Chapter 5 Topology Control 2015/10/261. Outline 5.1. Motivations and Goals 5.2. Power Control and Energy Conservation 5.3. Tree Topology 5.4

Chapter 5Topology Control

112/04/201

Outline

5.1. Motivations and Goals

5.2. Power Control and Energy Conservation

5.3. Tree Topology

5.4. k-hop Connected Dominating Set

5.5. Adaptive node activity

5.6. Conclusions

112/04/202

Outline

5.1. Motivations and Goals


5.3. Tree Topology



5.6. Conclusions

112/04/203

Motivations

A typical characteristic of wireless sensor networks deploying many nodes in a small area

ensure sufficient coverage of an area, or protect against node failures

Networks can be too dense: too many nodes in close (radio) vicinity

112/04/204

Motivations In a very dense networks, too many nodes

Too many collisions Too complex operation for a MAC protocol Too many paths to be chosen from for a routing protocol, …

112/04/205

Goals This chapter looks at methods to deal with such

networks by Reducing/controlling transmission power Deciding which links to use Turning some nodes off

112/04/206

Topology Control Topology control: Make topology less complex

Topology: Which node is able/allowed to communicate with which

other nodes Topology control needs to maintain invariants, e.g.,

connectivity

112/04/207

Options for topology control

Topology controlTopology control

Flat network

All nodes have essentially same role

Hierarchical network

Assign different roles to nodes and then control node/link activity

Dominating sets

Tree

Adaptive node activity

HybridPower control Clustering

112/04/208

Outline

5.1. Motivation and Goals


5.3. Tree Topology



5.6. Conclusions

112/04/209

Introduction of Power Control Power control

The transmitter’s power can be adjusted dynamically over a wide range Typical radio adjusts their transmitter’s power based on received signal strength

Controls the transmission power Topology control for desired connectivity Compensate topology changes incurred

by mobility and dead nodes

A

BC

D

A

Connected

Disconnected

112/04/2010

Interactions

Introduction of Power Control

Battery drain

Power control

Large Battery makes Longer Lifetime

112/04/2011

Interactions


A

B

C

DDestination

Source

Battery drain

Power control

Large Power makes Performance Degradation

Interference


112/04/2012

Interactions


CB

D

ASource

Destination

A

B

C

Source

Battery drain

Power control



Different Power makes Load Unbalancing

Interference

A consumes much more power than C

Adjusting power can balance the power consumption

DDestination

112/04/2013

Interactions


CB

D

A

Source

B

C A

B

C

E

D

Battery drain

Power control


Different Power makes Load Unbalancing

Destination

Small Power creates more Spatial Reuse Opportunities


Interference


A

D

Destination

C is forbid to communication with B

Adjusting the power of A can improve the spatial reuse

Source

112/04/2014

Interactions


CB

D

ASource

B

C

Battery drain

Error performance

Error rate

dB

Power control


Different Power makes

Load Unbalancing

Destination

Small Power creates more

Spatial Reuse Opportunities

Small Power causes More Retransmissions

A

B

C

E

D

Large Battery makes

Longer Lifetime

Interference


AD

Destination

Adjusting the power of A can improve the spatial reuse

Large power, small error rate

Source

112/04/2015

Introduction of Power Control Targets and Issues

Improve network throughput Improve transmission range Improve fairness Improve connectivity Power control helps in scheduling Reduce the interference and energy consumption Partial combination of above targets etc.

112/04/2016

Power Control and Energy Conservation

IEEE INFOCOM 2000IEEE INFOCOM 2000

R. Ramanathan and R. Rosales-HainR. Ramanathan and R. Rosales-Hain

Topology Control of Multihop Wireless Networks using Transmit Power Adjustment

Topology Control of Multihop Wireless Networks using Transmit Power Adjustment

112/04/2017

Introduction Topology

The set of communication links between node pairs used by routing mechanism Uncontrollable factor: mobility, weather, interference,

noise Controllable factor: transmission power, antenna direction

112/04/2018

Introduction A graph is called connected if every

pair of distinct vertices in the graph can be connected through some path

A bi-connected graph is a connected graph that is not broken into disconnected pieces by deleting any single vertex (and its incident edges)

Connected

Bi-connected

112/04/2019

Motivation Drawbacks of wrong topology

Reduce network capacity Increase interference Increase end-to-end packet delay

Sparse network A danger of network partitioning High end to end delays

Dense network Many nodes interfere with each other

112/04/2020

Static Networks: Min-Max Power Algorithm Goal

Find a per-node minimal assignment of transmitted power p

such that (1) the induced graph is connected and (2) max p is minimum

112/04/2021

Min-Max Power Algorithm- Connected Networks Phase I: CONNECTION

Construct a Minimum cost spanning tree

Successful transmit power between i and j

A B

C D

E F

2

2

1 1

3 3( ( , ))ij i jp d l l s

s : the receiver sensitivity

: path loss between i and j ( ( , ))i jd l l1

1

1

122

3

3 3

34

il : the location of node i

112/04/2022

Min-Max Power Algorithm- Connected Networks Phase II : Per Node Minimizing Power

A B

C D

E F

2

2

1 1

3 3

1

1

1

122

3

3 3

3

side-effect-edge :The edge of (C, D) is automatically connected

1 1

4

A has a path to B via C with smaller power→A adjusts the transmitted power from 2 to 1.

B has a path to A via D with smaller power→B adjusts the transmitted power from 2 to 1.

The edge (A, B) can be disconnected to save more energy

112/04/2023

Min-Max Power Algorithm- Bi-Connectivity Augmentation Phase I: BICONN-AUGMENT

Construct a Connected Minimum cost spanning tree

A B

C D

E F

2

2

1 1

3 3

1

1

1

122

43

3 3

3 Successful transmit power between i and j

( ( , ))ij i jp d l l s

s : the receiver sensitivity

: path loss between i and j ( ( , ))i jd l l

il : the location of node i

112/04/2024


Add (u, v) to graph G until the network is bi-connected

=> Add (C, D)

C

E

A

C

Bi-Conn. Comp. of C Bi-Conn. Comp. of DA B

C D

E F

2

2

1 1

3 3

1

1

1

122

3

3 3

34

D

F

B

D

Bi-Connected component of C

Bi-Connected component of D

112/04/2025


Add (u, v) to graph G until the network is bi-connected

A B

C D

E F

2

2

1 1

3 3

1

1

1

122

3

3 3

34

C

E

D

F

Bi-Connected component of E

Bi-Connected component of F

=> Add (E, F)

Bi-Conn. Comp. of E Bi-Conn. Comp. of F

112/04/2026

Min-Max Power Algorithm- Bi-Connectivity Augmentation

Phase II: Per Node Minimizing Power No side-effect-edge →Finish

A B

C D

E F

2

2

1 1

3 3

1

1

1

122

4

3 3

4

4

112/04/2027

Min-Max Power Algorithm- Bi-Connectivity Augmentation Phase II: Per Node Minimizing Power

An other example has side-effect-edge

1

2

2

3 3

3A

B

C D

1 1

2

2

3 3

3 3

side-effect-edge :

The edge of (A, D) is automatically connected

Disconnect the edge (A, C) and still Bi-Connectivity→C adjusts the transmitted power from 3 to 2 112/04/2028


An other example has side-effect-edge

1

2

2

3 3

3

A B

C D

1 1

2

2

3

3 32 Disconnect the edge (B, D) and still Bi-Connectivity→B adjusts the transmitted power from 3 to 2

112/04/2029


Finish

1

2

2

3 3

3

A B

C D

1 1

2

2

3

3 32

112/04/2030

Outline



5.3. Tree Topology



5.6. Conclusions

112/04/2031

Introduction of Tree Topology Control Example:

MPR (Multi-Point Relay) election

Retransmission node

(a)

Retransmission node

(b)(b) is better than (a) 112/04/2032

Introduction of Tree Topology Control

g h

a

b c

d e f

g h

a

b c

d e f

Example:

a to d needs 2 hops

(a) (b)

(a) is better than (b)a to d needs 7 hops

112/04/2033

Tree Topology


N. Li, J. C. Hou, and L. ShaN. Li, J. C. Hou, and L. Sha

Design and Analysis of an MST-Based Topology Control Algorithm

Design and Analysis of an MST-Based Topology Control Algorithm

112/04/2034

Motivation

The advantage of Topology Control Minimize the overhearing and then optimize the network spatial reuse Maintain a connected topology by minimal power Power-efficient

(1) No Topology Control

A

B

C

D

E

F

GH

I

(2) With Topology Control

A

B

C

D

E

F

GH

I

112/04/2035

Goal Determine the transmission power of each node

Maintain network connectivity Minimal power consumption

112/04/2036

Local Minimum Spanning Tree Algorithm (LMST) Local Minimum Spanning Tree Algorithm (LMST)

Step 1: Information Collection Step2: Topology Construction Step3: Determination of Transmission Power

112/04/2037

Information Exchange Each node broadcasts periodically a Hello message using its

maximal transmission power. The Hello message includes the ID and Location of the node.

LMST – Step1: Information Collection

u‘’s ID and Location

c

a

u

b

d

Maximal Transmission Power

112/04/2038

Information Exchange Since Hello message includes the node’s ID and Location,

after obtaining the Hello message of 1-hop neighbors, node u can construct the local view.

LMST – Step1: Information Collection

c

a

u

b

d

112/04/2039

LMST – Step2: Topology Construction The weight of edge between the two nodes is based on

Euclidean distance.

The weight of an edge also denotes the transmission power (or distance) between the two nodes

2, rdc r c ： Coefficientd ： distance

c

a

u

b

d

e

3

4

5

5 6

7

7

7

10

6

112/04/2040

c

a

u

b

d

e

LMST – Step 2: Topology Construction Each node applies Prim’s algorithm independently to obtain its

Local Minimum Spanning Tree.

3

4

5

5 6

7

7

7

10

6

local view of node u

Node u constructs the Local Minimum Spanning Tree using Prim’s algorithm according to its local view

According to the constructed Local Minimum Spanning Tree, node u will use small power to communicate with node a via node b instead of using large power to communicate with node a directly.

According to the constructed Local Minimum Spanning Tree, node u will use small power to communicate with node a via node b instead of using large power to communicate with node a directly.

Small power:Creates more spatial reuse opportunityDecreases energy consumption

112/04/2041

LMST – Step 3: Determination of Transmission Power By measuring the receiving power of Hello message, each node can

determine the specific power levels it needs to reach each of its neighbors. Two commonly-used propagation models

Free Space

Two-Ray

Sign Meaning

Pt Transmit power

Pr Receive power

Gt Antenna gain of the transmitter

Gr Antenna gain of the receiver

Wave length

d Distance between nodes

L System loss

ht Antenna height of the transmitter

hr Antenna height of the receiver

Ld

GGPP rtt

r 2

2

)4(

Ld

hhGGPP rtrtt

r 2

22

112/04/2042

In general, the relation between Pr and Pt is of the following form

Where G is a function of

Example Pth is the required power threshold to successfully receive the message

Pmax is the maximal transmission power

LMST – Step 3: Determination of Transmission Power

GPP tr Ld

GG rt2

2

)4(

max/ PPG r

rthth PPPGP // max

Node b will compute：

c

a

u

b

d

e

HelloData

Node b transmits data to u：

Hello with Pmax

Data with PthG

112/04/2043

Conclusions Advantages

Maintain network connectivity by low energy consumption Reduce the probability of interference Increase the spatial reuse Achieve high throughput

112/04/2044

Tree Topology


J. Wieselthier, G. Nguyen, and A. EphremidesJ. Wieselthier, G. Nguyen, and A. Ephremides

On the Construction of Energy-Efficient Broadcast and Multicast Trees in Wireless

Networks

On the Construction of Energy-Efficient Broadcast and Multicast Trees in Wireless

Networks

112/04/2045

Introduction The paper studies the problems of broadcasting and

multicasting in wireless networks.

To form a minimum-energy tree Energy efficiency Maintain network connectivity

112/04/2046

Network Assumptions The power level of a transmission can be chosen

within a given range of values.

The availability of a large number of bandwidth resources.

Sufficient transceiver resources are available at each of the nodes in the network.

112/04/2047

Wireless Communications Model Node-based transmission cost evaluation

Pi,(j,k) = max{Pij, Pik},

Pij : Transmission power for node i to transmit packets to node j

i

j

k

Pij

Pik

Pik > Pij

The larger power (Pik ) can cover both of node j and node k

The smaller power (Pij ) can only cover node j

112/04/2048

The Broadcast Incremental Power Algorithm

Assume node a is the source node

Step 1: Determining the node that the Source can reach with minimum expenditure of power.

0

1

2

3

4

5

0 1 2 3 4 5

i

c

h

g

f

d

e

b a

0.30.5

0.3

0.5

a

a c

b

j

10.9

1.1

1.21.5

1.71.3

0.7 0.81.3

112/04/2049


0

1

2

3

4

5

0 1 2 3 4 5

i

c

h

g

f

d

e

b a

0.31 0.5 ΔPa = 0.5 – 0.3 = 0.2

ΔPb= 1 – 0 = 1

j

10.9

1.1

1.21.5

1.71.3

0.7 0.81.3

0.5a cPac

Pa0.3a b

ΔPa

1b dPbd

Pbb

ΔPb

Minimum additional cost

Step 2: Determine which “new” node can be added to the tree at minimum additional cost.

112/04/2050

The Broadcast Incremental Power Algorithm Step 2: Determine which “new”

node can be added to the tree at minimum additional cost.

0

1

2

3

4

5

0 1 2 3 4 5

ij

c

h

g

f

d

e

b a

0.31 0.5

0.71.3 0.8

0.9

1.1

1.21.5

1.71.3

ΔPa = 1.3 – 0.5 = 0.8

1.3a jPaj

Pa0.5a c

ΔPa

ΔPc = 0.7 – 0 = 0.7

0.7c jPcj

Pcc

ΔPc

ΔPb = 1 – 0 = 1

1b dPbd

Pbb

ΔPb

Minimum additional cost

112/04/2051


Step 2: Determine which “new” node can be added to the tree at minimum additional cost.

0

1

2

3

4

5

0 1 2 3 4 5

ij

c

h

g

f

d

e

b a

0.31 0.5

0.71.3 0.8

0.9

1.1

1.21.5

1.71.3

And so forth：c → i

c → h

b → d

b → e

b → f

b → g

112/04/2052

The Broadcast Incremental Power Algorithm BIP is similar in principle to Prim’s algorithm.

One fundamental difference: The inputs to Prim’s algorithm are the link cost Pij. BIP must dynamically update the costs at each step.

112/04/2053

Conclusions Propose a centralized algorithm: The Broadcast

Incremental Power(BIP) Algorithm Advantages

Improved performance can be obtained when exploiting the properties of the wireless medium

Energy-efficient

112/04/2054

Outline



5.3. Tree Topology



5.6. Conclusions

112/04/2055

Connected Dominating Set Connected dominating set (CDS) - construct a virtual backbone. Communicate through the virtual backbone by dominators. Example: virtual backbone construction

Sensor node

112/04/2056


CDS edgeVirtual backbone

Sensor node

Dominators

1-hop Connected Dominating Set 112/04/2057


CDS edgeVirtual backbone

Sensor node

Dominators

1-hop Connected Dominating Set

2-hop Connected Dominating Set 112/04/2058

A Hardness Result The MDS (minimum dominating set) problem is NP-hard, it is

even a hard problem to approximate in general.

For the case of unit disk graphs, it is possible to find a Polynomial Time Approximation Scheme (PTAS).

112/04/2059

k-hop Connected Dominating Set

Journal of Communications and Networks 2002Journal of Communications and Networks 2002

Jie Wu, Fei Dai, Ming Gao, and Ivan StojmenovicJie Wu, Fei Dai, Ming Gao, and Ivan Stojmenovic

On Calculating Power-Aware Connected Dominating Sets for Efficient Routing in Ad Hoc

Wireless Networks

On Calculating Power-Aware Connected Dominating Sets for Efficient Routing in Ad Hoc

Wireless Networks

112/04/2060

Introduction Routing based on a connected dominating set is a promising-

approach Each gateway host keeps following information: gateway

domain membership list and gateway routing table.

Gateway host

Non-Gateway host

1

2

56

74

9

3

8 10

11

dominated set

destination member list next hop distance

9 (1,2,3,11) 9 1

4 (5,6) 7 2

7 (6) 7 1

Gateway routing table of host 8

3

10

11

Gateway domain member list of host 8

Receiver

Sender

112/04/2061

Introduction In order to prolong the life span of each node, power

consumption should be minimized and balanced among nodes. Unfortunately, nodes in the dominating set consume more

energy than nodes outside the set.

Propose a method of calculating power-aware connected dominating set based on a dynamic selection process.

Dominated set

Gateway host

Non-Gateway host

1

2

56

74

9

3

8 10

11

12

112/04/2062

Every v exchanges its neighbor set N(v) with all its neighbors. Each node has two-hop neighbors information.

Every v is marked if there exist two unconnected neighbors

Network Initialization

25

Non-Gateway host

Gateway host

1

2

3

5

6

7

8

910

4

11

12 1314

15

16

17

19

20

18

21 2227

262423

unconnected

Become a Gateway host

112/04/2063

Gateways Selection

Gateways Selection (Rules 1 and 2)Gateways Selection (Rules 1 and 2)

112/04/2064

Gateways Selection (by applying Rule 1) Rule 1: Consider two vertices v and u in G’. If N[u] N[v]in G and id( u )

< id(v), the marker v is unmarked, i.e., G' is changed to G' - {u}.

id N(id)

21 22, 23, 24

22 20, 21, 23, 24, 25, 26, 27

20

2122

27

2524

23

26

N(21) N(22)N(21) N(22)

Non-Gateway host

Gateway host

112/04/2065

Rule 2: Assume that u and w are two marked neighbors of marked vertex u in G’. If N(u) N(v) N(w) in G and id(u) = min{id(v),id(u),id( w)},then the marker of u is unmarked.

Gateways Selection (by applying Rule 2)

id N(id)

2 1, 3, 4, 5, 6, 7, 8, 9

4 1, 2, 3, 9, 10, 11

9 2, 4, 5, 6, 7, 8, 10

112/04/2066

1

2

3

5

6

7

8

910

4

11

N(2) N(4) N(9)and id(2) = min{id(2), id(4), id(9)}N(2) N(4) N(9)and id(2) = min{id(2), id(4), id(9)}

Non-Gateway host

Gateway host

Extended Rules Several extended approaches for selective removal

The node-degree-based approach aims at reducing the size of the connected dominating set

The energy-level-based approach tries to prolong the average life span of each node.

112/04/2067

Node-degree-based Approach (Rule 3) Rule 3: Consider two marked vertices v and u in G’. The marker v is

unmarked if one of the following conditions holds: N[u] N[v] in G and nd(u) < nd(v) N[u] N[v] in G and id(u) < id(v) when nd(u) = nd(v), where nd()

returns node degree.

id nd(id) N(id)

21 3 22,23,24

22 7 20,21,23,24,25,26,27

27 3 22,25,26 20

21 2227

252423

26

N(21) N(22) andnd(21)=3 < nd(22)=6N(21) N(22) andnd(21)=3 < nd(22)=6

N(27) N(22)nd(27)=3 < nd(22)=6N(27) N(22)nd(27)=3 < nd(22)=6

112/04/2068

Non-Gateway host

Gateway host

Node-degree-based Approach (Rule 4)

4

11

1213

15

16

17

19

20

18

22

Rule 4: Assume that u and w are two marked neighbors of marked vertex v in G . The marker v is unmarked if one of the following conditions holds:

Case 1. N(u) N(v) N(w), but N(v) N(u) N(w) and N(w) N(u) N(v) in G.

id N(id)

11 4,12,13,15,16,17,18,20

18 11,17,19,20

20 11,18,19,22

N(18) N(11) N(20)butN(11) N(18) N(20)N(20) N(11) N(18)

N(18) N(11) N(20)butN(11) N(18) N(20)N(20) N(11) N(18)

112/04/2069Non-Gateway host

Gateway host


1

2

3

5

6

7

8

910

4

11

Rule 4: Case 2. N(u) N(v) N(w) and N(v) N(u) N(w), but N(w) N(u)

N(v) in G; and one of the following conditions holds: (a) nd(u) < nd(v)(b) nd(u) = nd(v) and id(u) < id(v)

id nd(id) N(id)

2 8 1, 3, 4, 5, 6, 7, 8, 9

4 6 1, 2, 3, 9, 10, 11

9 7 2, 4, 5, 6, 7, 8, 10

nd(9)=7 < nd(2)=8nd(9)=7 < nd(2)=8

N(2) N(4) N(9)N(9) N(2) N(4)

butN(4) N(2) N(9)

N(2) N(4) N(9)N(9) N(2) N(4)

butN(4) N(2) N(9)

112/04/2070

Non-Gateway host

Gateway host


4

11

12 13 14

15

16

17

20

18

Rule 4: Case 3. N(u) N(v) N(w), N(v) N(u) N(w) and N(w) N(u)

N(v) in G; marker u should be unmarked if one of the following conditions holds: (a) nd(u) < nd(v) and nd(u) < nd(w) (b) nd(u) = nd(v) < nd(w) and id(u) < id(v)(c) nd(u) = nd(v) = nd(w) and id(u) = min{id(v), id(u), id(w)}

id nd(id) N(id)

11 8 4,12,13,15,16,17,18,20

13 4 11,12,14,15

15 4 11,13,14,16

id(13) < id(15)id(13) < id(15)

nd(13) = nd(15) = 4nd(13) = nd(15) = 4

N(13) N(11) N(15)N(15) N(11) N(13)

butN(11) N(13) N(15)

N(13) N(11) N(15)N(15) N(11) N(13)

butN(11) N(13) N(15)

112/04/2071

Non-Gateway host

Gateway host

Energy-level-based Approach (Rules 5 、 6、 7 、 8)

Energy-level-based rules Let EL denote energy level Rules 5, 6

Similar to rules 1 and 2, the only difference is to compare EL prior to node ID.

Rules 7, 8 Similar to rules 3 and 4 The only difference: when nodes u and v have the same

EL, they compare ND prior to node ID.

112/04/2072

Conclusions Advantages

Overall energy consumption is balanced A relatively small connected dominating set is generated

112/04/2073

Outline



5.3. Tree Topology



5.6. Conclusions

112/04/2074

What’s Adaptive Node Activity?

Influence the topology of a graph by Selecting certain nodes to be turned on or Selecting certain nodes to be turned off

An operation that of course also fits well into the context of clustering or backbone mechanisms.

Nodes that are sources or sinks of data are always kept active

112/04/2075

Adaptive node activity

ACM/IEEE MobiCom 2001ACM/IEEE MobiCom 2001

Y. Xu, J. Heidemann, and D. EstrinY. Xu, J. Heidemann, and D. Estrin

Geography-Informed Energy Conservation for Ad Hoc Routing

Geography-Informed Energy Conservation for Ad Hoc Routing

112/04/2076

Introduction Motivation

Nodes consume high energy during routing, especially during transmission

Reduce the energy consumption in ad hoc wireless networks Increase the network lifetime

Goal Identifies equivalent nodes for routing

Based on location information Turns off unnecessary nodes Load balancing energy usage

Lifetime of all nodes remain as long as possible

112/04/2077

Geographical Adaptive Fidelity(GAF) Routing Distribute routing duties by electing new local leaders

periodically. Leaders (active nodes) handle all routing traffic,

allowing other nodes to sleep for extended periods of time and conserve energy.

112/04/2078

Determining Node Equivalence The physical space is divided into equal size squares.

Based on radio communication range Any two nodes in adjacent squares can communicate with each other. In each grid, one node will stay in active state.

5

Rr

r ： the length of each gridR ： communication range of sensor node

r r r

r

r

r

Rr

2r

Active node

Sleeping node

Source

Destination

112/04/2079

GAF State Transitions GAF consists of three states

Discovery: Due to mobility, node in this state aims to discover all nodes in the same grid

Active: In each grid, one node will stay in active state Sleeping: In a grid, all nodes except the active node will stay in sleeping state

After TdAfter Td

Dis

cove

ry m

sg

Dis

cove

ry m

sg

Afte

r Ts

Afte

r Ts D

iscovery msg

Discovery m

sg

After TaAfter Ta

Sleeping

Discovery Active

112/04/2080

GAF State Transitions

75%92%

23%

54%

　： sleeping state　： discovery state　： active state

Initially nodes start in the Discovery state

Node turns on its radio and find the other nodes within the same grid.

The node finish the discovery duration Td, broadcasts its discovery message (node id, grid id, estimated node active time, and node state) and enters Active state. Td = random [0 ~ constant]

The other node switches its state into Sleeping state after receive the discovery message sentby the node which has higher rank value then itself.

a

b

c

d

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Given any two node i and jRanki > Rankj , if and only if (enati > enatj)

enat = estimated node active time duration

(enlt = expected node lifetime)

Node Ranking Rule

, when enlt becomes less than a threshold

, when enlt larger than a threshold

If node’s lifetime is less than a threshold, stay active state until energy exhaustion.

If node’s lifetime is larger than a threshold, balancing the remain energy to avoid frequent switches between active/sleep states.

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75%92%

23%

54%


70%

A node in the Sleeping state wakes up after an application-dependent sleep time Ts, and switches its state into Discovery state. Avoiding the active node

leaving the grid and energy unbalance.

Ts = random [enat/2 ~ enat]

Larger remain energy, higher rank

Energy drain

Switches to Discovery state after Ts

a

b

c

d

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The active node periodically rebroadcasts its discovery message

The active node leave active state: After the time duration Ta = enat. Receiving discovery message send

by the other node which has higher rank value than itself.

70%


75%

23%

54%


Larger remain energy, higher rankBroadcasts its discovery messageBecome the active node

Receiving discovery messageSwitches to Discovery state

a

b

c

d

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Conclusions GAF increases the network lifetime without decreases

the performance substantially

Distribute routing duties by electing new local leaders periodically

All nodes remain up for as long as possible

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Conclusions Various approaches exist to adjust the topology of a

network to a desired shape Most of them produce some non-negligible overhead

Some distributed coordination among neighbors require additional information.

Constructed structures can turn out to be somewhat brittle and the overhead might be wasted.

Benefits have to be carefully weighted against risks for the particular scenario at hand

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References R. Ramanathan and R. Rosales-Hain. Topology Control of Multihop Wireless Networks using Transmit Power

Adjustment. In Proceedings of IEEE Infocom, pages 404–413, Tel-Aviv, Israel, March 2000 N. Li, J. C. Hou, and L. Sha. Design and Analysis of an MST-Based Topology Control Algorithm. In Proceedings

of IEEE INFOCOM, San Francisco, CA, March 2003 J. Wieselthier, G. Nguyen, and A. Ephremides, On the Construction of Energy-Efficient Broadcast and Multicast

Trees in Wireless Networks, in Proc. IEEE Infocom’2000, Tel Aviv, Israel, pp. 585–594, 2000 Jie Wu, Fei Dai, Ming Gao, and Ivan Stojmenovic, On Calculating Power-Aware Connected Dominating Sets for

Efficient Routing in Ad Hoc Wireless Networks, Journal of Communications and Networks, vol. 4, No. 1, march 2002

B. Chen, K. Jamieson, H. Balakrishnan, and R. Morris. Span: An Energy-Efficient Coordination Algorithm for Topology Maintenance in Ad Hoc Wireless Networks. Wireless Networks, 8(5): 481–494, 2002

Y. Xu, J. Heidemann, and D. Estrin. Geography-Informed Energy Conservation for Ad Hoc Routing. In Proceedings of the 7th Annual International Conference on Mobile Computing and Networking (MobiCom), pages 70–84, Rome, Italy, July 2001. ACM.)

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Documents

Chapter 5 Topology Control 2015/10/261. Outline 5.1. Motivations and Goals 5.2. Power Control and Energy Conservation 5.3. Tree Topology 5.4