptC
p
tCtw
Time-Demand Function
25
14
2)( 22
11
33
tte
p
te
p
tCtw
ttw )(1 41)4(4 1 wt
Ok!
ttw )(2 54)5(,43)4(4,5 22 wwt
Ok!
78)7(
,56)5(,45)4(4,5,7
3
33
w
wwt
Not satisfied!
ttw )(3
Real-Time Systems
Time Demand Analysis
1. For each , determine the time-demand function
according to
2. Check whether the inequality is satisfied for values of that are equal to
3. The time complexity of the time-demand analysis for each task is
1
1
)(i
kk
kii C
p
tCtw)(twi
ni ,,2,1
ttwi )(
t
kik ppjikpjt ,,2,1;,,2,1;
))(( 1ppnO n
Another example
Real-Time Systems
Another Example: Step 1
Real-Time Systems
Example: Step 2
Real-Time Systems
Example: Step 3
Real-Time Systems
Example: Step 4
Real Time System
Time demand Analysis: Summary