1 / 26

Snap-Stabilization in Message-Passing Systems

Snap-Stabilization in Message-Passing Systems. Sylvie Dela ët (LRI) Stéphane Devismes (CNRS, LRI) Mikhail Nesterenko (Kent State University) Sébastien Tixeuil (LIP6). 1. 2. m 2. 3. 4. m a. m a. m b. m b. m 1. m 3. m 3. Message-Passing Model.

maree
Download Presentation

Snap-Stabilization in Message-Passing Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. 1 2 m2 3 4 ma ma mb mb m1 m3 m3 Message-Passing Model • Network bidirectionnal and fully-connected • Communications by messages • Links asynchronous, fair, and FIFO • Ids on processes • Transient faults Orsay, réunion SOGEA

  3. Stabilizing Protocols • Self-Stabilization [Dijkstra, 1974] c1 c2 c3 c4 c5 c6 c7 Convergence time correct behavior correct behavior uncorrect behavior Transient Faults Arbitrary initial state Orsay, réunion SOGEA

  4. Stabilizing Protocols • Snap-Stabilization [Bui et al, 1999] c1 c2 c3 c4 c5 c6 c7 time correct behavior correct behavior uncorrect behavior Transient Faults Arbitrary initial state Orsay, réunion SOGEA

  5. 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 ? <How old are you, Captain?> ? <I’m 21> <I’m 12> <I’m 50> Orsay, réunion SOGEA

  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 Orsay, réunion SOGEA

  7. Related Works (snap-stabilization) • Nothing in the Message-Passing Model • Only in State Model: • Locally Shared Memory • Composite Atomicity • [Cournier et al, 2003] Orsay, réunion SOGEA

  8. Snap-Stabilization in Message-Passing Systems

  9. Case 1: unbounded capacity links • Impossible for safety-distributed specifications Orsay, réunion SOGEA

  10. Safety-distributed specification A p B q Example : Mutual Exclusion Orsay, réunion SOGEA

  11. Safety-distributed specification sp A p m1 m2 m3 m4 m5 sq B q m’1 m’2 m’3 m’4 Orsay, réunion SOGEA

  12. Safety-distributed specification sp A p m1 m2 m3 m4 m5 sq B q m’1 m’2 m’3 m’4 Orsay, réunion SOGEA

  13. Case 2: bounded capacity links • Problem to solve: Reliable Communication • Starting from any configuration, if Tintin sends a question to CaptainHaddock, then: • Tintin eventually receives good answers • Tintin takes only the good answers into account ? ? Orsay, réunion SOGEA

  14. Case 2: bounded capacity links • Case Study: Single-Message Capacity 0 or 1 message 0 or 1 message Orsay, réunion SOGEA

  15. Case 2: bounded capacity links • Sequence number State {0,1,2,3,4} p q <1,NeigStatep,Qp,Ap> <0,NeigStatep,Qp,Ap> <Stateq,0,Qq,Aq> Until Statep = 4 Statep Stateq ? 0 1 ? NeigStatep NeigStateq ? ? 0 Orsay, réunion SOGEA

  16. Case 2: bounded capacity links • Pathological Case: p <2,?,?,?> <3,NeigStatep,Qp,Ap> q <Stateq,3,Qq,Aq> <?,1,?,?> <?,2,?,?> <?,0,?,?> Statep Stateq 4 3 2 ? 1 0 NeigStatep NeigStateq ? 1 3 2 Orsay, réunion SOGEA

  17. Generalizations • Arbitrary Bounded Capacity • 2xCmax+3 values Cmax values p q Cmax values 1 value 1 value Orsay, réunion SOGEA

  18. Generalizations • PIF in fully-connected network m Am m m Am Am Orsay, réunion SOGEA

  19. Application Mutual Exclusion in a fully-connected & identified networkusing the PIF Orsay, réunion SOGEA

  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 Orsay, réunion SOGEA

  21. Principles (1/3) • Let L be the process with the smallest ID • L decides using ValueLwhich 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) Orsay, réunion SOGEA

  22. 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 Orsay, réunion SOGEA

  23. Principles (3/3) For a process p: • Phase 1: p evaluates the IDs using a PIF • Phase 2: p asks if Valueq = 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 Valuep • (upon reception of EXITCS, L increments ValueL) Orsay, réunion SOGEA

  24. Conclusion Snap-Stabilization in message-passing is no more an open question Orsay, réunion SOGEA

  25. Extensions • Apply snap-stabilization in message-passing to: • Other topologies (tree, arbitrary topology) • Other problems • Other failure patterns • Space requirement Orsay, réunion SOGEA

  26. Thank you

More Related