Snap-Stabilization in Message-Passing Systems Sylvie Delaët (LRI) Stéphane Devismes (CNRS, LRI) Mikhail Nesterenko (Kent State University) Sébastien Tixeuil (LIP6)

02/04/2008Orsay, réunion SOGEA2 Message-Passing Model Network bidirectionnal and fully-connected Communications by messages Links asynchronous, fair, and FIFO Ids on processes Transient faults m1m1 m2m2 m3m3 m3m3 mama mbmb mama mbmb 1234

02/04/2008Orsay, réunion SOGEA3 Stabilizing Protocols Self-Stabilization [Dijkstra, 1974] time Transient Faults Convergence c1c1 c3c3 c2c2 c5c5 c4c4 c6c6 c7c7 Arbitrary initial state uncorrect behavior correct behavior

02/04/2008Orsay, réunion SOGEA4 Stabilizing Protocols Snap-Stabilization [Bui et al, 1999] time Transient Faults c1c1 c3c3 c2c2 c5c5 c4c4 c6c6 c7c7 Arbitrary initial state uncorrect behavior correct behavior

02/04/2008Orsay, réunion SOGEA5 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 ? ?

02/04/2008Orsay, réunion SOGEA6 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

02/04/2008Orsay, réunion SOGEA7 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

02/04/2008Orsay, réunion SOGEA9 Case 1: unbounded capacity links Impossible for safety-distributed specifications

02/04/2008Orsay, réunion SOGEA10 B A Safety-distributed specification p q Example : Mutual Exclusion

02/04/2008Orsay, réunion SOGEA11 A Safety-distributed specification p spsp m1m1 m2m2 m3m3 m4m4 m5m5 B q sqsq m’ 1 m’ 2 m’ 3 m’ 4

02/04/2008Orsay, réunion SOGEA12 A Safety-distributed specification p spsp m1m1 m2m2 m3m3 m4m4 m5m5 B q sqsq m’ 1 m’ 2 m’ 3 m’ 4

02/04/2008Orsay, réunion SOGEA13 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 ? ?

02/04/2008Orsay, réunion SOGEA14 Case 2: bounded capacity links Case Study: Single-Message Capacity 0 or 1 message

02/04/2008Orsay, réunion SOGEA15 Case 2: bounded capacity links Sequence number State  {0,1,2,3,4} p q State p State q 0 NeigState p NeigState q ? ?? 0 1 Until State p = 4 ?

02/04/2008Orsay, réunion SOGEA16 Case 2: bounded capacity links Pathological Case: p q State p State q 0 NeigState p NeigState q ? 1?

02/04/2008Orsay, réunion SOGEA17 Generalizations Arbitrary Bounded Capacity  2xC max +3 values p q C max values 1 value

02/04/2008Orsay, réunion SOGEA18 Generalizations PIF in fully-connected network m m m AmAm AmAm AmAm

02/04/2008Orsay, réunion SOGEA19 Application Mutual Exclusion in a fully-connected & identified network using the PIF

02/04/2008Orsay, réunion SOGEA20 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

02/04/2008Orsay, réunion SOGEA21 Principles (1/3) Let L be the process with the smallest ID L decides using Value L which is authorized to access the CS 1.if Value L = 0, then L is authorized 2.if Value L = i, then the i th neighbor of L is authorized When a process learns that it is authorized by L to access the CS: 1.It ensures that no other process can execute the CS 2.It executes the CS, if it requests it 3.It notifies L when it terminates Step 2 (so that L increments Value L )

02/04/2008Orsay, réunion SOGEA22 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

02/04/2008Orsay, réunion SOGEA23 Principles (3/3) For a process p: Phase 1: p evaluates the IDs using a PIF Phase 2: p asks if Value q = 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 Value p (upon reception of EXITCS, L increments Value L )

02/04/2008Orsay, réunion SOGEA24 Conclusion Snap-Stabilization in message-passing is no more an open question

02/04/2008Orsay, réunion SOGEA25 Extensions Apply snap-stabilization in message-passing to:  Other topologies (tree, arbitrary topology)  Other problems  Other failure patterns Space requirement

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