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 JiangDepartment of Computer Science and Information Engineering

National Central University

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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

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MANET Applications

BattlefieldsDisaster RescueSpontaneous MeetingsOutdoor Activities

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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

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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 energyPower Consumption:(ORiNOCO IEEE 802.11b PC Gold Card)

Vcc:5V, Speed:11Mbps

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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 IntervalsFor sending beacons and ATIM (Ad hoc Traffic

Indication Map) Asynchronous [Jiang et al. 2005]

Asynchronous Beacon IntervalsFor sending beacons and MTIM (Multi-Hop

Traffic Indication Map)

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Beacon:

1.For a device to notifyothers of its existence

2.For devices to synchronize their clocks

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How to sense others?

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IEEE 802.11 Syn. PS Algorithm

Beacon Interval Beacon Interval

Host A

Host B

ATIM Window

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

Active modePower saving Mode

Power saving Mode

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Clock Drift Example

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

200 s MaximumTolerance

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Network-Partitioning Example

Host A

Host B

A

B

C D

E

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.

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Asynchronous PS Algorithms (1/2)

Try to solve the network partitioning problem to achieve Neighbor discovery Wakeup prediction

Without synchronizing hosts’ clocks

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Asynchronous PS Algorithms (2/2)

Three existent asynchronous PS algorithms

Dominating-Awake-Interval

Periodical-Fully-Awake-Interval

Quorum-Based (QAPS)

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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]

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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]

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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

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Numbering Beacon Intervals

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

And they are organized

as a n n array

n consecutive beacon intervals are numbered as 0 to n-1

101514131211109876543210 …

Beacon interval

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Quorum Intervals (1/4)

Intervals from one row and one column are called

Quorum Intervals

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

Example:Quorum intervals arenumbered by2, 6, 8, 9, 10, 11, 14

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Quorum Intervals (2/4)

Intervals from one row and one column are called

Quorum Intervals

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

Example:Quorum intervals arenumbered by0, 1, 2, 3, 5, 9, 13

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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 915141312

111098

7654

3210

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Quorum Intervals (4/4)

1514131211109876543210

2 151413121110987654310

2 overlapping quorum intervals

Host DHost C

2 151413121110987654310Host D

1514131211109876543210Host C

Even when the beacon interval numbers are not aligned (they are rotated), there are always at least two overlapping quorum intervals

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Structure of Quorum Intervals

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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

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FPP quorum system Example

0 1 2

3 4

5

6

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

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Torus quorum system

For a tw 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

171615141312

11109876

543210

One full column

One half column cover in a wrap around manner

{ {1,7,13,8,3,10}, {5,11,17,12,1,14},…}

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Cyclic (difference set) quorum system

Def: A subset D={d1,…,dk} of Zn is called a difference set if for every e0 (mod n), thereexist elements di and djD 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)

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E-Torus quorum system

Trunk

Branch

Branch

Branch

Branch

cyclic

cyclic

E(t x w, k)

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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

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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

f-torus quorum system

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New Contributio

n

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New Contributio

n

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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

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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)

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Thanks

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Rotation Closure Property (1/3)

Definition. Given a non-negative integer i and a quorum H in a quorum system Q under U = {0,…, n1}, we define rotate(H, i) = {j+ijH} (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}

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Rotation Closure Property (2/3)

Definition. A quorum system Q under U = {0,…, n1} is said to have the rotation closure property ifG,H Q, i {0,…, n1}: G rotate(H, i) .

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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