Principles of Reliable Distributed Systems Recitation 7: Sbased Consensus

1
Principles of Reliable Distributed Systems
Recitation 7 ?S-based Consensus

• Spring 2006
• Eddie Bortnikov Aran Bergman

2
The Model

• Asynchronous model
• n gt 1 processes, t crash failures
• Failure detectors
• ?P strong completeness, eventual strong accuracy
• ?S strong completeness, eventual weak accuracy
• Lower bound for consensus
• With ?S, we need n gt 2t

3
ltgtS-based Consensus Mostefaoui, Raynal 99

• val ? input est ? ?
• for r 0,1, 2, do
• coord ? (r mod n)1
• if I am coord, then send (r,val) to all
• wait for ( (r, val) from coord OR suspect coord
  (by ?S))
• if receive val from coord then est ? val else est
  ? ?
• send (r, est) to all
• wait for (r,est) from n-t processes
• if any non-? est received then val ? est
• if all ests have same non-? value v then
• send (decide, v) to all
• return(v)
• od
• Upon receive (decide, v), forward to all
  return(v)

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Some Definitions

• Asynchronous round made of 2 phases
  (communication steps)
• Each round is managed by a coordinator
• Asynchronous communication step
• Phase I starts when the coordinator sends (r,
  val) (or not) and terminates for each pi when it
  receives (r,v) or when it suspects coord.
• Phase II starts when pi sends (r, est) and
  terminates when it receives (r, est) from n-t
  processes.
• Rounds do not start and end at the same time in
  all processes (asynchrony)

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MR Principles Phase 1

• The purpose of the 1st phase
• Ensure that for every pi, esti ? valcoord, ?
• Progress
• Why does the 1st phase terminate?

6
MR Principles Phase 2

• The purpose of the 2nd phase
• Ensure that the Agreement property is never
  violated
• If process pi decides v during r, and if process
  pj progresses to r1, then pj does it with est
  v.
• Progress
• Why does the 2nd phase terminate?

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Second Phase

• A process pi finishes the 2nd phase when it has
  received (r, est) from a majority of processes
• Why is the majority important?
• Every two majority sets intersect
• If one process got n-t values of v, then some
  other process got at least one value of v

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Second Phase (contd)

• Notation
• v valcoord
• reci the set of received est values at the end
  of phase II.
• reci ? or v or v, ?
• Consider three cases
• reci v ? (recj v) or (recj ?, v)
  ? decide v
• reci ? ? (recj ?) or (recj ?, v)
  ? skip to the next round
• reci v,? ? (recj v) or (recj ?) or
  (recj ?, v)
• ? update est to v
  (why?)

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What do we need decide for?

• val ? input est ? ?
• for r 0,1, 2, do
• coord ? (r mod n)1
• if I am coord, then send (r,val) to all
• wait for ( (r, val) from coord OR suspect coord
  (by ?S))
• if receive val from coord then est ? val else est
  ? ?
• send (r, est) to all
• wait for (r,est) from n-t processes
• if any non-? est received then val ? est
• if all ests have same non-? value v then
• send (decide, v) to all
• return(v)
• od

10
n4, t1
v
v
v
v
v
v
v
return(v)
Suspect p1
?
v
v
Round 1
Round 2
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Disseminating the decision

• Q ok, so we need the 1st decide. Why forward
  to all?
• A to prevent a process from blocking forever. A
  process that decides uses reliable broadcast to
  disseminate its decision value.

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n4, t1
v
v
v
v
return(v)
v
v
v
v
v
Suspect p1
?
v
v
Round 1
Round 2