Transcript Diapositiva 1

Adding Precedence Relations to the
Response-Time Analysis of EDF
Distributed Real-Time Systems
Unai Díaz de Cerio (IK4-Ikerlan)
Michael González Harbour (Univ. Cantabria)
J. Carlos Palencia (Univ. Cantabria)
Juan P. Uribe (IK4-Ikerlan)
© COPYRIGHT IKERLAN 2014
22nd International Conference on Real-Time Networks and Systems
Versailles, France, October 8-10, 2014
Motivation
 Context
- Distributed real-time systems
- Response-time schedulability analysis
- EDF scheduling:
• GC-EDF (Global-Clock EDF)
 Global clock or clock synchronization available
• LC-EDF (Local-Clock EDF)
 One clock per processor and no clock synchronization available
 Problem
- No exact solution for schedulability analysis in distributed systems
- More techniques to reduce the pessimism in the analysis for FP (fixedpriorities) than for EDF
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Motivation
Analysis technique
FP
Holistic
Tindell and Clark, 94
GC-EDF
LC-EDF
Spuri, 96
Rivas et al., 10
WCDO
Palencia and
Palencia and
González Harbour, 98 González Harbour, 03
X
WCDOPS
Palencia and
González Harbour, 99
X
X
WCDO : Worst Case Dynamic Offsets
WCDOPS: Worst Case Dynamic Offset with Precedence Schemes
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Objectives
 Reduce the pessimism of the response time analysis for EDF scheduled
systems
- Extending dynamic offsets technique (WCDO) to LC-EDF scheduled systems
- Extending precedence relations technique (WCDOPS) to LC-EDF and GC-EDF
scheduled systems
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System model
 Distributed system of n task/messages statically allocated in m
processors/networks
 Tasks/messages (τij) linked making up end-to-end flows (Γi)
 Periodic end-to-end flows with minimum time between instances: Ti
 Task offset:
ij  max(ij , Rijb1 )
 Task release jitter:
Jij  max(Rijw1, ij)  ij
 Task release time interval:
t  
ij
, t  ij  J ij

- t = external event arrival time
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System model
 Task worst case execution time (WCET): Cij
 Relative global deadline (related to external event arrival): Dij
 Relative local deadline (related to task release in its processor): dij
di3
Di3
 Global response time (related to external event arrival): Rij
 Local response time (related to task release in its processor): rij
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WCDO-EDF (LC-EDF)
Analysis technique
FP
Holistic
Tindell and Clark, 94
GC-EDF
LC-EDF
Spuri, 96
Rivas et al., 10
WCDO
Palencia and
Palencia and
González Harbour, 98 González Harbour, 03
X
WCDOPS
Palencia and
González Harbour, 99
X
X
WCDO : Worst Case Dynamic Offsets
WCDOPS: Worst Case Dynamic Offset with Precedence Schemes
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WCDO-EDF (LC-EDF)
 Find worst case busy period (length t and deadline D, created with the task τik)
and calculate the contribution of the tasks to this busy period.
 Jobs categorized in 3 sets:
- Set 0: Activations that occur before the busy period and that, even applying its
maximum jitter, cannot be delayed until the busy period.
- Set 1: Activations that occur before the busy period and can be delayed with an
amount of jitter such that they coincide with the beginning of the busy period.
- Set 2: Activations that occur inside the busy period.
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WCDO-EDF (LC-EDF)
 Maximum contribution when jobs in Set 1 suffer an amount of jitter that
they are release at the beginning of the busy period and job in Set 2 suffer
an amount of jitter equal to zero:
  t  ijk   D  ijk  d ij  
 J ij  ijk 

Wijk (t , D)  
*
H
(
D

d
)
*
C

min
ij
ij

, 
  1 * Cij

Ti
 Ti 
 0
  Ti  
Number of
jobs in Set1
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Only jobs with
deadline
previous to D
can contribute
Number
of jobs in
Set2
Jobs with
deadline
previous to D
9
WCDOPS-EDF (LC-EDF)
Analysis technique
FP
Holistic
Tindell and Clark, 94
GC-EDF
LC-EDF
Spuri, 96
WCDO
Palencia and
Palencia and
González Harbour, 98 González Harbour, 03
WCDOPS
Palencia and
González Harbour, 99
X
Rivas et al., 10
X
WCDO : Worst Case Dynamic Offsets
WCDOPS: Worst Case Dynamic Offset with Precedence Schemes
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Precedence relation and activation conflicts
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Precedence relation and activation conflicts
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Precedence relation and activation conflicts
 Activation conflicts: Two tasks are in conflict when their executions are
incompatible in the same busy period for the purpose of analyzing task
τab .
 H-section: Two tasks τij and τik are in the same H-section, for the analysis
of τab, if both execute in the same processor as τab with priority equal to
or higher than τab and there are no intermediate tasks between them in
the same processor and with priority lower than τab. Hij(τab) identifies the
H-section to which τij belongs.
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Applicability for EDF
 Priority depends on absolute deadlines
 Absolute deadline change from one job to the next
 Contrary to fixed priorities
 Activation conflicts between jobs, instead of between tasks
 H-sections composed by jobs, instead of tasks
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Applicability for GC-EDF
Not useful
 Task absolute deadlines are related to the external event arrival
 Task deadlines ordered Di1 < Di2
 No activation conflicts
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Applicability for LC-EDF
Applicable
 Task absolute deadlines are related to the task release
 Task deadlines are not ordered
 There are activation conflicts
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WCDOPS-EDF (LC-EDF)
 Contribution of each task:
- First job that can be delayed to the busy period:
 J ij   'ijk 
p '0,ijk   
 1
 Ti

- Last job in the busy period that have its deadline previous to the deadline of
the task under analysis:
  t   'ijk   D   'ijk d ij  
p't , D ,ijk  min 
, 
  1
Ti
 
  Ti  
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WCDOPS-EDF (LC-EDF)
 Construct an activation conflict table for the contribution of the end-toend flow Γi
t1
t2
t3
t4
t5
p=-3
C1
0
0
C4
0
Wi(p=-3) = max(C1, C4)
p=-2
C1
C2
0
C4
0
Wi (p=-2) = max(C1+C2, C4)
p=-1
C1
C2
0
C4
C5
Wi (p=-1) = max(C1+C2, C4+C5)
p=0
C1
C2
C3
C4
C5
Wi (p=0) = C1+C2+C3+C4+C5
p=1
C1
0
C3
C4
C5
Wi (p=1) = max(C1,C3+C4+C5)
p=2
C1
0
C3
0
0
Wi (p=-3) = max(C1, C3)
Wi = Wi (p=-3) + Wi (p=-2) + Wi (p=-1) + Wi (p=0) + Wi (p=1) + Wi (p=2)
= max(C1, C4) + max(C1+C2, C4) + max(C1+C2, C4+C5) + C1+C2+C3+C4+C5 + max(C1,C3+C4+C5) + max(C1, C3)
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Simulation results
 Extensive simulations with random task sets generated
with GEN4MAST [Rivas et al., 13] and analysed with MAST
 Compared holistic technique [Rivas et al., 10] with the new
algorithms WCDO-EDF and WCDOPS-EDF for LC-EDF
distributed systems
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Simulation results
 Processor maximum utilization:
 Around 9% better utilization for WCDO-EDF
 Around 16% better utilization for WCDOPS-EDF
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Conclusions and future work
Analysis technique
FP
Holistic
Tindell and Clark, 94
GC-EDF
Spuri, 96
WCDO
Palencia and
Palencia and
González Harbour, 98 González Harbour, 03
WCDOPS
Palencia and
González Harbour, 99
LC-EDF
Rivas et al., 10
Not useful
WCDO : Worst Case Dynamic Offsets
WCDOPS: Worst Case Dynamic Offset with Precedence Schemes
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Conclusions and future work
 Reduced significantly the pessimism of the response time analysis for
systems scheduled by LC-EDF.
 Improvements come “for free”. Only affect the analysis, not the scheduling
policy, nor the system’s architecture.
 Some works have slightly improved the WCDO and WCDOPS analysis for
fixed-priorities (Mäki-Turja and Nolin, 08; Redell, 04). We have not taken
into account for our analysis.
 Future work:
- Analyse previous improvements to try to reduce even more the pessimism.
- Analyse the possibility to develop an exact test that will allow us to quantify
the pessimism of these analysis.
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Bibliography
[Palencia and González Harbour, 98] J. C. Palencia and M. González Harbour. Schedulability analysis for tasks
with static and dynamic offsets. In Proc. 19th IEEE Real-time Systems Symp., pages 26–37, 1998.
[Palencia and González Harbour, 99] J. C. Palencia and M. González Harbour. Exploiting precedence relations in
the schedulability analysis of distributed real-time systems. In Proc. 20th IEEE Real-Time Systems Symp.,
pages 328–339, 1999.
[Palencia and González Harbour, 05] J. C. Palencia and M. González Harbour. Response time analysis of EDF
distributed real-time systems. J. Embedded Comput., 1(2):225–237, 2005.
[Rivas et al., 10] J. M. Rivas, J. J. Gutiérrez García, J. C. Palencia, and M. González Harbour. Optimized deadline
assignment and schedulability analysis for distributed real-time systems with local EDF scheduling. In
Proc. 8th Int. Conf. on Embedded Systems and Applications, 2010.
[Spuri, 96] M. Spuri. Holistic analysis for deadline scheduled real-time distributed systems. Technical report,
INRIA, 1996.
[Tindell and Clark, 94] K. Tindell and J. Clark. Holistic schedulability analysis for distributed hard real-time
systems. Microprocessing and microprogramming, 40(2), 1994.
[Rivas et al., 13] J. M. Rivas, J. J. Gutiérrez, and M. González Harbour. Fixed priorities or edf for distributed realtime systems? SIGBED Rev., 10(2):21–21, 2013.
[Mäki-Turja and Nolin, 08] J. Mäki-Turja and M. Nolin. Efficient implementation of tight response-times for tasks
with offsets. Real-Time Systems, 40(1):77–116, 2008.
[Redell, 04] O. Redell. Analysis of tree-shaped transactions in distributed real time systems. In Proc. 16th
Euromicro Conf. on Real-Time Systems, 2004., pages 239–248.
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Eskerrik asko
Muchas gracias
Thank you
Merci beaucoup
P.º J.M. Arizmendiarrieta, 2
20500 Arrasate-Mondragón (Gipuzkoa)
Tel.: 943 71 24 00
Fax: 943 79 69 44
www.ikerlan.es
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