SnapStabilization in MessagePassing Systems

1
Snap-Stabilization in Message-Passing Systems

• Sylvie Delaët (LRI)
• Stéphane Devismes (CNRS, LRI)
• Mikhail Nesterenko (Kent State University)
• Sébastien Tixeuil (LIP6)

2
Message-Passing Model

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

3
Stabilizing Protocols

• Self-Stabilization Dijkstra, 1974

c1
c3
c2
c5
c4
c6
c7
Convergence
time
correct behavior
correct behavior
uncorrect behavior
Transient Faults
Arbitrary initial state
4
Stabilizing Protocols

• Snap-Stabilization Bui et al, 1999

c1
c3
c2
c5
c4
c6
c7
time
correct behavior
correct behavior
uncorrect behavior
Transient Faults
Arbitrary initial state
5
Related Works in message-passing(reliable
communication in self-stabilization)
?
ltHow old are you, Captain?gt
?
ltIm 21gt
ltIm 12gt
ltIm 60gt

• Gouda Multari, 1991
• Deterministic Unbounded Capacity gt Unbounded
  Counter
• Deterministic Bounded Capacity gt Bounded
  Counter
• Afek Brown, 1993
• Probabilistic Unbounded Capacity Bounded
  Counter

6
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

7
Related Works (snap-stabilization)

• Nothing in the Message-Passing Model
• Only in State Model
• Locally Shared Memory
• Composite Atomicity
• Cournier et al, 2003

8
Snap-Stabilization in Message-Passing Systems
9
Case 1 unbounded capacity links

• Impossible for safety-distributed specifications

10
Safety-distributed specification
A
p
B
q
Example Mutual Exclusion
11
Safety-distributed specification
sp
A
p
m1
m2
m3
m4
m5
sq
B
q
m1
m2
m3
m4
12
Safety-distributed specification
sp
A
p
m1
m2
m3
m4
m5
sq
B
q
m1
m2
m3
m4
13
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

?
?
14
Case 2 bounded capacity links

• Case Study Single-Message Capacity

0 or 1 message
0 or 1 message
15
Case 2 bounded capacity links

• Sequence number State ? 0,1,2,3,4

p
q
lt0,NeigStatep,Qp,Apgt
lt1,NeigStatep,Qp,Apgt
ltStateq,0,Qq,Aqgt
Until Statep 4
Statep
Stateq
?
0
1
?
NeigStatep
NeigStateq
?
?
0
16
Case 2 bounded capacity links

• Pathological Case

p
q
lt2,?,?,?gt
lt3,NeigStatep,Qp,Apgt
lt?,0,?,?gt
lt?,1,?,?gt
lt?,2,?,?gt
ltStateq,3,Qq,Aqgt
Statep
Stateq
?
2
3
4
0
1
NeigStatep
NeigStateq
1
?
2
3
17
Generalizations

• Arbitrary Bounded Capacity
• 2xCmax3 values

Cmax values
p
q
Cmax values
1 value
1 value
18
Generalizations

• PIF in fully-connected network

m
Am
m
m
Am
Am
19
Application

• Mutual Exclusion in a fully-connected
  identified networkusing the PIF

20
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

21
Principles (1/6)

• 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)

22
Principles (2/6)

• 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

23
Principles (3/6)

• Process p evaluates the IDs

Id?
Phase1
5
3
Leader2
3
Id?
Id?
8
2
2
8
24
Principles (4/6)

• Process p asks if Valueq p to each other
  process q

Ok?
Phase2
1
5
3
Leader2
No
Value0
Oktrue
Ok?
2
3
Ok?
Yes
No
1
1
2
2
2
8
3
3
Value2
Value3
25
Principles (5/6)

• If Winner(p) then p broadcasts EXIT to every
  other process

Winner(5)true
Winner(3)?
Exit
Phase3
Phase?
Phase1
1
5
3
Leader2
Leader?
Ok
Exit
Ok?
Oktrue
2
3
Exit
Value0
Winner(2)?
Winner(8)?
Ok
Ok
Phase?
Phase1
Phase?
Phase1
1
1
2
Leader?
2
Leader?
2
8
Ok?
Ok?
3
3
Value3
Value2
26
Principles (6/6)

• If Winner(p) then CS If p?L, then p broadcasts
  ExitCS, else p increments Valuep

Winner(5)true
Winner(3)?
ExitCS
Phase1
Phase4
ltCSgt
1
5
3
Leader?
Leader2
Ok
Ok?
ExitCS
Oktrue
2
Value0
3
ExitCS
Winner(2)?
Winner(8)?
Ok
Ok
Phase1
Phase1
1
1
2
2
Leader?
Leader?
2
8
Ok?
Ok?
3
3
Value3
Value2
Value3
27
Conclusion

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

28
Extensions

• Apply snap-stabilization in message-passing to
• Other topologies (tree, arbitrary topology)
• Other problems
• Other failure patterns
• Space requirement

29
Thank you