Snap-Stabilization in Message-Passing Systems

Sylvie Delaët (LRI)

Stéphane Devismes (CNRS, LRI)

Mikhail Nesterenko (Kent State University)

Sébastien Tixeuil (LIP6)

02/04/2008 Orsay, réunion SOGEA 2

Message-Passing Model

• Network bidirectionnal and fully-connected• Communications by messages• Links asynchronous, fair, and FIFO• Ids on processes• Transient faults

m1m2m3 m3mamb mamb

1 2

3 4

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Stabilizing Protocols

• Self-Stabilization [Dijkstra, 1974]

timeTransient Faults

Convergence

c1 c3c2 c5c4 c6 c7

Arbitrary initial state

uncorrect behavior correct behaviorcorrect behavior

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Stabilizing Protocols

• Snap-Stabilization [Bui et al, 1999]

timeTransient Faults

c1 c3c2 c5c4 c6 c7

Arbitrary initial state

uncorrect behavior correct behaviorcorrect behavior

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Related Works in message-passing(reliable communication in self-stabilization)

• [Gouda & Multari, 1991] Deterministic + Unbounded Capacity => Unbounded Counter Deterministic + Bounded Capacity => Bounded Counter

• [Afek & Brown, 1993] Probabilistic + Unbounded Capacity + Bounded Counter

?

?<I’m 12>

<How old are you, Captain?>

<I’m 21><I’m 50>

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Related Works in message-passing (self-stabilization)

• [Varghese, 1993] Deterministic + Bounded Capacity

• [Katz & Perry, 1993] Unbounded Capacity, deterministic, infinite counter

• [Delaët et al] Unbounded Capacity, deterministic, finite memory Silent tasks

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Related Works (snap-stabilization)

• Nothing in the Message-Passing Model

• Only in State Model: Locally Shared Memory

Composite Atomicity

• [Cournier et al, 2003]

Snap-Stabilization in Message-Passing Systems

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Case 1: unbounded capacity links

• Impossible for safety-distributed specifications

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B

A

Safety-distributed specification

p

q

Example : Mutual Exclusion

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A

Safety-distributed specification

p

sp

m1 m2 m3 m4 m5

Bq

sq

m’1 m’2 m’3 m’4

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A

Safety-distributed specification

p

sp

m1m2m3m4m5

Bq

sq

m’1m’2m’3m’4

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Case 2: bounded capacity links

• Problem to solve: Reliable Communication

• Starting from any configuration, if Tintin sends a question to Captain Haddock, then:

• Tintin eventually receives good answers

• Tintin takes only the good answers into account

?

?

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Case 2: bounded capacity links

• Case Study: Single-Message Capacity

0 or 1 message

0 or 1 message

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Case 2: bounded capacity links

• Sequence number State {0,1,2,3,4}

p q

Statep Stateq0

NeigStatep NeigStateq

?

??

<0,NeigStatep,Qp,Ap>

0

<Stateq,0,Qq,Aq>

1

<1,NeigStatep,Qp,Ap>

Until Statep = 4?

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Case 2: bounded capacity links

• Pathological Case:

p q

Statep Stateq0

NeigStatep NeigStateq

?

1?

<2,?,?,?>

<?,0,?,?>

1

<?,1,?,?>

2

2

<?,2,?,?>

3

<3,NeigStatep,Qp,Ap>

3

<Stateq,3,Qq,Aq>

4

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Generalizations

• Arbitrary Bounded Capacity 2xCmax+3 values

p q

Cmax values

Cmax values

1 value 1 value

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Generalizations

• PIF in fully-connected network

mm

m

AmAm

Am

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Application

Mutual Exclusion in a fully-connected & identified network

using the PIF

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Mutual Exclusion

• Specification:

Any process that requests the CS enters in the CS in finite time (Liveness)

If a requesting process enters in the CS, then it executes the CS alone (Safety)

N.b. Some non-requesting processes may be initially in the CS

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Principles (1/3)

• Let L be the process with the smallest ID

• L decides using ValueL which is authorized to access the CS§ if ValueL = 0, then L is authorized§ if ValueL = i, then the ith neighbor of L is authorized

• When a process learns that it is authorized by L to access the CS:§ It ensures that no other process can execute the CS§ It executes the CS, if it requests it § It notifies L when it terminates Step 2 (so that L increments ValueL)

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Principles (2/3)

• Each process sequentially executes 4 phases infinitely often

• A requesting process p can enter in the CS only after executing Phases 1 to 4 consecutively The CS is in Phase 4

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Principles (3/3)

For a process p:

• Phase 1: p evaluates the IDs using a PIF

• Phase 2: p asks if Valueq = p to each other process q (PIF)

• Phase 3: If Winner(p) then p broadcasts EXIT to every other process (PIF)

• Phase 4: If Winner(p) then CS; If p≠L, then p broadcasts EXITCS (PIF), else p increments Valuep

• (upon reception of EXITCS, L increments ValueL)

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Conclusion

Snap-Stabilization in message-passing is no more an open question

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Extensions

• Apply snap-stabilization in message-passing to:

Other topologies (tree, arbitrary topology)

Other problems

Other failure patterns

• Space requirement

Thank you