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Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks Presented by Jehn-Ruey Jiang Department of Computer Science and Information Engineering National Central University

Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks. Presented by Jehn-Ruey Jiang Department of Computer Science and Information Engineering National Central University. To Rest, to Go Far!. Outline. IEEE 802.11 Ad hoc Network Power Saving Problem - PowerPoint PPT Presentation

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Page 1: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Quorum-Based Asynchronous Power-Saving Protocols for

IEEE 802.11 Ad Hoc Networks

Presented by

Jehn-Ruey Jiang

Department of Computer Science and Information Engineering

National Central University

Page 2: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

To Rest, to Go Far!

Page 3: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Outline IEEE 802.11 Ad hoc Network Power Saving Problem Asynchronous Quorum-based PS Protocols Optimal Asyn. Quorum-Based PS Protocols Analysis and Simulation Conclusion

Page 4: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Outline IEEE 802.11 Ad hoc Network Power Saving Problem Asynchronous Quorum-based PS Protocols Optimal Asyn. Quorum-Based PS Protocols Analysis and Simulation Conclusion

Page 5: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

IEEE 802.11 Overview

Approved by IEEE in 1997

Extensions approved in 1999 (High Rate)

Standard for Wireless Local Area Networks ( WLAN )

Page 6: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

IEEE 802.11 Family(1/2)

802.11a (1999)(WiFi5):6 to 54 Mbps in the 5 GHz band

802.11b (1999)(WiFi, Wireless Fidelity):5.5 and 11 Mbps in the 2.4 GHz band

802.11g (2001):54 Mbps in the 2.4 GHz band

802.11n (2006)(MIMO):160 Mbps in the 2.4 and the 5 GHz bands

Page 7: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

IEEE 802.11 Family(2/2) 802.11c: support for 802.11 frames 802.11d: new support for 802.11 frames 802.11e: QoS enhancement in MAC 802.11f: Inter Access Point Protocol 802.11h: channel selection and power control 802.11i: security enhancement in MAC 802.11j: 5 GHz globalization

Page 8: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Infrastructure vs Ad-hoc Modesinfrastructure network

ad-hoc network

APAP

AP

wired network

ad-hoc network

Multi-hop ad hoc network

Page 9: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Ad hoc Network (1/3)

A collection of wireless mobile hosts forming a temporary network without the aid of established infrastructure or centralized administration(by D. B. Johnson et al.)

Also called MANET (Mobile Ad hoc Network)(by Internet Society IETF)

Page 10: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Ad hoc Network (2/3)

Single-Hop Each node is within each other’s transmission

rangeFully connected

Multi-HopA node reaches another node via a chain of

intermediate nodesNetworks may partition and/or merge

Page 11: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Ad hoc Network (3/3)

Applications:

Battlefields

Disaster rescue

Spontaneous meetings

Outdoor activities

Page 12: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Outline IEEE 802.11 Ad hoc Network Power Saving Problem Asynchronous Quorum-based PS Protocols Optimal Asyn. Quorum-Based PS Protocols Analysis and Simulation Conclusion

Page 13: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Power Saving

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

Page 14: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Solutions to Power Saving

PHY Layer: transmission power controlHuang (ICCCN’01), Ramanathan (INFOCOM’00)

MAC Layer: power mode managementTseng (INFOCOM’02), Chiasserini (WCNC’00)

Network Layer: power-aware routingSingh (ICMCN’98), Ryu (ICC’00)

Page 15: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Transmission Power Control

Tuning transmission energy for higher channel reuse

Example:A is sending to B (based on IEEE 802.11)Can (C, D) and (E, F) join?

A

BCD

F E

No!Yes!

Page 16: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Power Mode Management

doze mode vs. active mode Example:

A is sending to BDoes C need to stay awake?

A

B

C

No!It can turn off its radio to save energy!

But it should turn on its radio periodiclally for possible data comm.

Page 17: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Power-Aware Routing

Routing in an ad hoc network with energy-saving (prolonging network lifetime) in mind

Example:

+

+

+

+

+

+

SRCN1 N2

DEST

N4N3

Better!!

Page 18: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Our Focus

Among the three solutions:PHY Layer: transmission power controlMAC Layer: power mode managementNetwork Layer: power-aware routing

Page 19: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

IEEE 802.11 PS Mode(2/2)

Environments: Infrastructure (O)

Ad hoc (infrastructureless)Single-hop (O)Multi-hop

Page 20: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

IEEE 802.11 PS Mode(1/2)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

Page 21: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

PS for 1-hop Ad hoc Networks (1/3)

Host

ATIM Window

Beacon Interval

Power Saving Mode

Beacon Interval Beacon Interval Beacon Interval

Beacon

Time axis is divided into equal-length intervals called beacon intervals

In the beginning of a beacon interval, there is ATIM window, in which hosts should wake up and contend to send a beacon frame with the backoff mechanism for synchronizing clocks

Page 22: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

PS for 1-hop Ad hoc Networks (2/3)

A possible sender also sends ATIM (Ad hoc Traffic Indication Map) message with DCF procedure in the ATIM window to its intended receivers in the PS mode

ATIM demands an ACK. And the pair of hosts receiving ATIM and ATIM-ACK should keep themselves awake for transmitting and receiving data

Page 23: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

ATIM Window

ATIM Window

PS for 1-hop Ad hoc Networks (3/3)

Beacon Interval Beacon Interval

ATIM Window

ATIM Window

Host A

Host B

Beacon

BTA=2, BTB=5

power saving mode

power saving mode

Beacon

ATIM

ACK

active state

data frame

ACK

Target Beacon Transmission Time (TBTT)

No ATIM means no data to send

or to receive

Page 24: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

PS: m-hop Ad hoc NetworkProblems:

Clock Synchronizationit is hard due to communication delays and mobility

Network Partitionunsynchronized hosts with different wakeup times may not recognize each other

Page 25: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Clock Drift Example

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

Page 26: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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.

Page 27: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Asynchronous PS Protocols (1/2)

Try to solve the network partitioning problem to achieveNeighbor discoveryWakeup prediction

without synchronizing hosts’ clocks

Page 28: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Asynchronous PS Protocols (2/2)

Three existent asyn. PS protocols:Dominating-Awake-IntervalPeriodical-Fully-Awake-IntervalQuorum-BasedRef:

“Power-Saving Protocols for IEEE 802.11-BasedMulti-Hop Ad Hoc Networks,”Yu-Chee Tseng, Chih-Shun Hsu and Ten-Yueng HsiehInfoCom’2002

Page 29: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Outline IEEE 802.11 Ad hoc Network Power Saving Problem Asynchronous Quorum-based PS Protocols Optimal Asyn. Quorum-Based PS Protocols Analysis and Simulation Conclusion

Page 30: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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

201514131211109876543210 …

Beacon interval

Page 31: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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

Page 32: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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

Page 33: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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

Page 34: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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

Page 35: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Structure of quorum intervals

Page 36: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Networks Merge Properly

Host A

Host B

A

B

C D

E

F

Host C

Host D

Host E

Host F

ATIM window

Beacon window

Monitor window

Page 37: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Short Summary

There is an asynchronous power-saving protocol that achievesasynchronous neighbor discovery

Hearing beacons twice or more in every n consecutive beacon intervals

wakeup predictionvia a simple quorum concept.

Page 38: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Observation 1

It is a simple grid quorum system [Maekawa 1985] in Tseng’s work.

There are many more complicated quorum systems in the literature of distributed systems:FPP [Maekawa 1985], Tree [Agrawal 1990],

Hierarchical[Kumar 1991], Cohorts [Jiang 1997], Cyclic [Luk 1997], Torus [Lang 1998], etc.

Question: Can these quorum systems be directly applied to solve the power-saving problem in a MANET?

Page 39: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

The Answer Is … Not all quorum systems can be used here!

Counter example: { {1}} under {1,2,3}

Only those quorum systems with the rotation closure property can be used!

Page 40: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Observation 2

Smaller quorums are better because they imply lower active ratio (better energy-efficiency)

But quorums cannot be too small less the quorum system does not satisfy the rotation closure property

Question 1: What is the smallest quorum size? Question 2: Is there any quorum systems to have

the smallest quorum size?

Page 41: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Outline IEEE 802.11 Ad hoc Network Power Saving Problem Asynchronous Quorum-based PS Protocols Optimal Asyn. Quorum-Based PS Protocols Analysis and Simulation Conclusion

Page 42: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

What are quorum systems?Quorum system:

a collection of mutually intersecting subsets of a universal set U, where each subset is called a quorumE.G. {{1, 2},{2, 3},{1,3}} is a quorum system

under U={1,2,3}

A quorum system is a collection of sets satisfying the intersection property

Page 43: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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}

Page 44: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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) .

Page 45: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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

Page 46: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Examples of quorum systems

Majority quorum system Tree quorum system Hierarchical quorum system Cohorts quorum system ………

Page 47: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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 )

Page 48: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Optimal Quorum System (2/2)

Optimal quorum systemFPP quorum system

Near optimal quorum systemsGrid quorum systemTorus quorum systemCyclic (difference set) quorum system

Page 49: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Outline IEEE 802.11 Ad hoc Network Power Saving Problem Asynchronous Quorum-based PS Protocols Optimal Asyn. Quorum-Based PS Protocols Analysis and Simulation Conclusion

Page 50: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Analysis (1/3)

Active Ratio:the number of quorum intervals over n,where n is cardinality of the universal set

Neighbor Sensibility (NS)the worst-case delay for a PS host to detect the existence of a newly approaching PS host in its neighborhood

Page 51: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Analysis (2/3)

Page 52: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Analysis (3/3)

Optimal!

Page 53: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation Model

Area: 1000m x 1000m Speed: 2Mbps Radio radius: 250m Battery energy: 100J. Traffic load: Poisson Dist. , 1~4 routes/s,

each having ten 1k packets Mobility: way-point model (pause time: 20s) Routing protocol: AODV

Page 54: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation ParametersUnicast send 454+1.9 * L

Broadcast send 266+1.9 * L

Unicast receive 356+0.5 * L

Broadcast receive 56+0.5 * L

Idle 843

Doze 27 L: packet length

Unicast packet size 1024 bytes

Broadcast packet size 32 bytes

Beacon window size 4ms

MTIM window size 16ms

Page 55: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation Metrics

Survival ratioNeighbor discovery timeThroughputAggregate throughput

Page 56: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation Results (1/10)

Survival ratio vs. mobility (beacon interval = 100 ms, 100 hosts, traffic load = 1 route/sec).

Cyclic quorum systemE-torus quorum system

Always Active

Page 57: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation Results (2/10)

Neighbor discovery time vs. mobility(beacon interval =100 ms, 100 hosts, traffic load = 1 route/sec).

0

500

1000

1500

2000

2500

3000

0 5 10 15 20

Moving speed (m/sec)

Neig

hb

or

dis

covery

tim

e (

ms)

C(98)

E(7x14)

A faster host can be discovered in

shorter time.

Page 58: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation Results (3/10)

Throughput vs. mobility(beacon interval = 100 ms, 100 hosts, traffic load = 1 route/sec).

For the aggregate throughput: C(98)>E(7x74)>AA

For the throughput: AA>E(7x74)>C(98)

Page 59: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation Results (4/10)

Survival ratio vs. beacon interval length(100 hosts, traffic load = 1 route/sec, moving speed = 0~20 m/sec with

mean = 10m/sec).

Page 60: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation Results (5/10)

Neighbor discovery time vs. beacon interval length(100 hosts, traffic load = 1 route/sec, moving speed = 0~20 m/sec with

mean = 10m/sec).

0

2000

4000

6000

8000

10000

12000

14000

16000

100 200 300 400

Beacon interval (ms)

Nei

ghbor disco

ver

y tim

e (m

s)

C(98)

E(7x14)

Page 61: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation Results (6/10)

Throughput vs. beacon interval length(100 hosts, traffic load = 1 route/sec, moving speed = 0~20 m/sec with

mean =10m/sec).

Page 62: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation Results (7/10)

Survival ratio vs. traffic load(beacon interval = 100 ms, 100 hosts, mobility = 0~20 m/sec with mean =

10 m/sec).

Page 63: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation Results (8/10)

Throughput vs. traffic load(beacon interval =100 ms, 100 hosts, mobility = 0~20 m/sec with mean =

10 m/sec).

Page 64: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation Results (9/10)

Survival ratio vs. host density(beacon interval = 100ms, traffic load 1 route/sec, mobility = 0~20 m/sec

with mean= 10 m/sec).

Page 65: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Simulation Results (10/10)

Throughput vs. host density (beacon interval = 100ms, traffic load 1 route/sec, mobility = 0~20m/sec

with mean= 10 m/sec).

Page 66: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Outline IEEE 802.11 Ad hoc Network Power Saving Problem Asynchronous Quorum-based PS Protocols Optimal Asyn. Quorum-Based PS Protocols Analysis and Simulation Conclusion

Page 67: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Conclusion Quorum systems with the rotation closure

property can be translated to an asyn. PS protocol.

The active ratio is bounded by 1/ n, where n is the number of a group of consecutive beacon intervals.

Optimal, near optimal and adaptive AQPS protocols save a lot of energy w/o degrading performance significantly

Page 68: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Publication

ICPP’03 Best Paper Award

ACM Journal on Mobile Networks and Applications

Page 69: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Future work To incorporate the clustering concept into the

design of hybrid (syn. and asyn.) power saving protocols (NSC 93-2213-E-008-046-)

To design more flexible adaptive asyn. power saving protocols with the aid of the expectation quorum system (a novel quorum system which is a general form of probabilistic quorum systems) (93CAISER-中央大學分部計畫 )

To incorporate power saving mode management to wireless sensor networks with comm. and sensing coverage in mind (中大新進教師學術研究經費補助計畫 )

Page 70: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

Thanks!

Page 71: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

FPP quorum system

Proposed by Maekawa in 1985 For solving distributed mutual exclusion 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

Page 72: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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

Page 73: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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},…}

Page 74: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

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)

Page 75: Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

E-Torus quorum systemTrunk

Branch

Branch

Branch

Branch

cyclic

cyclic

E(t x w, k)