| Date post: | 17-Feb-2018 |
| Category: |
Documents |
| Upload: | rktiwary256034 |
| View: | 221 times |
| Download: | 0 times |
of 17
7/23/2019 RTOS_schedulng
1/17
2010-09-11
1
Fixed-Priority Multiprocessor Scheduling
[RTAS 2010]
Joint work with
Nan Guan, Martin Stigge and Yu Ge
Northeastern University, ChinaUppsala University, Sweden
Real-time Systems
N periodic tasks (of different rates/periods)
How to schedule the jobs to avoid deadline miss?
ri1 ri2 ri3 ri4
Ti Ti
Ji1 Ji2 Ji3
TiCi C
i
Ci
Utilization/workload:
On Single-processors
Liu and Laylands Utilization Bound [1973]
(the 19th most cited paper in computer science)
Scheduled by RMS (Rate Monotonic Scheduling)
number oftasks
Rate Monotonic Scheduling
Priority assignment: shorter period higher prio.
Run-time schedule: the highest priority first
How to check whether all deadlines are met?
high priority
mediate priority
low priority
Run-time schedule
Liu and Laylands Utilization Bound
Schedulability Analysis
P
100%
Schedulable?
77.9%Ui 1 2 3
Ui= Ci/ Ti
Liu and Laylands bound:
Liu and Laylands Utilization Bound
Schedulability Analysis
CPU
100%Yes, schedulable!77.9%
Liu and Laylands bound:
1
2
3
7/23/2019 RTOS_schedulng
2/17
2010-09-11
2
Multiprocessor (multicore) Scheduling
Significantly more difficult:
Timing anomalies
Hard to identify the worst-case scenario
Bin-packing/NP-hard problems
Multiple resources e.g. caches, bandwidth
Open Problem (since 1973)
Find a multiprocessor scheduling algorithm thatcan achieve Liu and Laylands utilization bound
number of
processors
?
Multiprocessor Scheduling
52
1 6
8
4
new task
waiting queue
cpu 1 cpu 2 cpu 3
Global Scheduling
cpu 1 cpu 2 cpu 3
5
1
2
8
6
3
9
7
4
cpu 1 cpu 2 cpu 3
2
5
2
1
22
3
6
7
4
2 3
Partitioned SchedulingPartitioned Scheduling
with Task Splitting
Best Known Results (before 2010)
Best Known Results (before 2010)
Lehoczky et al. CMU
ECRTS 2009
Best Known Results
20
10
30
40
60
50
70
80
Multiprocessor Scheduling
Global Partitioned
FixedPriority
DynamicPriority
Task Splitting
FixedPriority
DynamicPriority
FixedPriority
DynamicPriority
38
%
50
Liu and Laylands
Utilization Bound
50 50
65 66
[OPODIS08]
[TPDS05] [ECRTS03] [RTSS04]
[RTCSA06]
Our New ResultRTAS 2010
RTSS 2010_submitted
69.3
7/23/2019 RTOS_schedulng
3/17
2010-09-11
3
Multiprocessor Scheduling
52
1 6
8
4
new task
waiting queue
cpu 1 cpu 2 cpu 3
Global Scheduling
Would fixed-priority schedulinge.g. RMS work?
Multiprocessor Scheduling
52
1 6
8
4
new task
waiting queue
cpu 1 cpu 2 cpu 3
Global Scheduling
Would fixed-priority schedulinge.g. RMS work?
Unfortunately RMS suffersfrom the Dhalls anomali
Utilization may be 0%
Dhalls anomali
1Task 1
Task 22
3
1
2
0 1+ 1
Task 3
Dhalls anomali
1CPU1
CPU22
1
2
0 1+ 1
3 3
Schedule the 3 tasks on 2 CPUs using RMS
Deadline miss
Dhalls anomali
P1 P2 PM
#1 #2 #M #M+1
M* + 1/(1+ )
/1 /1 /1
1/(+1)
0M
U
(M+1 tasks and M processors)
Multiprocessor Scheduling
cpu 1cpu 2 cpu 3
5
1
2
8
6
3
9
7
4
Partitioned Scheduling
7/23/2019 RTOS_schedulng
4/17
2010-09-11
4
Multiprocessor Scheduling
cpu 1 cpu 2 cpu 3
5
1
2
8
6
3
9
7
4
Partitioned Scheduling
Resource utilization maybe limited to 50%
Partitioned Scheduling
The Partitioning Problem is similar to
Bin-packing Problem (NP-hard)
Limited Resource Usage, 50% necessary condition toguarantee schedulability
P1 P2 PM
#1 #2 #M #M+1 50%+
Partitioned Scheduling
The Partitioning Problem is similar to
Bin-packing Problem (NP-hard)
Limited Resource Usage necessary condition toguarantee schedulability
P1 P2 PM
#1 #2 #M
#M+150%+
Partitioned Scheduling
The Partitioning Problem is similar to
Bin-packing Problem (NP-hard)
Limited Resource Usage necessary condition toguarantee schedulability
P1 P2 PM
#1 #2 #M
#M+1,1 50%+
#M+1,2
Partitioned Scheduling
The Partitioning Problem is similar to
Bin-packing Problem (NP-hard)
Limited Resource Usage necessary condition toguarantee schedulability
P1 P2 PM
#1 #2 #M
#M+1,1
50%+
#M+1,2
Multiprocessor Scheduling
cpu 1 cpu 2 cpu 3
2
5
2
1
22
3
6
7
4
2 3
Partitioned Schedulingwith Task Splitting
7/23/2019 RTOS_schedulng
5/17
2010-09-11
5
Partitioned Scheduling
Partitioning
P1
1
P2 P3
1 31 2
4 5 6
7 8 9
Bin-Packing with Item Splitting
Resource can be fully (better) utilized
Bin1 Bin2 Bin3
123
11
2 45
782
681
Previous Algorithms[Kato et al. IPDPS08] [Kato et al. RTAS09] [Lakshmanan et al. ECRTS09]
Sort the tasks in some order e.g. utilization or priority order
Select a processor, and assign as many tasks as possible
3
4
2
5
1
6
8
7
P1
Lakshmanans Algorithm [ECRTS09]
Sort all tasks in decreasing order of utilization
3
4
2
5
1
6
8
7
lowest util.
highest util.
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
3
4
2
5
1
6
8
7
lowest util.
highest util.
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
3
4
2
5
1
6
7
lowest util.
highest util.
7/23/2019 RTOS_schedulng
6/17
2010-09-11
6
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
3
4
2
5
1
6
7
lowest util.
highest util.
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
3
4
2
5
1
62
7
61
lowest util.
highest util.
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
3
4
2
5
1
62
7
61
P2
lowest util.
highest util.
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
3
4
2
5
1
7
61
P2
62
lowest util.
highest util.
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
3
4
2
1
7
61
P2
562
lowest util.
highest util.
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
3
2
1
7
61
P2
562
4
lowest util.
highest util.
7/23/2019 RTOS_schedulng
7/17
2010-09-11
7
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
2
1
7
61
P2
562
4
3
lowest util.
highest util.
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
1
7
61
P2
562
4
321
22
lowest util.
highest util.
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
7
61
P2
562
4
321
P3
22
1lowest util.
highest util.
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
7
61
P2
562
4
321
P3
122
lowest util.
highest util.
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
7
61
P2
562
4
321
P3
122
key feature:
depth-first partitioningwith decreasing utilization order
lowest util.
highest util.
Lakshmanans Algorithm [ECRTS09]
Pick up one processor, and assign as many
tasks as possible
P1
8
7
61
P2
562
4
321
P3
122
Utilization Bound:
65%lowest util.
highest util.
7/23/2019 RTOS_schedulng
8/17
2010-09-11
8
Our Algorithm[RTAS10]
width-first partitioning
with increasing priority order
Our Algorithm
Sort all tasks in increasing priority order
7
6
5
4
3
2
1highest priority
lowest priority
Our Algorithm
Select the processor on which the assigned
utilization is the lowest
7
6
5
4
3
2
1
P1 P2 P3
highest priority
lowest priority
Our Algorithm
Select the processor on which the assigned
utilization is the lowest
6
5
4
3
2
1
P1 P2 P3
7
highest priority
lowest priority
Our Algorithm
Select the processor on which the assigned
utilization is the lowest
5
4
3
2
1
P1 P2 P3
76
highest priority
lowest priority
Our Algorithm
Select the processor on which the assigned
utilization is the lowest
4
3
2
1
P1 P2 P3
76 5
highest priority
lowest priority
7/23/2019 RTOS_schedulng
9/17
2010-09-11
9
Our Algorithm
Select the processor on which the assigned
utilization is the lowest
3
2
1
P1 P2 P3
76 54
highest priority
lowest priority
Our Algorithm
Select the processor on which the assigned
utilization is the lowest
2
1
P1 P2 P3
76 54
3
highest priority
lowest priority
Our Algorithm
Select the processor on which the assigned
utilization is the lowest
1
P1 P2 P3
76 54
321
22
highest priority
lowest priority
Our Algorithm
Select the processor on which the assigned
utilization is the lowest
1
P1 P2 P3
76 54
321
22
highest priority
lowest priority
Our Algorithm
Select the processor on which the assigned
utilization is the lowest
P1 P2 P3
76 54
321
12
1122
highest priority
lowest priority
Our Algorithm
Select the processor on which the assigned
utilization is the lowest
P1 P2 P3
76 54
321 1
21122
7/23/2019 RTOS_schedulng
10/17
2010-09-11
10
Our Algorithm
Select the processor on which the assigned
utilization is the lowest
P1 P2 P3
76 54
321 1
21122
highest priority
lowest priority
key feature:
width-first partitioningwith increasing prio order
Comparison
P1
8
7
61
P2
562
4
31
P3
1
2
32
P1 P2
3
P3
11
8
4
2
7 6
5
12
Why is our algorithm better?
& increasing priority order
Ours: width-first Previous: depth-first
& decreasing utilization order
Comparison
P1
8
7
61
P2
562
4
31
P3
1
2
32
P1 P2
3
P3
11
8
4
2
7 6
5
12
Why is our algorithm better?
& increasing priority order
Ours: width-first Previous: depth-first
& decreasing utilization order
By our algorithm split tasks generally have higher priorities
Split Task
Consider an extreme scenario:
suppose each subtask has the highest priority
schedulable anyway, we do not need to worry abouttheir deadlines
The difficult case is when the tail task is not on the top
the key point is to ensure the tail task is schedulable
38
42
7 6
5
12 1113
Split Task
Subtasks should execute in the correct order
i
i1
i2
i3
P1
P2
P3
r d
Split Task
Subtasks get shorter deadlines
i
i1
i2
i3
P1
P2
P3
r d
i = Ti - Ri1 - Ri
2
Ri1
Ri2
7/23/2019 RTOS_schedulng
11/17
2010-09-11
11
Split Task
Subtasks should execute in the correct order
i
i1
i2
i3
P1
P2
P3
r d
i = Ti - Ri1 - Ri
2
Ri1
Ri2
These two are on the top: no problem with schedulability
Split Task
Subtasks should execute in the correct order
i
i1
i2
i3
P1
P2
P3
r d
i = Ti - Ri1 - Ri
2
Ri1
Ri2
These two are on the top: no problem with schedulability
?
Why the tail task is schedulable?
21 22
X1 X2
Y2
Y2 + U22
7/23/2019 RTOS_schedulng
12/17
2010-09-11
12
Problem of Heavy Tasks
P1 P2 P3
highest priority
lowest priority
5
4
2
1
8
7
6
9
3
Problem of Heavy Tasks
P1 P2 P3
highest priority
lowest priority
5
4
2
1
8
7
6
9
3
Problem of Heavy Tasks
P1 P2 P3
highest priority
lowest priority
5
4
2
1
8 7
6
9
3
Problem of Heavy Tasks
P1 P2 P3
highest priority
lowest priority
5
4
2
1
8 762
9
3
61
Problem of Heavy Tasks
P1 P2 P3
highest priority
lowest priority
5
4
21
8 762
9
3
61
Problem of Heavy Tasks
P1 P2 P3
highest priority
lowest priority
5
4
21
8 762
9
3
61
7/23/2019 RTOS_schedulng
13/17
2010-09-11
13
Problem of Heavy Tasks
P1 P2 P3
highest priority
lowest priority
54
2
1
8 762
9
3
61
Problem of Heavy Tasks
P1 P2 P3
highest priority
lowest priority
54
2
1
8 762
9
361
Problem of Heavy Tasks
P1 P2 P3
highest priority
lowest priority
54
2
1
8 762
936
1
Problem of Heavy Tasks
P1 P2 P3
54
21
8 762
936
1
Problem of Heavy Tasks
P1 P2 P3
54
21
8 762
9
361
the heavy tasks tail task
may have too low priority level
Solution for Heavy Tasks
Pre-assigning the heavy tasks (that may have
low priorities)
P1 P2 P3
highest priority
lowest priority
5
4
2
1
8
7
6
9
3
7/23/2019 RTOS_schedulng
14/17
2010-09-11
14
Solution for Heavy Tasks
Pre-assigning the heavy tasks (that may have
low priorities)
P1 P2 P3
highest priority
lowest priority
5
4
2
1
8
7
6
9
3
Solution for Heavy Tasks
Pre-assigning the heavy tasks (that may have
low priorities)
P1 P2 P3
highest priority
lowest priority
5
4
2
1
8
7
6
9
3
Solution for Heavy Tasks
Pre-assigning the heavy tasks (that may have
low priorities)
P1 P2 P3
highest priority
lowest priority
5
4
2
1
8
7
6
9
3
Solution for Heavy Tasks
Pre-assigning the heavy tasks (that may have
low priorities)
P1 P2 P3
highest priority
lowest priority
5
4
2
1
876
9
3
Solution for Heavy Tasks
Pre-assigning the heavy tasks (that may have
low priorities)
P1 P2 P3
highest priority
lowest priority
5
4
2
1
876
9
3
Solution for Heavy Tasks
Pre-assigning the heavy tasks (that may have
low priorities)
P1 P2 P3
highest priority
lowest priority
54
2
1
876
9
3
7/23/2019 RTOS_schedulng
15/17
2010-09-11
15
Solution for Heavy Tasks
Pre-assigning the heavy tasks (that may have
low priorities)
P1 P2 P3
highest priority
lowest priority
54
2
1
876
9
3
Solution for Heavy Tasks
Pre-assigning the heavy tasks (that may have
low priorities)
P1 P2 P3
highest priority
lowest priority
542
1
876
9
3
Solution for Heavy Tasks
Pre-assigning the heavy tasks (that may have
low priorities)
P1 P2 P3
highest priority
lowest priority
542
12
876
9
311
Solution for Heavy Tasks
Pre-assigning the heavy tasks (that may have
low priorities)
P1 P2 P3
542
876
9
311
12
Solution for Heavy Tasks
Pre-assigning the heavy tasks (that may have
low priorities)
P1 P2 P3
542
876
9
31112
avoid to split heavy tasks(that may have low priorities)
Theorem
By introducing the pre-assignment mechanism,
we have
Liu and Laylands utilization bound for all task sets!
7/23/2019 RTOS_schedulng
16/17
2010-09-11
16
Overhead
In both previous algorithms and ours
The number of task splitting is at most M-1
task splitting -> extra migration/preemption
Our algorithm on average has less task splitting
P1 P2 P3P1 P2 P3
Ours: width-first depth-first
Implementation
Easy!
One timer for each split task
Implemented as task migration
i1
Ci1
P1
P2
task i
higher prio
tasks
i2
until finished
as being resumed
as being preempted
lower prio
tasks
Further Improvement
P1
100%
Schedulable?P2 P3
3
2
1
6
5
4
9
8
7
Uisng Liu and Laylands Utilization Bound
P1 P2 P3
Yes, schedulable
by our algorithm100%
Utilization Bound is Pessimistic
The Liu and Layland utilization bound is
sufficient but not necessary
many task sets are actually schedulable even if
the total utilization is larger than the bound
P
10.69
(1, 4)
(2, 12)
(1, 4)
(2, 8)
Exact Analysis
Exact Analysis: Response Time Analysis [Lehoczky_89]
pseudo-polynomial
(1, 4)
(2, 12)
(1, 4)
(2, 8)
Rk
task k is schedulable iffRk
7/23/2019 RTOS_schedulng
17/17
2010-09-11
Utilization Bound v.s. Exact Analysis
On single processors
P
100%
Utilization bound Testfor RMS
P
Exact Analysisfor RMS
[Lehoczky_89]
88%100%
On Multiprocessors
Can we do something similar on multiprocessors?
P1 P2 P3
Utilization bound Testthe algorithm introduced above ?
P1 P2 P3
100% 100%
Beyond Layland & Lius Bound [RTSS 2010, rejected!]
Our RTAS10 algorithm: Increasing RMS priority order & worst-f it partitioning
Utilization test to determine the maximal load for each processor
The maximal load for each processor bounded by 69.3%
Improved algorithm: Employ Response Time Analysis to determine the maximal
workload on each processor
more flexible behavior (more difficult to prove )
Same utilization bound for the worst case, but
Much better average perfo rmance (by simulation)
I believe this is the best algorithm one can hopefor fixed-prioritiy multiprocessor scheduling
Conclusions
The (multicore) Timing Problem is challenging
Difficult to guarantee Real-Time
and Difficult to analyze/predict
Solutions: Partition & Isolation
Shared caches: coloring/partition
Memory bus/bandwidth: TDMA, ? Processor cores: partition-based scheduling
Thanks!
