Self-Stabilization:%20An%20approach%20for%20Fault-Tolerance%20in%20Distributed%20Systems

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Self-StabilizationAn approach for
Fault-Tolerance in Distributed Systems

• Stéphane Devismes

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Fault-Tolerance

• Robustness
• Correct behaviour even when faults hit the system
• Pessimistic approach
• For permanent failures (e.g. process crash)
• Self-Stabilization Dijkstra, 1974
• Forward recovery approach
• Optimistic approach
• For transient faults (e.g. memory corruption)

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Roadmap

• From an example to the definition
• A practical example
• Advantages
• Drawbacks
• Circumvent the drawbacks
• Conclusion

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Self-Stabilization Dijkstra, 1974

• Example Dijkstras Token Ring

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Starting from an arbitrary state
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Does it converges in any case? (1/3)

• There always exists at least one token

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i
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Does it converges in any case? (2/3)

• At each step, at least one token moves forward or
  disappears
• Eventually, the root generates a value that did
  not exist in the initial configuration (because K
  gt N)

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Does it converges in any case? (3/3)
j
j
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a
j
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Definition Closure Convergence
Closure
Legitimate States
Illegitimate States
Convergence
States of the System
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Is the Dijkstras token ring realistic?

• Computational Model
• Topology
• Knowledge about the network

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BFS Spanning Tree Huang Chen, 1992
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d1 0
d1 0
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d22
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d4 0
d11
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d11
d11
d21
d22
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d43
Variable D D0 for the root D in 1k for the
other (kgtDiam)
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d32
d32
d32
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d12
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Every process periodically sends D to its
neighbours Every non-root process stores in di
the last D-value it receives from i Each time a
di variable is updated, D is set to the minimal
value of the di -variables 1
d11
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d23
d22
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Advantage of self-stabilization (1/3)

• Tolerance to any transient fault
• Transient fault
• Duration finite
• Periodicity rare
• Effect alter the contain of some component(s) of
  the network (processes and/or links)
• E.g., memory/message corruption, crash-recover,
  lose of messages

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Advantage of self-stabilization (1/3)
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Advantage of self-stabilization (2/3)

• No initialization
• Large-scale network
• Self-organization in sensor network

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Advantage of self-stabilization (3/3)

• Dynamicity

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Drawbacks of self-stabilization (1/3)
Stabilization Time

• Eventually safe

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Drawbacks of self-stabilization (2/3)

• No detection of stabilization
• Permanent local checks

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Drawbacks of self-stabilization (3/3)

• Do not tolerant any kind of faults, e.g.
• Crash
• Byzantine faults

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Reduce the local checkings

• Example Maximal Independent Set

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MIS Algorithm
dominated
Dominator
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MIS Algorithm
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MIS Algorithm

• Case

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MIS Algorithm

• Case

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MIS Algorithm
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Tolerate more type of faults

• E.g. Robust Stabilization
• Leader Election

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Model

• Fully-connected network
• Message-passing
• Link
• Not necessarily FIFO
• Reliable and synchronous
• Process
• Synchronous or crashed
• Identity

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Leader Election (1/4)

• A process p periodically sends ALIVE,p to every
  other if Leader p

ALIVE,1
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LEADER1
ALIVE,1
ALIVE,1
ALIVE,2
ALIVE,2
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LEADER2
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ALIVE,2
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Leader Election (2/4)

• When a process p such that LEADER p receives
  ALIVE from q, then LEADER q if q lt p

ALIVE,1
LEADER1
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ALIVE,1
ALIVE,1
ALIVE,2
ALIVE,2
LEADER2
LEADER2
LEADER1
ALIVE,2
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Leader Election (3/4)

• Any process q such that LEADER ? q always chooses
  as leader the process from which it receives
  ALIVE the most recently

ALIVE,1
LEADER1
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ALIVE,1
ALIVE,1
LEADER2
LEADER1
LEADER1
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Leader Election (4/4)

• On Time out, a process p sets LEADER to p

ALIVE,1
LEADER3
LEADER1
4
ALIVE,1
ALIVE,1
ALIVE,2
ALIVE,2
LEADER2
LEADER4
LEADER2
ALIVE,2
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Conclusion (1/3)

• Start of the art
• Many stabilizing solutions for wired networks
• Katz Perry
• Delaet, Ducourthial, Tixeuil
• Recently, focus on
• Large-scale networks
• Peer-to-peer systems
• Sensor networks

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Conclusion (2/3)

• Derived properties
• Strengthened Forms
• Tolerating more types of faults, e.g., byzantine
  and crash failures
• Enhance the convergence property
  Fault-containing Self-Stabilization

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Conclusion (3/3)

• Derived properties
• Weakened Forms
• Probabilistic self-stabilization
• Weak-stabilization
• K-stabilization
• Aim Circumvent impossibility results, e.g.,
  Colouring, Leader Election, Token Circulation in
  anonymous network

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Stabilization Time of the Dijkstras Token Ring?
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