1. Maekawa: Quorum Size Research Jeremy Miller Kent State University November 28 th, 2011 1

2. Outline Overview of Maekawa Quorum Creation Experimental Setup Results Future Work Conclusions 2

3. Outline Overview of Maekawa Quorum Creation Experimental Setup Results Future Work Conclusions 3

4. 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 4

5. Outline Overview of Maekawa Quorum Creation Experimental Setup Results Future Work Conclusions 5

6. Billiards Algorithm 1 st Path 2 nd Path 3 rd Path 1 st Path 2 nd Path 3 rd Path Where to start Quorums: Quorum[0]= { } Quorum[1]= { } Quorum[2]= { } Quorum[3]= { } 6

7. Billiards Algorithm 1 st Path 2 nd Path 3 rd Path 1 st Path 2 nd Path 3 rd Path Where to start Quorums: Quorum[0]= {0, 1, 2} Quorum[1]= { } Quorum[2]= { } Quorum[3]= { } 7

8. Billiards Algorithm 1 st Path 2 nd Path 3 rd Path 1 st Path 2 nd Path 3 rd Path Where to start Quorums: Quorum[0]= {0, 1, 2} Quorum[1]= {1, 2, 3} Quorum[2]= { } Quorum[3]= { } 8

9. Billiards Algorithm 1 st Path 2 nd Path 3 rd Path 1 st Path 2 nd Path 3 rd Path Where to start Quorums: Quorum[0]= {0, 1, 2} Quorum[1]= {1, 2, 3} Quorum[2]= {0, 2, 3} Quorum[3]= { } 9

10. Billiards Algorithm 1 st Path 2 nd Path 3 rd Path 1 st Path 2 nd Path 3 rd Path Where to start Quorums: Quorum[0]= {0, 1, 2} Quorum[1]= {1, 2, 3} Quorum[2]= {0, 2, 3} Quorum[3]= {0, 1, 3} 10

11. 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]= { } 11

12. 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]= { } 12

13. 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]= { } 13

14. 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]= { } 14

15. 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} 15

16. Outline Overview of Maekawa Quorum Creation Experimental Setup Results Future Work Conclusions 16

17. 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 17

18. Outline Overview of Maekawa Quorum Creation Experimental Setup Results Future Work Conclusions 18

19. Results 19

20. Results (Cont.) 20

21. 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. 21

22. Outline Overview of Maekawa Quorum Creation Experimental Setup Results Future Work Conclusions 22

23. 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. 23

24. Outline Overview of Maekawa Quorum Creation Experimental Setup Results Future Work Conclusions 24

25. 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 25

26. References Agrawal, D. "Billiard Quorums on the Grid." Information Processing Letters 64.1 (1997): 9-16. Print. Code Defense Link: Code DefenseCode Defense Thank you. Questions? 26