CprE 458/558: Real-Time Systems
Dynamic Planning Based
Scheduling
CprE 458/558: Real-Time Systems (G. Manimaran)
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The big picture
CprE 458/558: Real-Time Systems (G. Manimaran)
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Planning based scheduling approach
• A planning based approach will evaluate
different possible schedules for a given task
set and chooses a final feasible schedule
which satisfies all the constraints
• Ideally, one should evaluate all the possible
schedules before choosing the final schedule.
• However, the number of possible schedules
for a reasonable number of tasks is huge.
Therefore, all the possible schedules in the
search space cannot be evaluated
CprE 458/558: Real-Time Systems (G. Manimaran)
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Scheduler model
CprE 458/558: Real-Time Systems (G. Manimaran)
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Scheduler model (contd.)
• Schedulability checking (on-line)
– by the scheduler
• Schedule construction (on-line)
– by the scheduler
• Dispatching & Resource reclaiming
– by the processors; each processor runs reclaiming
algorithm when it finishes a task execution.
Sched-check at a most opportune time
(punctual point)
– Too early: tend to reject tasks because reclaiming
may not be exploited fully
– Too late: if rejected, the application has no time to
take any recovery action
CprE 458/558: Real-Time Systems (G. Manimaran)
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Task set model
• Planning based scheduler assumes
worst case computation time for each
task
• Planning based scheduler performs nonpreemptive scheduling
CprE 458/558: Real-Time Systems (G. Manimaran)
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Planning based scheduling: search space
• The search space for the planning based
scheduling consists of different possible
schedules for the given task set
• A typical planning based scheduler will
prune the search space by exploring
different schedules and choose a final
feasible schedule based on a heuristic
function
CprE 458/558: Real-Time Systems (G. Manimaran)
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Search space: example
Aperiodic Task set: Ti = (ri, ci, di)
Different possible
schedules
T1 = (0,2,8) and T2 = (1,5,6)
Schedule #1
T1
T2
2
0
6
7
8
Schedule #2
T2
1
T1
6
7
8
CprE 458/558: Real-Time Systems (G. Manimaran)
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Spring/Myopic Scheduling Algorithm
• Notations/Jargon
– EATSK = earliest available time when
resource Rk becomes available for shared
access
– EATeK = earliest available time when
resource Rk becomes available for exclusive
access
– Avail_time(j) = earliest time at which the
processor Pj becomes available for
executing a task
– EST(Ti) = Max(ri, min(avail_time(j)), max(EATUK) )
CprE 458/558: Real-Time Systems (G. Manimaran)
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Understanding EST: Example
R1
Time = 10
P1
Tx
Time = 5
Arrival of
tasks
Ti
Time = 3
EST(Ti) = max(3, 5, 10) = 10
CprE 458/558: Real-Time Systems (G. Manimaran)
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Definitions
• Feasible task:
– A task Ti is feasible in a schedule if its
timing constraint and resource requirements
are met in the schedule, that is, if
– EST(Ti) + Ci ≤ Di.
• Feasible schedule:
– A schedule for a set of tasks is said to be a
feasible schedule if all the tasks are feasible
in the schedule.
CprE 458/558: Real-Time Systems (G. Manimaran)
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Definitions (contd..)
• Strongly feasible schedule:
– A partial schedule for a subset of tasks. A
partial schedule is said to be strongly
feasible if all the schedules obtained by
extending the current schedule by any one
of the remaining tasks within a window,
called the feasibility check window K are
also feasible.
CprE 458/558: Real-Time Systems (G. Manimaran)
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Spring/Myopic Scheduling Algorithm
Heuristic search algorithm based on a notion of
strong feasibility. Branch & Bound search.
1. Sort the “n” tasks in deadline order.
2. Check for strong feasibility for K tasks which
are in the feasibility check window.
(i.e., Check if EST(Ti) + Ci <= di)
3. If the current vertex is strongly feasible
– Compute heuristic value Hi = di + W * EST(Ti)
– Choose the best (smallest) H value, let it be Hx.
– Extend the schedule with task Tx.
CprE 458/558: Real-Time Systems (G. Manimaran)
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Spring/Myopic Scheduling (contd.)
4. Else Backtrack to the previous vertex,
Extend the schedule with next best task.
5. Repeat steps 2-4 until either:
– Feasible schedule is obtained.
– Maximum backtracks reached.
– No more backtracking is possible.
Algorithm Complexity: O(Kn + Backtracks).
Exhaustive search algorithm: O(m^n) where
m: # processors; n: # tasks.
CprE 458/558: Real-Time Systems (G. Manimaran)
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Myopic scheduling: Example
Task Id
Ready time
WCET
Deadline
R1 usage
R2 usage
T1
0
28
80
S
N
T2
0
24
73
N
E
T3
14
39
93
E
E
T4
5
25
89
S
N
T5
35
21
108
N
S
Ordered by their
deadlines
T2 T1 T4 T3 T5
Feasibility
check window,
K=3
Assume, w = 1
H2 = 73 + 0
H1 = 80 + 0
H4
89 ++ 0
5
H1 == 80
H4 = 89 + 5
H4 = 89 + 24
H3 = 93 + 24
H3 = 93 + 28
H5 == 93
108+ +49
35
H3
H5 = 108 + 35
T3 on P1
Search Tree
(0,0)
(24,0)
(24,28)
(49,28)
(88,28)
CprE 458/558: Real-Time Systems (G. Manimaran)
Strongly
feasible
T2
on P1
T1Strongly
on T5
P2 on P2
Strongly
feasible
Strongly
T4feasible
on
P1
Strongly
feasible
feasible
T3 on P1
(49,56)
(95,56)
NOT
Strongly
feasible
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Myopic scheduling: Example
Search Tree
(0,0)
(24,0)
T1 on P2
(24,28)
P2
P1
T1
T2 on P1
T4 on P1
T5 on P2
(49,28)
(49,56)
(88,28)
(95,56)
T3 on P1
T5
28 35
T2
56
T4
24
T3
49 56
95
Feasible schedule obtained using Myopic algorithm
CprE 458/558: Real-Time Systems (G. Manimaran)
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