1 / 62

Lecture 4 Introduction to Principles of Distributed Computing

This lecture introduces the principles of distributed computing, focusing on consensus in partially synchronous systems and the role of failure detectors. It explores realistic timing models, upper bounds on consensus algorithms, and new directions and extensions in the field.

culbreath
Download Presentation

Lecture 4 Introduction to Principles of Distributed Computing

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. Lecture 4Introduction to Principles of Distributed Computing Sergio Rajsbaum Math Institute UNAM, Mexico

  2. Lecture 4 Consensus in partially synchronous systems, and failure detectors • Part I: Realistic timing model and metric • Part II: Failure detectors, algorithms • Part III: this is the best possible • Part IV: New directions and extensions

  3. CONSENSUS A fundamental Abstraction Each process has an input, should decide an output s.t. Agreement: correct processes’ decisions are the same Validity: decision is input of one process Termination: eventually all correct processes decide There are at least two possible input values 0 and 1. all possible vectors over the input values V

  4. L2(X0) L(X0) X0 The lecture in a nutshell • Consensus solvability depends on how long connectivity preserved by a particular model • In synchronous it is solvable, in asynchronous not. What about intermediate, more realistic models? Connectivity destroyed Initial states states after one round Connectivity preserved states after 2 rounds

  5. Basic Model • Message passing (essentially equivalent to read/write shared memory model) • Channels between every pair of processes • Crash failures t < n potential failures out of n >1 processes • No message loss among correct processes

  6. Is consensus solvable?If so, how long does it take to solve it? • It depends on what exactly the model is • But what is a realistic model? • And what are the common scenarios within the model? The nature of a distributed system is to include complex combinations of failures and delays

  7. How Fast Can We Solve Consensus? Depends on the timing model: • Message delays • Processing times • Clocks • And on the metric used: • Worst case • Average • etc

  8. The Rest of This Lecture • Part I: Realistic timing model and metric • Part II: Upper bounds • Part III: this is the best possible • Part IV: New directions and extensions

  9. Part I: Realistic Timing Model

  10. First two simple models

  11. Asynchronous Model • Unbounded message delay, processor speed Consensus impossible even for t=1 [FLP85]

  12. Synchronous Model • Algorithm runs in synchronous rounds: • send messages to any set of processes, • receive messages from previous round, • do local processing (possibly decide, halt) Round • If process i crashes in a round, then any subset of the messages i sends in this round can be lost

  13. Synchronous Consensus • In a run with f failures (f<t) • Processes can decide in f+1 rounds [Lamport Fischer 82; Dolev, Reischuk, Strong 90](early-deciding) • 1 round with no failures • In this talk deciding • halting takes min(f+2,t+1) [Dolev, Reischuk, Strong 90]

  14. The Middle Ground Many real networks are neither synchronous nor asynchronous • During long stable periods, delays and processing times are bounded • Like synchronous model • Some unstable periods • Like asynchronous model

  15. Partial Synchrony Model [Dwork, Lynch, Stockmeyer 88] • Processes have clocks (with bounded drift) • D, upper bound on message delay • r, upper bound on processing time • GST, global stabilization time • Until GST, unstable: bounds do not hold • After GST, stable: bounds hold • GST unknown

  16. Partial Synchrony in Practice • For D, r, choose bounds that hold with high probability • Stability forever? • We assume that once stable remains stable • In practice, has to last “long enough” for given algorithm to terminate • A commonly used model that alternates between stable and unstable times: Timed Asynchronous Model [Cristian, Fetzer 98]

  17. Consensus with Partial Synchrony • Solvable • requires t < n/2 [DLS88] Unbounded running time by [FLP85], because model can be asynchronous for unbounded time

  18. Exercise • Prove that consensus is not solvable in the partially synchronous model, if t ≥ n/2 • Prove that if t<n/2, it takes unbounded running time to be solved

  19. In a Practical System Can we say more than: consensus will be solved eventually ?

  20. Performance Metric Number of rounds in well-behavedruns • Well-behaved: • No failures • Stable from the beginning • Motivation: common case

  21. The Rest of This Lecture • Part II: best known algorithms decide in 2 rounds in well-behaved runs • 2 time (with delay bound , 0 processing time) • Part III: this is the best possible • Part IV: new directions and extensions

  22. Part II: Algorithms, and the Failure Detector Abstraction II.a Failure Detectors and Partial Synchrony -= II.b Algorithms

  23. Time-Free Algorithms • Goal: abstract away time, get simpler algorithms • We describe the algorithms using failure detector abstraction [Chandra, Toueg 96]

  24. Unreliable Failure Detectors [Chandra, Toueg 96] • Each process has local failure detector oracle • Typically outputs list of processes suspected to have crashed at any given time • Unreliable: failure detector output can be arbitrary for unbounded (finite) prefix of run

  25. Performance of Failure Detector Based Consensus Algorithms • Implement a failure detector in the partial synchrony model • Design an algorithm for the failure detector • Analyze the performance in well-behaved runs of the combined algorithm

  26. A Natural Failure Detector Implementation in Partial Synchrony Model • Implement failure detector using timeouts: • When expecting a message from a process i, wait D + r + clock skew before suspecting i • In well-behaved runs, D, r always hold, hence no false suspicions

  27. The resulting failure detector is <>P - Eventually Perfect • Strong Completeness: From some point on, every faulty process is suspected by every correct process • Eventual Strong Accuracy: From some point on, every correct process is not suspected

  28. Weakest Failure Detectors for Consensus • <>S - Eventually Strong • Strong Completeness • Eventual Weak Accuracy: From some point on, some correct process is not suspected • W - Leader • Outputs one trusted process • From some point, all correct processes trust the same correct process

  29. A Simple W Implementation • Use <>P implementation • Output lowest id non-suspected process In well-behaved runs: process 1 always trusted

  30. Exercise • Write the algorithm code for this failure detector W, and prove it is correct

  31. Relationships among Failure Detector Classes • <>S is a subset of <>P • <>S is strictly weaker than <>P • <>S ~ W[Chandra, Hadzilacos, Toueg 96] Food for thought: What is the weakest timing model where <>S and/or W are implementable but <>P is not?

  32. Relationships among Failure Detector Classes- Recent Results Partial Answer: In PODC’03 Aguilera et al present a system with synchronous processes S : • any number of them may crash, and • only the output links of an unknown correct process are eventually timely (all other links can be asynchronous and/or lossy) <>P is not implementable in S, W yes New proof that: <>S is strictly weaker than <>P

  33. Note on the Power of Consensus • Consensus cannot implement <>P, interactive consistency, atomic commit, … • So its “universality”, in the sense of • wait-free objects in shared memory [Herlihy 93] • state machine replication [Lamport 78; Schneider 90] does not cover sensitivity to failures, timing, etc.

  34. Other Failure Detector Implementations Food for thought: When is building <>P more costly than <>S or W? Partial answer: Aguilera at al PODC’03 observe • any implementation of <>P (even in a perfectly synchronous system) requires all alive processes to send messages forever, while W can be implemented such that eventually only the leader sends messages

  35. Other Failure Detector Implementations • Message efficient <>S implementation [Larrea, Fernández, Arévalo 00] • QoS tradeoffs between accuracy and completeness [Chen, Toueg, Aguilera 00] • Leader Election [Aguilera, Delporte, Fauconnier, Toueg 01] • Adaptive <>P[Fetzer, Raynal, Tronel 01]

  36. Part II: Algorithms, and the Failure Detector Abstraction II.a Failure Detectors and Partial Synchrony II.b Algorithms

  37. Algorithms that Take 2 Rounds in Well-Behaved Runs • <>S-based [Schiper 97; Hurfin, Raynal 99; Mostefaoui, Raynal 99] • W-based for t < n/3[Mostefaoui, Raynal 00] • W-based for t < n/2[Dutta, Guerraoui 01] • Paxos (optimized version) [Lamport 89; 96] • Leader-based (W) • Also tolerates omissions, crash recoveries • COReL - Atomic Broadcast [Keidar, Dolev 96] • Group membership based (<>P)

  38. Of This Laundry List, We Present Two Algorithms • <>S-based [MR99] • Paxos

  39. <>S-based Consensus [MR99] • val  input v; est null for r =1, 2, … do coord(r mod n)+1 if I am coord,then send (r,val) to all wait for ( (r, val)from coordOR suspect coord (by <>S)) if receive val from coord then estval elseest null send (r, est)to all wait for (r,est) from n-t processes if any non-null est received thenvalest if all ests have same vthen send (“decide”, v) to all; return(v) od • Upon receive (“decide”, v), forward to all, return(v) 1 2

  40. In Well-Behaved Runs 1 1 1 decide v1 (1, v1) 2 2 . . . . . . n n est = v1 (1, v1)

  41. In Case of Omissions The algorithm can block in case of transient message omissions, waiting for a specific round message that will not arrive

  42. Paxos [Lamport 88; 96; 01] • Uses W failure detector • Phase 1: prepare • A process who trusts itself tries to become leader • Chooses largest unique (using ids) ballot number • Learns outcome of all smaller ballots • Phase 2: accept • Leader proposes a value with his ballot number. • Leader gets majority to accept his proposal. • A value accepted by a majority can be decided

  43. Paxos - Variables • Type Rank • totally ordered set with minimum element r0 • Variables: Rank BallotNum, initially r0 Rank AcceptNum, initially r0 Value  {^} AcceptVal, initially ^

  44. Paxos Phase I: Prepare • Periodically, until decision is reached do: if leader (by W) then BallotNum  (unique rank > BallotNum) send (“prepare”, rank) to all • Upon receive (“prepare”, rank) from i if rank > BallotNum then BallotNum  rank send (“ack”, rank, AcceptNum, AcceptVal) to i

  45. Paxos Phase II: Accept Upon receive (“ack”, BallotNum, b, val) from n-t if all vals = ^ then myVal = initial value else myVal = received val with highest b send (“accept”, BallotNum, myVal) to all /* proposal */ Upon receive (“accept”, b, v) with b  BallotNum AcceptNum  b; AcceptVal  v /* accept proposal */ send (“accept”, b, v) to all (first time only)

  46. Paxos – Deciding Upon receive(“accept”, b, v) from n-t decide v periodically send (“decide”, v) to all Upon receive (“decide”, v) decide v

  47. In Well-Behaved Runs 1 1 1 1 1 2 2 2 (“prepare”,1) (“accept”,1 ,v1) . . . . . . . . . (“ack”,1,r0,^) n n n (“accept”,1 ,v1) Our W implementation always trusts process 1 decide v1

  48. Optimization • Allow process 1 (only!) to skip Phase 1 • use rank r0 • propose its own initial value • Takes 2 rounds in well-behaved runs • Takes 2 rounds for repeated invocations with the same leader

  49. What About Message Loss? • Does not block in case of a lost message • Phase I can start with new rank even if previous attempts never ended • But constant omissions can violate liveness • Specify conditional liveness: If n-t correct processes including the leader can communicate with each other then they eventually decide

  50. Synchronous Consensus • In a run with f failures (f<t) • Processes can decide in f+1 rounds • And no less ! [Lamport Fischer 82; Dolev, Reischuk, Strong 90](early-deciding) • 1 round with no failures • In this talk deciding • halting takes min(f+2,t+1) [Dolev, Reischuk, Strong 90]

More Related