Failure Models and Consensus Algorithms in Distributed Systems - Prof. Sayan Mitra, Study notes of Electrical and Electronics Engineering

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Lecture 8

consensus 1:

distributed systems

CS425 / ECE 428 / CSE 424

sayan mitra

failure models

• crash failure: ceases to execute
  • permanent
  • dead for finite period of time then resumes
  • cause: e.g. power loss
• omission failure: sender sends a sequence of messages

but receiver does not receive some subset of messages

• cause: e.g. interference in medium
• transient failure: process jumps to arbitrary state and

resumes normal execution

• cause: e.g. gamma rays
• Byzantine failure: arbitrary messages and transitions
• cause: e.g. software bugs, malicious attacks

byzantine generals (BG)

• n>2 generals ,0,1,2,…,n-1}
• one of the generals is the commander who issues attack

or retreat commands to all the other generals

• all generals try to agree about whether to attack or retreat
• some generals (including the commander) may be

traitors (byzantine)

• requirements

• termination: all correct generals decide
• agreement: if pi and pj are correct then di = dj
• integrity: if commander is correct then all correct processes decide value issued by commander
• if commander is correct then integrity implies agreement

interactive consistency (IC)

• n processes ,0,1,2,…,n-1} try to agree on vector

of values

• pi begins in undecided state and proposes a

value vi  D

• pi sets its decision value di and enters decided

state

• consensus requirements

• termination: all correct processes decide
• agreement: the decision vector for all correct

processes is the same

• integrity: if pi is correct then for any correct process

pj, dj[i] = vi

solving consensus with reliable

totally ordered-multicast

• all processes form a group
• pi performs RTO-multicast(vi,g)
• pi sets di = mi where mi is the first msg

delivered by RTO-multicast

• termination guaranteed by reliable multicast
• agreement and validity by definition of majority
• could use max, min instead of majority if D is ordered
• solving consensus using basic multicast in

the case where upto f processes crash

Dolev and Strong algorithm for

consensus in synchronous system

• algorithm for process pi
• initally Valuesi[1] = {vi} Valuesi[0] = {};
• round r (1 ≤r≤f+1)
  • B-multicast(g, Valuesi[r] – Valuesi[r-1])
  • Valuesi[r+1] = Valuesi[r]
  • while (in round r)
    • On B-deliver(Vj) from pj
    • Valuesi[r+1] = Valuesi*r+1+ ∪ Vj
• after (f + 1) rounds
  • set di = min(Valuesi[f+1])

BG in synchronous system

impossibility with N ≤ 3f

• Lamport et al. suggested solution in the

synchronous message passing model

• bounded computation delay
• bounded message delay
• bounded clock drift