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

2/38 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

Mobile Ad hoc Network MANET 3/38

4/38 MANET Applications  Battlefields  Disaster Rescue  Spontaneous Meetings  Outdoor Activities

5/38 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

6/38 IEEE PS Mode  An IEEE Card is allowed to turn off its radio to be in the PS mode to save energy  Power Consumption: (ORiNOCO IEEE b PC Gold Card) Vcc:5V, Speed:11Mbps

7/38 MAC Layer Power-Saving Algorithm  Two types of MAC layer PS algorithm for IEEE based MANETs Synchronous (IEEE 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)

8/38 Beacon: 1.For a device to notify others of its existence 2.For devices to synchronize their clocks

9/38 How to sense others?

10/38 IEEE Syn. PS Algorithm Beacon Interval Host A Host B ATIM Window Beacon Frame Target Beacon Transmission Time(TBTT) No ATIM means no data to send or to receive with each other ATIM Window Clock Synchronized by TSF (Time Synchronization Function) ATIM Window ATIM ACK Data Frame ACK Active mode Power saving Mode

11/38 Clock Drift Example Max. clock drift for IEEE TSF (200 DSSS nodes, 11Mbps, aBP=0.1s) 200  s Maximum Tolerance

12/38 Network-Partitioning Example Host A Host B A B C DE F Host C Host D Host E Host F ╳ ╳ ATIM window ╳ ╳ Network Partition The blue ones do not know the existence of the red ones, not to mention the time when they are awake. The red ones do not know the existence of the blue ones, not to mention the time when they are awake.

13/38 Asynchronous PS Algorithms (1/2)  Try to solve the network partitioning problem to achieve Neighbor discovery Wakeup prediction  Without synchronizing hosts’ clocks

14/38 Asynchronous PS Algorithms (2/2)  Three existent asynchronous PS algorithms Dominating-Awake-Interval Periodical-Fully-Awake-Interval Quorum-Based (QAPS)

15/38 Quorum System  What is a quorum system? A collection of mutually intersecting subsets of an universal set U, where each subset is called a quorum. E.G. {{1, 2},{2, 3},{1,3}} is a quorum system under U={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]

16/38 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]

17/38 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

18/38 Numbering Beacon Intervals And they are organized as a  n   n array n consecutive beacon intervals are numbered as 0 to n … Beacon interval

19/38 Quorum Intervals (1/4) Intervals from one row and one column are called Quorum Intervals Example: Quorum intervals are numbered by 2, 6, 8, 9, 10, 11, 14

20/38 Quorum Intervals (2/4) Intervals from one row and one column are called Quorum Intervals Example: Quorum intervals are numbered by 0, 1, 2, 3, 5, 9, 13

21/38 Quorum Intervals (3/4) Any two sets of quorum intervals have two common 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

22/38 Quorum Intervals (4/4) overlapping quorum intervals Host D Host C Host D Host C Even when the beacon interval numbers are not aligned (they are rotated), there are always at least two overlapping quorum intervals

23/38 Structure of Quorum Intervals

24/38 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

25/38 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} } 0 3 5

26/38 Torus quorum system 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  One full column One half column cover in a wrap around manner { {1,7,13,8,3,10}, {5,11,17,12,1,14},…}

27/38 Cyclic (difference set) quorum system  Def: A subset D={d 1,…,d k } of Z n is called a difference set if for every e  0 (mod n), there exist elements d i and d j  D such that d i -d j =e.  {0,1,2,4} is a difference set under Z 8  { {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)

28/38 E-Torus quorum system Trunk Branch cyclic E(t x w, k)

29/38 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

30/38 Performance Metrics  SQOS: smallest quorum overlap size for worst-case neighbor sensibility  MQOS: maximum quorum overlap separation for longest delay of discovering a neighbor  EQOS: expected quorum overlap size for average-case neighbor sensibility New Contribution

f-torus quorum system 31/38 New Contribution

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33/38 New Contribution

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36/38 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

37/38 Conclusion (2/2)  f-torus quorum systems may be applied to other applications: location management, information dissemination/retrieval data aggregation in mobile ad hoc networks (MANETs) and/or wireless sensor networks (WSNs)

38/38 Thanks

39/38 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}

40/38 Rotation Closure Property (2/3) D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)  .

41/38 Rotation Closure Property (3/3)  For example, Q 1 ={{0,1},{0,2},{1,2}} under U={0,1,2}} Q 2 ={{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