Presented by Jehn-Ruey Jiang Department of Computer Science and Information Engineering

1. Expected Quorum Overlap Sizes of Optimal Quorum Systems with the Rotation Closure Property for Asynchronous Power-Saving Algorithms in Mobile Ad Hoc Networks Presented by Jehn-Ruey Jiang Department of Computer Science and Information Engineering National Central University

2. Outline • Mobile Ad hoc Networks • Quorum-Based Asynchronous Power Saving Algorithm • Expected Quorum Overlap Size • The f-Torus Quorum System • Analysis and Simulation Results of EQOS • Conclusion

3. Mobile Ad hoc Network MANET

4. MANET Applications • Battlefields • Disaster Rescue • Spontaneous Meetings • Outdoor Activities

5. Power Saving Problem • Battery is a limited resource for portable devices • Battery technology does not progress fast enough • Power saving becomes a critical issue in MANETs, in which devices are all supported by batteries

6. IEEE 802.11 PS Mode • An IEEE 802.11 Card is allowed to turn off its radio to be in the PS mode to save energy • PowerConsumption:(ORiNOCO IEEE 802.11b PC Gold Card) Vcc:5V, Speed:11Mbps

7. MAC Layer Power-Saving Algorithm • Two types of MAC layer PS algorithm for IEEE 802.11-based MANETs • Synchronous (IEEE 802.11 PS Algorithm) • Synchronous Beacon Intervals • For sending beacons and ATIM (Ad hoc Traffic Indication Map) • Asynchronous [Jiang et al. 2005] • Asynchronous Beacon Intervals • For sending beacons and MTIM (Multi-Hop Traffic Indication Map)

8. Beacon: • For a device to notifyothers of its existence • For devices to synchronize their clocks

9. How to sense others?

10. BeaconFrame Data Frame ACK IEEE 802.11 Syn. PS Algorithm Target Beacon Transmission Time(TBTT) Beacon Interval Beacon Interval ATIM Window ATIM Window Active mode Power saving Mode Host A No ATIM means no data to send or to receive with each other ATIM Power saving Mode ATIM Window ATIM Window Active mode Host B ACK Clock Synchronized by TSF (Time Synchronization Function)

11. Clock Drift Example MaximumTolerance 200 s Max. clock drift for IEEE 802.11 TSF (200 DSSS nodes, 11Mbps, aBP=0.1s)

12. D ╳ F Network Partition ╳ E ╳ ╳ Network-Partitioning Example The red ones do not know the existence of the blue ones, not to mention the time when they are awake. The blue ones do not know the existence of the red ones, not to mention the time when they are awake. C A B Host A ATIM window Host B Host C Host D Host E Host F

13. Asynchronous PS Algorithms (1/2) • Try to solve the network partitioning problem to achieve • Neighbor discovery • Wakeup prediction • Without synchronizing hosts’ clocks

14. Asynchronous PS Algorithms (2/2) • Three existent asynchronous PS algorithms • Dominating-Awake-Interval • Periodical-Fully-Awake-Interval • Quorum-Based (QAPS)

15. Quorum System • What is a quorum system?A collection of mutually intersectingsubsets of an universal set U, where each subset is called a quorum.E.G. {{1, 2},{2, 3},{1,3}} is a quorum system underU={1,2,3}, where {1, 2}, {2, 3} and {1,3} are quorums. • Not all quorum systems are applicable to QAPS algorithms • Only those quorum systems with the rotation closure property are applicable. [Jiang et al. 2005]

16. Optimal Quorum System (1/2) • Quorum Size Lower Bound for quorum systems satisfying the rotation closure property:k, where k(k-1)+1=n, the cardinality of the universal set,and k-1 is a prime power(k n) [Jiang et al. 2005]

17. Optimal Quorum System (2/2) • Optimal quorum system • FPP quorum system • Near optimal quorum systems • Grid quorum system • Torus quorum system • Cyclic (difference set) quorum system • E-Torus quorum system

18. … 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 Beacon interval Numbering Beacon Intervals n consecutive beacon intervals are numbered as 0 to n-1 And they are organized as an n array

19. Quorum Intervals (1/4) Intervals from one row and one column are called Quorum Intervals Example: Quorum intervals arenumbered by 2, 6, 8, 9, 10, 11, 14

20. Quorum Intervals (2/4) Intervals from one row and one column are called Quorum Intervals Example: Quorum intervals arenumbered by 0, 1, 2, 3, 5, 9, 13

21. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Quorum Intervals (3/4) Any two sets of quorum intervals havetwocommon members For example: The set of quorum intervals {0, 1, 2, 3, 5, 9, 13} and the set of quorum intervals {2, 6, 8, 9, 10, 11, 14} have two common members: 2 and 9

22. Host D 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Host C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Quorum Intervals (4/4) Host D 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Host C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 overlapping quorum intervals Even when the beacon interval numbers are not aligned (they are rotated), there are always at least two overlapping quorum intervals

23. Structure of Quorum Intervals

24. FPP quorum system • Constructed with a hypergraph • An edge can connect more than 2 vertices • FPP:Finite Projective Plane • A hypergraph with each pair of edges having exactly one common vertex • Also a Singer difference set quorum system

25. FPP quorum system Example A FPP quorum system: { {0,1,2}, {1,5,6}, {2,3,6}, {0,4,6}, {1,3,4}, {2,4,5}, {0,3,5} } 5 5 3 4 3 6 2 0 0 1

26. Torus quorum system 0 1 2 3 4 5 { {1,7,13,8,3,10},{5,11,17,12,1,14},…} 6 7 8 9 10 11 12 13 14 15 16 17 One half column cover in a wrap around manner One full column For a tw torus, a quorum contains all elements from some column c, plus w/2 elements, each of which comes from column c+i, i=1.. w/2

27. Cyclic (difference set) quorum system • Def: A subset D={d1,…,dk} of Zn is called a difference set if for every e0 (mod n), thereexist elements di and djD such that di-dj=e. • {0,1,2,4} is a difference set under Z8 • { {0, 1, 2, 4}, {1, 2, 3, 5}, {2, 3, 4, 6}, {3, 4, 5, 7},{4, 5, 6, 0}, {5, 6, 7, 1}, {6, 7, 0, 2}, {7, 0, 1, 3} }is a cyclic (difference set) quorum system C(8)

28. E-Torus quorum system Trunk E(t x w, k) Branch Branch cyclic Branch Branch cyclic

29. Outline • Mobile Ad hoc Networks • Quorum-Based Asynchronous Power Saving Algorithm • Expected Quorum Overlap Size • The f-Torus Quorum System • Analysis and Simulation Results of EQOS • Conclusion

30. Performance Metrics • SQOS: smallest quorum overlap sizefor worst-case neighbor sensibility • MQOS: maximum quorum overlap separationfor longest delay of discovering a neighbor • EQOS: expected quorum overlap sizefor average-case neighbor sensibility New Contribution

31. New Contribution f-torus quorum system

33. New Contribution

36. Conclusion (1/2) • We have proposed to evaluate the average-case neighbor sensibility of a QAPS algorithm by EQOS • We have proposed a new quorum system, called the fraction torus (f-torus) quorum system, for the construction of flexible mobility-adaptive PS algorithms. • We have analyzed and simulate EQOS for the FPP, grid, cyclic, torus, e-torus and f-torus quorum systems

37. Conclusion (2/2) • f-torus quorum systems may be applied to other applications: • location management, • information dissemination/retrieval • data aggregationin mobile ad hoc networks (MANETs)and/or wireless sensor networks (WSNs)

38. Thanks

39. Rotation Closure Property (1/3) • Definition. Given a non-negative integer i and a quorum H in a quorum system Q under U = {0,…, n1}, we define rotate(H, i) = {j+ijH} (mod n). • E.G. Let H={0,3} be a subset of U={0,…,3}. We have rotate(H, 0)={0, 3}, rotate(H, 1)={1,0}, rotate(H, 2)={2, 1}, rotate(H, 3)={3, 2}

40. Rotation Closure Property (2/3) • Definition. A quorum system Q under U = {0,…, n1} is said to have the rotation closure property if • G,HQ, i {0,…, n1}: Grotate(H, i) .

41. Rotation Closure Property (3/3) • For example, • Q1={{0,1},{0,2},{1,2}} under U={0,1,2}} • Q2={{0,1},{0,2},{0,3},{1,2,3}} under U={0,1,2,3}   Because {0,1} rotate({0,3},3) = {0,1}  {3, 2} =  Closure