Une Heuristique d

1
Une Heuristique dOrdonnancement et de
Distribution Tolérante aux Pannes pour Sytèmes
Temps-Réel Embarqués
MSR'03

• Alain Girault - Hamoudi Kalla - Yves Sorel

POP ART OSTRE Teams
Metz, France - 06 Octobre 2003
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Outline

• Introduction
• Modeling distributed real-time systems
• Problem How to introduce fault-tolerance ?
• The proposed solution for fault-tolerance
• Principles and example
• Simulations
• Conclusion and future work

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1. Introduction

High level program
Compiler
Model of the algorithm
Architecture specification Distribution
constraints Execution times Real-time
constraints Failure specification
Distribution and scheduling fault-tolerant
heuristic
Fault-tolerant distributed static schedule
Code generator
Fault-tolerant distributed code
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1. Modeling distributed real-time systems

1. Architecture Model

1. Algorithm Model

P1
I1
B
C
O
m1
m2
A
I2
P2
P3
m3
I1 and I2 are inputs operations O is
output operation A, B and C are computations
operations
P1, P2 and P3 are processors m1, m2 and m3
are communications links
5

1. Problem How to introduce fault-tolerance ?

Problem

• Find a distributed schedule of the algorithm on
  the architecture which is fault-tolerant to
  processors failures ?

P1
I1
B
schedule
m1
m2
C
O
A
I2
P2
P3
m3
6

1. The proposed solution for fault-tolerance

Solution

• A list scheduling heuristic which use the active
  software replication of operations and
  communications.

• Tolerate a number of processor failures Npf ? 1

Assumption

• Processors are assumed to be fail-silent

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1. The proposed solution for fault-tolerance

Principles (1)

• Each operation/communication is replicated more
  than Npf1 times on different processors/links of
  the architecture graph.

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1. The proposed solution for fault-tolerance

Principles (2)
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1. The proposed solution for fault-tolerance

Principles (3)
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1. The proposed solution for fault-tolerance

Principles (4)

• The schedule pressure ? is used as a cost
  function to select the best processor p for each
  operation o

where,
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1. Heuristic

• ? ? o o is an input operation?
  ? ?
• While ? ? do
• Compute the schedule pressure ? for each
  operation o of on each processor p and
  keep the smallest Npf1 results
• Select the best candidate operation obest which
  has the greatest schedule pressure ? (obest , p)
  
• Schedule obest on each processor p computed at
  step a and the communications implied by this
  schedule are replicated Npf1 times and scheduled
  on parallel links
• Try to minimise the start time of obest on each
  processor p computed at step a by replicating
  these predecessors on p ahmad and al.
• Update the list of candidate operations
• ? - ?obest? ? ? o o ?
  (succs obest) (preds o) ? )?
• ? ? ?obest?
• end while

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1. Example

P1
I1
B
C
O
m1
m2
A
I2
P2
P3
m3
Algorithm graph
Architecture graph
Number of fail-silent processor that the system
must tolerate Npf 1
Failures
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1. Heuristic

• ? ? o o is an input operation?
  ? ?
• While ? ? do
• Compute the schedule pressure ? for each
  operation o of on each processor p and
  keep the smallest Npf1 results
• Select the best candidate operation obest which
  has the greatest schedule pressure ? (obest , p)
  
• Schedule obest on each processor p computed at
  step a and the communications implied by this
  schedule are replicated Npf1 times and scheduled
  on parallel links
• Try to minimise the start time of obest on each
  processor p computed at step a by replicating
  these predecessors on p ahmad and al.
• Update the list of candidate operations
• ? - ?obest? ? ? o o ?
  (succs obest) (preds o) ? )?
• ? ? ?obest?
• end while

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1. Example

Step 1.(1)
I1
B
C
O
I1 , I2
A
I2
?
Npf 1
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1. Example

Step 2.(1)
Schedule I1 on P1 and P2
I1
B
C
O
A
I2
I1
I1
Npf 1
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1. Example

Step 2.(2)
Schedule I2 on P1 and P2
I1
B
C
O
A
I2
I1
I1
I2
I2
Npf 1
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1. Example

Step 2.(3)
I1
B
C
O
I1, I2
A
I2
A, B
I1
I1
I2
I2
Npf 1
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1. Heuristic

• ? ? o o is an input operation?
  ? ?
• While ? ? do
• Compute the schedule pressure ? for each
  operation o of on each processor p and
  keep the smallest Npf1 results
• Select the best candidate operation obest which
  has the greatest schedule pressure ? (obest , p)
  
• Schedule obest on each processor p computed at
  step a and the communications implied by this
  schedule are replicated Npf1 times and scheduled
  on parallel links
• Try to minimise the start time of obest on each
  processor p computed at step a by replicating
  these predecessors on p ahmad and al.
• Update the list of candidate operations
• ? - ?obest? ? ? o o ?
  (succs obest) (preds o) ? )?
• ? ? ?obest?
• end while

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1. Example

Step 2.a.(3)
I1, I2
I1
B
A, B
C
O
A
I2
I1
I1
I2
I2
Npf 1
20

1. Heuristic

• ? ? o o is an input operation?
  ? ?
• While ? ? do
• Compute the schedule pressure ? for each
  operation o of on each processor p and
  keep the smallest Npf1 results
• Select the best candidate operation obest which
  has the greatest schedule pressure ? (obest , p)
  
• Schedule obest on each processor p computed at
  step a and the communications implied by this
  schedule are replicated Npf1 times and scheduled
  on parallel links
• Try to minimise the start time of obest on each
  processor p computed at step a by replicating
  these predecessors on p ahmad and al.
• Update the list of candidate operations
• ? - ?obest? ? ? o o ?
  (succs obest) (preds o) ? )?
• ? ? ?obest?
• end while

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1. Example

Step 2.b.(3)
I1, I2
A, B
I1
B
C
O
A
I2
? ( A, P1 , P3 ) 7, 9
? ( B, P2 , P3 ) 6, 8
I1
I1
I2
I2
Npf 1
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1. Heuristic

• ? ? o o is an input operation?
  ? ?
• While ? ? do
• Compute the schedule pressure ? for each
  operation o of on each processor p and
  keep the smallest Npf1 results
• Select the best candidate operation obest which
  has the greatest schedule pressure ? (obest , p)
  
• Schedule obest on each processor p computed at
  step a and the communications implied by this
  schedule are replicated Npf1 times and scheduled
  on parallel links
• Try to minimise the start time of obest on each
  processor p computed at step a by replicating
  these predecessors on p ahmad and al.
• Update the list of candidate operations
• ? - ?obest? ? ? o o ?
  (succs obest) (preds o) ? )?
• ? ? ?obest?
• end while

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1. Example

Step 2.c.(3)
I1
B
? ( A, P1 , P3 ) 7, 9
C
O
A
I2
Schedule A on P1 and P3
I1
I1
I2
I2
A
A
Npf 1
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1. Heuristic

• ? ? o o is an input operation?
  ? ?
• While ? ? do
• Compute the schedule pressure ? for each
  operation o of on each processor p and
  keep the smallest Npf1 results
• Select the best candidate operation obest which
  has the greatest schedule pressure ? (obest , p)
  
• Schedule obest on each processor p computed at
  step a and the communications implied by this
  schedule are replicated Npf1 times and scheduled
  on parallel links
• Try to minimise the start time of obest on each
  processor p computed at step a by replicating
  these predecessors on p ahmad and al.
• Update the list of candidate operations
• ? - ?obest? ? ? o o ?
  (succs obest) (preds o) ? )?
• ? ? ?obest?
• end while

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1. Example

Step 2.d.(3)
I1
B
C
O
A
I2
I2
I1
I1
Replicating I2 on P3
I2
I2
A
A
Npf 1
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1. Heuristic

• ? ? o o is an input operation?
  ? ?
• While ? ? do
• Compute the schedule pressure ? for each
  operation o of on each processor p and
  keep the smallest Npf1 results
• Select the best candidate operation obest which
  has the greatest schedule pressure ? (obest , p)
  
• Schedule obest on each processor p computed at
  step a and the communications implied by this
  schedule are replicated Npf1 times and scheduled
  on parallel links
• Try to minimise the start time of obest on each
  processor p computed at step a by replicating
  these predecessors on p ahmad and al.
• Update the list of candidate operations
• ? - ?obest? ? ? o o ?
  (succs obest) (preds o) ? )?
• ? ? ?obest?
• end while

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1. Example

Step 2.e.(3)
I1
B
C
O
A, B
A
I2
I1, I2
I1
I1
I2
I2
I2
A
A
Npf 1
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1. Simulations

• Aim
• Compare the proposed heuristic with the HBP
  heuristic Hashimoto and al. 2002.
• Assumptions
• Architecture with fully connect processors,
• Number of fail-silent processor Npf 1.
• Simulation parameters
• Communication-to-computation ratio, defined as
  the average communication time divided by the
  average computation time, CCR 0.1, 0.5, 1, 2, 5
  and 10,
• Number of operations N 10, 20, , 80.
• Comparison parameter
• Overhead

length (HTBR or HBP) - length (HTBR without
fault-tolerance)
x 100
longueur (HTBR without fault-tolerance)
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Impact of the number of operation
One processor fails
No processor failure
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Impact of the communication-to computation ratio
No processor failure
One processor fails
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1. Conclusion and future work

Result

• A new scheduling heuristics based on the
  active replication strategy.
• It produces a static distributed schedule of a
  given algorithm on a given distributed
  architecture, tolerant to Npf processor failures.

Future work

• A new fault-tolerant scheduling heuristics
• Processors and communications links failures.
• Maximise the systems reliability.

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Merci