An evaluation of ring-based algorithms for the Eventually Perfect failure detector class

Joachim WielandMikel LarreaAlberto Lafuente

The University ofthe Basque Country

An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 2

Contents

Motivation Unreliable failure detectors System model Communication-efficient implementations of P A non communication-efficient approach Performance evaluation Conclusion

An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 3

Motivation

FLP impossibility result (Fischer, Lynch, and Paterson): Consensus cannot be solved deterministically in an asynchronous system subject to even a single process crash

Possibility result (Chandra and Toueg): Consensus can be solved in an asynchronous system subject to failures with an unrenreliable failure detector

An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 4

Motivation (2)

Evaluate different ring-based algorithms for P

Two kinds of performance parameters:– Communication efficiency– Quality of service

Two families of algorithms:– Communication-efficient P + some optimizations– Non communication-efficient Q + transformation to P

modular approach designed with quality of service in mind

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Unreliable failure detectors

Distributed oracle that provides (possibly incorrect) hints about the operational status of other processes

Abstractly characterized in terms of two properties: completeness and accuracy

– Completeness characterizes the degree to which crashed processes are suspected by correct processes

– Accuracy characterizes the degree to which correct processes are not suspected, i.e., restricts the false suspicions that a failure detector can make

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Unreliable failure detectors (2)

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System model

Finite set of n processes = {p1, p2, ..., pn} that communicate only by message-passing

Every pair of processes is connected by two unidirectional and reliable communication links

Processes can fail by crashing. Once a process crashes, it does not recover

Processes are arranged in a logical ring

Partially synchronous system

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Communication-efficient implementations of P

A basic communication-efficient algorithm (LLW0):– each process p sends heartbeats to the processes in the ring

between itself (excluded) and its successor succp (included)– p monitors its predecessor predp by hearing heartbeats from it

upon timeout on predp, p suspects it and monitors the predecessor of predp

– if p erroneously suspected q, p starts monitoring q again– processes propagate the list of suspicions around the ring,

piggybacked in the heartbeats upon reception of the list of suspicions from predp, p builds a new list

by merging the list received with its local suspicions. Then, p sets succp to its nearest and non suspected process

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Communication-efficient implementations of P (2)

p1

p2

p3

p4

p6

p5

pred1 = p6, succ1 = p2

pred2 = p1

succ2 = p3

pred3 = p2

succ3 = p4

pred4 = p3, succ4 = p5

pred5 = p4

succ5 = p6

pred6 = p5

succ6 = p1

pred6 = p4

succ6 = p1

{ p5 } { p5 }

{ p5 }

{ p5 }

pred4 = p3, succ4 = p6

LLW0

An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 10

Communication-efficient implementations of P (3)

Providing a faster stabilization of the ring (LLW1): sending sporadic one-to-one messages

– upon timeout on predp, p sends (START, p) to pred(predp). Upon reception of this message, pred(predp) sets its successor to p

– when p learns that it is erroneously suspecting q, p sends (START, q) to p’s current predp. Upon reception of this message, p’s current predp sets its successor to q

Broadcasting suspicions to reduce the detection latency (LLW2): sending sporadic one-to-all messages

– upon timeout on predp, p sends (SUSPICION, predp) to all processes– when a process p is being erroneously suspected, it sends

(REFUTATION, p) to all processes

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Communication-efficient implementations of P (4)

p1

p2

p3

p4

p6

p5

pred1 = p6, succ1 = p2

pred2 = p1

succ2 = p3

pred3 = p2

succ3 = p4

pred4 = p3, succ4 = p5

pred5 = p4

succ5 = p6

pred6 = p5

succ6 = p1

pred6 = p4

succ6 = p1

{ p5 } { p5 }

{ p5 }

{ p5 }

pred4 = p3, succ4 = p6

(START, p6)

LLW1

An evaluation of ring-based algorithms for the Eventually Perfect failure detector class - PDP 2007 12

Communication-efficient implementations of P (5)

p1

p2

p3

p4

p6

p5

pred1 = p6, succ1 = p2

pred2 = p1

succ2 = p3

pred3 = p2

succ3 = p4

pred4 = p3, succ4 = p5

pred5 = p4

succ5 = p6

pred6 = p5

succ6 = p1

pred6 = p4

succ6 = p1

{ p5 } { p5 }

{ p5 }

{ p5 }

pred4 = p3, succ4 = p6

(SUSPICION, p5)

(START, p6)

LLW2

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A non communication-efficient approach

A basic ring-based algorithm implementing Q:– identical monitoring schema to LLW0 + …– … the list of suspicions does not circulate around the ring– … every process p periodically sends (START, p) to predp. When a

process p receives (START, new_succ), it sets succp to new_succ

Providing a faster stabilization of the ring

Transforming Q into P:– propagating suspicions through the ring (LLWQP1)– broadcasting suspicions to reduce the detection latency (LLWQP2)

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A non communication-efficient approach (2)

p1

p2

p3

p4

p6

p5

pred1 = p6, succ1 = p2

pred2 = p1

succ2 = p3

pred3 = p2

succ3 = p4

pred4 = p3, succ4 = p5

pred5 = p4

succ5 = p6

pred6 = p5

succ6 = p1

pred6 = p4

succ6 = p1

pred4 = p3, succ4 = p6

LLWQ

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Performance evaluation

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Performance evaluation (2)

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Performance evaluation (3)

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Performance evaluation (4)

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Performance evaluation (5)

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Performance evaluation (6)

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Conclusion

Evaluation of two families of heartbeat-, ring-based algorithms implementing P

Communication-efficient family– n links are eventually used

Non communication-efficient family– modular approach– n + C links are eventually used (with 1 ≤ C ≤ n)– better quality of service