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Fault-Tolerance in Distributed Systems: Token Ring Stabilization and Two-Phase Commit Protocol

This lecture covers the fundamentals of fault-tolerance in distributed systems, focusing on Token Ring stabilization and the Two-Phase Commit Protocol. It discusses the limitations of binary and integer token rings in achieving stability and presents the Atomic Commitment Protocol, which ensures consistency among processes through voting mechanisms. The criteria for committing or aborting decisions in face of faults are highlighted, along with the impossibility of reliable agreement in asynchronous systems when even a single process fails. Key findings are backed by the works of Fisher, Lynch, and Paterson.

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Fault-Tolerance in Distributed Systems: Token Ring Stabilization and Two-Phase Commit Protocol

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  1. Lecture 4:Fault-Tolerance Anish Arora CSE 6333

  2. Token Ring Stabilization .  .  .  …  .  . 0 1 2 N-1 N begin x.0 = x.N  x.0 := (x.0 + 1 mod 2) x.0 = x.N  x.0 := x.0 + 1 ▯ x.(i+1)  x.i  x.(i+1) := x.i end where 0  i and i < N and x.i is binary valued • Binary token ring is not stabilizing • Integer token ring is stabilizing

  3. Atomic Commitment Protocol Specification • Each process casts one of two votes, Yes or No, then reaches one of two decisions, Commit or Abort, such that a process reaches a Commit decision iff all processes voted Yes • Faults may stop or restart processes

  4. Two-Phase Commit Protocol For each process j, let • ph.j be the current phase of j; ph.j is 0 initially, 1 after j has cast its vote, and 2 after j has reached a decision • v.j be the vote of j; v.j is true iff the vote is Yes • d.j be the decision of j; d.j is true iff the vote is Yes • up.j be the current status of j; up.j is true iff j is executing

  5. Two-Phase Commit Protocol program Two-phase constant X : set of ID; c: X; var ph: array X of 0..2; up, v, d: array X of Boolean; process j: X; parameter k: X; begin j=c  up.j  ph.j = 0  ph.j , v.j := 1 , ? ▯ j=c  up.j  ph.j = 1 ∧ (l  X: up.l  ph.l = 1  v.l)  ph.j , d.j := 2 , true ▯ j=c  up.j  ph.j = 1  ( l  X: up.l  ph.l=2  (ph.l=1  v.l))  ph.j , d.j := 2, false ▯ jc  up.j ∧ ph.j = 0  (up.c  ph.c=1)  ph.j , v.j := 1 , ? ▯ jc  up.j  ph.j = 0  ¬up.c  ph.j , d.j := 2, false ▯ jc  up.j  ph.j < ph.k  (up.k  ph.k = 2)  ph.j , d.j := 2, d.k end faults F true up.j := ¬up.j

  6. Two-Phase Commit Protocol Program Two-phase is F-tolerant for S, where S = ph.c=0  (j : ph.j = 0  (ph.j = 2  d.j))  ph.c=1  (j : ph.j  2  ¬d.j)  (ph.c=2  d.c)  (j : ph.j  0  v.j  (ph.j  2  d.j))  (ph.c=2  d.c)  (j : ph.j  2  ¬d.j )

  7. Impossibility of robust commit In an asynchronous system election is impossible if even one site fails (halts) Worse, agreement on a single bit-value is impossible Fisher, Lynch, Paterson

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