Post on 06-Jan-2016
description
Unreliable Failure Detectors
for
Reliable Distributed Systems
Tushar Deepak Chandra
Sam Toueg
Presentation for EECS454
Lawrence Leinweber
Two-Army Problem
• Unreliable Channel
– Can’t Guarantee Correct Communication
– Last Message May be Lost
Byzantine Generals Problem (1)
• Unreliable Processors (Traitors)
– Report Incorrect Values (Troop Levels)
1 1
1
3
3
3
4
4 4
7
2
1
Byzantine Generals Problem (2)
• Loyal Generals Need to Verify Reports
– Use Reports as Votes on Correct Values– That’s About It with the Color Diagrams
1,2,3,4 1,2,3,4
1,2,3,4
1,7,3,4
1,7,3,4
1,7,3,4
1,2,3,4
1,1,3,4
1,1,3,4
1,1,3,4
4,6,6,81,1,1,1
Distributed System
1. System of Processors
2. Connected In a Network
3. Running Independently
4. Solving Problems Together
Types of Failure
1. Unreliable Communication Channels
2. Processors Crash or Create Mischief
3. Synchronizing Processors
• Atomic Broadcast
4. Problems Agreeing On Results
• Consensus
Scope of This Solution
1. Processors Can Crash• Crashed Processors Never Recover
• Processors are Not Malicious
2. Reliable Communication Channels
3. Asynchronous• Synchronize After a Finite Number of Steps
4. At Least One Processor is Correct• Every Down Processor is Detected By at Least One Up
Processor
• At Least One Up Processor is Detected By All Up Processors
Failure Detectors
• Attached to Each Processor
• Determine the Crash State of Some Processors– Processors Communicate Crash State Information
• Imperfect– Suspect Processors Crashed
– Slow Processors Might Become “Unsuspected”
– Cause Host Processor to Abandon Other Processors
Completeness & Accuracy
• Completeness
– Down Processors are Abandoned
• Accuracy
– Up Processors are Not Abandoned
Function Definitions
• abandons(p, q, t)
– Processor p Abandons Processor q
at Time t
• isDown(q, t)
– Processor q is Really Down at Time t
Completeness
• Strong Completeness
– Every Down Processor is Abandoned by Every Up
Processor Eventually
p, q, t0, t > t0: isDown(q, t) abandons(p, q, t)
• Weak Completeness
– Every Down Processor is Abandoned by At Least
One Up Processor Eventually
p, q, t0, t > t0: isDown(q, t) abandons(p, q, t)
Accuracy
• Strong Accuracy (Perpetual/Eventual)– Every Up Processor is Not Abandoned by Every Processor
Ever/Eventually
– Perpetual: p, q, t: isDown(q, t) abandons(p, q, t)
– Eventual: p, q, t0, t > t0: isDown(q, t) abandons(p, q, t)
• Weak Accuracy (Perpetual/Eventual)– At Least One Up Processor is Not Abandoned by Any Processor
Ever/Eventually
– Perpetual: p, q, t: isDown(q, t) abandons(p, q, t)
– Eventual: p, q, t0, t > t0: isDown(q, t) abandons(p, q, t)
Classes of Failure Detectors
Strong
Perpetual
Accuracy
Weak
Perpetual
Accuracy
Strong
Eventual
Accuracy
Weak
Eventual
Accuracy
Strong
CompletenessP S P S
Weak
CompletenessQ W Q W
• 8 Combinations of Completeness and Accuracy
Reducibility (Emulation)
• Some Classes are More Powerful Than Others– Strong Complete Can Emulate Weak Complete
• Some Classes Can Emulate Others Using an Algorithm:– Up Processors Share Lists of Abandoned Processors,
Exclude Themselves
– Abandoned by One Becomes Abandoned by All
– Weak Complete Can Emulate Strong Complete
Completeness Classes Are Equivalent
Strong
Perpetual
Accuracy
Weak
Perpetual
Accuracy
Strong
Eventual
Accuracy
Weak
Eventual
Accuracy
Strong
CompletenessP S P S
Weak
CompletenessQ W Q W
• 4 Distinct Accuracy Classes
Relationship of Accuracy Classes
• Perpetual is More Powerful Than Eventual
– Perpetual: t
– Eventual: t0, t > t0
• Strong is More Powerful Than Weak
– Strong: q
– Weak: q
Relationship of Failure Detector Classes
Strong
Perpetual
Accuracy
Weak
Perpetual
Accuracy
Strong
Eventual
Accuracy
Weak
Eventual
Accuracy
Strong
CompletenessP S P S
Weak
CompletenessQ W Q W
• P is Most Powerful; S is Least Powerful
The Consensus Problem
• Processors Reach Agreement on a Value– Termination: All Up Processors
– Agreement: All Agree to Same Value
– Integrity: Decision is Final
– Validity: A Proposed Value is Chosen
• If They Can Agree on One Thing,They Can Agree on Anything
• Algorithms for S and S Detectors– At Least One Up Processor Using S Detectors
– A Majority of Up Processors Using S Detectors
Algorithm for S Detectors
• S Detectors – At Least One Up Processor is Not
Abandoned by Any Up Processor Ever
1. Collect Proposed Values from Each Processor– or the News That the Process Crashed
2. Collect Other Processors’ Knowledge of Proposed Values– Discard Values not Known to All
3. Pick (Consistently) a Value from Known Values
• All Processors Get Phase 1 & 2 Information from the
Processor That is Never Abandoned
Algorithm for S Detectors
• Rotating Coordinator
– Each Processor Takes Their Turn
– Tries to Make Decision
– If the Processor is Up and is Not
Abandoned by Any Up Processor, the
Decision is Made
Each Round of S Algorithm
• At Least One Up Processor is Not Abandoned by Any Up Processor Eventually
1. All Processors Send Value and the Round Number to Coordinator
2. Coordinator Waits for a Majority and Sends the Value with the Latest Round Number to All Processors
3. Each Processor Indicates If It Abandoned Coordinator
4. Coordinator Waits for a Majority, If No Processor Abandoned Coordinator, the Value is Decided
• Repeat Until Coordinator is Not Abandoned Eventually
Atomic Broadcast
• All Processors Receive the Same
Messages in the Same Order
• Atomic Broadcast is Equivalent to
Consensus
– Each Can Be Reduced to the Other
– Solution to Consensus Applies to
Atomic Broadcast
Atomic Broadcast Reduces to Consensus
• Atomic Broadcast Can Be Implemented
Using a Consensus Algorithm
– Each Processor Proposes a Message
– Consensus is Used to Decide Which
Message is Recognized as the Next
Atomically Broadcast Message
Consensus Reduces to Atomic Broadcast
• Consensus Can Be Implemented Using
An Atomic Broadcast Algorithm
– To Decide a Value, a Process Atomically
Broadcasts It
– Go to Lunch Early
Summary
• Reliable Distributed Systems
• Unreliable Failure Detectors
• Relationship of Detector Classes
• Algorithms for Consensus
• Equivalence with Atomic Broadcast