Maekawa: Quorum Size Research

Jeremy MillerKent State UniversityNovember 28th, 2011

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Outline

•Overview of Maekawa•Quorum Creation•Experimental Setup•Results•Future Work•Conclusions

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Outline

•Overview of Maekawa•Quorum Creation•Experimental Setup•Results•Future Work•Conclusions

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Overview of Maekawa•Permission based DMX solution•Each process has a quorum•Each process only has one permission to give•Process is granted access to the critical

section if it receives permission from its entire quorum

•6 Message types:▫Request, Permission, Release

Message Complexity: 3√N▫Failure, Inquire, Yield (Deadlock Messages)

Message Complexity: 6√N

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Outline

•Overview of Maekawa•Quorum Creation•Experimental Setup•Results•Future Work•Conclusions

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Billiards Algorithm

1st Path2nd Path 3rd Path

1st Path 2nd Path3rd Path

Where to start

Where to start

Quorums:Quorum[0]= { }Quorum[1]= { }Quorum[2]= { }Quorum[3]= { }

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Billiards Algorithm

1st Path2nd Path 3rd Path

1st Path 2nd Path3rd Path

Where to start

Where to start

Quorums:Quorum[0]= {0, 1, 2}Quorum[1]= { }Quorum[2]= { }Quorum[3]= { }

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Billiards Algorithm

1st Path2nd Path 3rd Path

1st Path 2nd Path3rd Path

Where to start

Where to start

Quorums:Quorum[0]= {0, 1, 2}Quorum[1]= {1, 2, 3}Quorum[2]= { }Quorum[3]= { }

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Billiards Algorithm

1st Path2nd Path 3rd Path

1st Path 2nd Path3rd Path

Where to start

Where to start

Quorums:Quorum[0]= {0, 1, 2}Quorum[1]= {1, 2, 3}Quorum[2]= {0, 2, 3}Quorum[3]= { }

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Billiards Algorithm

1st Path2nd Path 3rd Path

1st Path 2nd Path3rd Path

Where to start

Where to start

Quorums:Quorum[0]= {0, 1, 2}Quorum[1]= {1, 2, 3}Quorum[2]= {0, 2, 3}Quorum[3]= {0, 1, 3}

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Non-Billiards Algorithm•Make a matrix

counting upwards

•Find the process

•Draw two lines, add all of the processes hit to the quorum.

0 1

2 3

Quorums:Quorum[0]= { }Quorum[1]= { }Quorum[2]= { }Quorum[3]= { }

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Non-Billiards Algorithm•Make a matrix

counting upwards

•Find the process

•Draw two lines, add all of the processes hit to the quorum.

0 1

2 3

Quorums:Quorum[0]= {0, 1, 2}Quorum[1]= { }Quorum[2]= { }Quorum[3]= { }

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Non-Billiards Algorithm•Make a matrix

counting upwards

•Find the process

•Draw two lines, add all of the processes hit to the quorum.

0 1

2 3

Quorums:Quorum[0]= {0, 1, 2}Quorum[1]= {0, 1, 3}Quorum[2]= { }Quorum[3]= { }

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Non-Billiards Algorithm•Make a matrix

counting upwards

•Find the process

•Draw two lines, add all of the processes hit to the quorum.

0 1

2 3

Quorums:Quorum[0]= {0, 1, 2}Quorum[1]= {0, 1, 3}Quorum[2]= {0, 2, 3}Quorum[3]= { }

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Non-Billiards Algorithm•Make a matrix

counting upwards

•Find the process

•Draw two lines, add all of the processes hit to the quorum.

0 1

2 3

Quorums:Quorum[0]= {0, 1, 2}Quorum[1]= {0, 1, 3}Quorum[2]= {0, 2, 3}Quorum[3]= {1, 2, 3}

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Outline

•Overview of Maekawa•Quorum Creation•Experimental Setup•Results•Future Work•Conclusions

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Billiards vs. Non-Billiards•Testing 2 parameters: Message Complexity and

Correctness in critical section entry.•Hypothesis: Billiards will have smaller message

complexity but a worse correctness in CS entry.•Methods:

▫Set up 2 fixed quorums for each type. Run increasingly large sample sizes of CS entry. Run each test 10 times and average the results.

▫Billiards: 24 Processes, 7 Quorum Size.▫Non-Billiards: 25 Processes, 9 Quorum Size

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Outline

•Overview of Maekawa•Quorum Creation•Experimental Setup•Results•Future Work•Conclusions

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Results

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Results (Cont.)

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Results (Cont.)

•On all tests done the correctness of CS entry was 100% for both Billiards and Non-Billiards

•Not once was there incorrect order in entry.

•Expected a wrong entry in the first 1-3 entries every once in a while.

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Outline

•Overview of Maekawa•Quorum Creation•Experimental Setup•Results•Future Work•Conclusions

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Future Work

•Test different sizes of quorums, not only 2 fixed sizes.

•Force the algorithms into out-of-order situations initially and see if there is any difference in correctness between the two algorithms.

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Outline

•Overview of Maekawa•Quorum Creation•Experimental Setup•Results•Future Work•Conclusions

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Conclusions

•Billiards algorithm is the all-around best algorithm for quorum creation

•Both algorithms level off in messages sent around 500 critical section entries

•No advantage to use anything other than billiards quorum creation

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References

•Agrawal, D. "Billiard Quorums on the Grid." Information Processing Letters 64.1 (1997): 9-16. Print.

•Code Defense Link: Code Defense•Thank you.•Questions?

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