Unified Clustering Mechanism for Multi-Cluster Mobile Ad Hoc Networks

Unified Clustering Mechanism for Multi-Cluster

Mobile Ad Hoc Networks

Department of Electrical Engineering

The University of Texas at Dallas

Final Oral Examination for Ph.D.

Summer 2003

Aqeel A. Siddiqui

2

Research Objectives

• Unification of clustering mechanisms

• Is the unified clustering mechanism stable?

• Propose new performance measures for clustering mechanisms

• Performance analysis of clustering mechanisms

3

A Cluster-based Ad Hoc Network

0

1

6

8

53

4

7

9

2

Clusterheads: 1, 5, 8

Gateways: 3, 4, 6

Backbone: 1, 3, 4, 5, 6, 8

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RESEARCH BACKGROUND

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Mobile Ad Hoc Network (MANET)

• Characteristics:• Wireless links• Dynamic network topology• All nodes can act as router• Resource poor nodes• Also called wireless multihop networks

• Applications: • Military• Emergency• Sensor networks• Bluetooth

• MANET: http://www.ietf.org/html.charters/manet-charter.html

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MANET – Other Routing Approaches

• Flooding

• Destination-Sequenced Distance Vector (DSDV)

• Ad Hoc on Demand Distance Vector (AODV)

• Dynamic Source Routing (DSR)

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Cluster-basedAd Hoc Network Protocol Layers

Physical Layer Protocol

Link Layer Protocol

Clustering Protocol

Routing Protocol

Packet Forwarding Protocol

Data Transport Protocol

Data Application Protocol

Signalling Data

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Existing Clustering Mechanisms

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Existing Node-id Based Clustering

• Each node at most one hop away from clusterhead

• Node with highest ID in a cluster becomes clusterhead

• Poor clusterhead load distribution• Dennis J. Baker and Anthony Ephremides. The Architectural

Organization of a Mobile Radio Network via a Distributed Algorithm. IEEE Transactions on Communications, Vol. Com-29, No. 11, November 1981, pages 1694-1701.

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Existing Connectivity-based Clustering

• Node with highest connectivity in a cluster becomes clusterhead

• Yields minimum number of clusters

• Poor clusterhead load distribution and clusterhead stability

• Mario Gerla and Jack Tzu-Chieh Tsai. Multicluster, Mobile, Multimedia Radio Network. ACM Journal on Wireless Networks, Vol.

1, No. 3:255-265, 1995.

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Research Objectives

• Unification of clustering mechanismsUnification of clustering mechanisms

• Is the unified clustering mechanism stable?

• Propose new performance measures for clustering mechanisms

• Performance analysis of clustering mechanisms

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Clusterhead-time Based Clustering

• In node-id and connectivity-based mechanisms, the load distribution is unfair.

• Nodes with less average clusterhead-time should be preferred to become clusterhead

• Good clusterhead load distribution• Poor clusterhead stability• A threshold to prevent too frequent changes in

clusterheads

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Unified Clustering Mechanism

Availability Factor Availability factor ai(t), range 0-1,

dependant on either one of the following: identity of node, i

connectivity, ci(t)

fraction of time the ith node remains a clusterhead, qi(t)

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Unified Clustering Algorithm Few definitions

t: Incremental period

• wi(t): Indication if ith node is clusterhead

• vi(t): Indication if ith node is covered

• li,j (t): Link status between ith and jth node

•

otherwise ;1

)()( and if ;0

)()( and if ;0

)(,,

THji

THji

aji atataji

atataji

tATH

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Unified Clustering Algorithm Clustering Criteria

• The ith node decides at time (t+t) to become a clusterhead, if at time t- wi(t)=0,

- wj(t)=0 for all neighbors j,

- ai(t) aj(t), for all uncovered neighbors j < i, and

- ai(t) aj(t), for all uncovered neighbors j > i.

j

jijjii Avlv 0,,,

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Unified Clustering Algorithm Clustering Criteria (contd.]

• The ith node decides at time (t+t) to remain a clusterhead, if at time t - wi(t)=1,

- ai(t) aj(t), for all clusterhead neighbors j < i, and

- ai(t) aj(t), for all clusterhead neighbors j > i.

j

jijjii Awlw 0,,,

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Unified Clustering Algorithm Clustering Criteria (contd.]

• The ith node decides at time (t+t) to takeover the role of clusterhead, if at time t - wi(t)=0,

- wj(t)=1 for at least one neighbor j, and

- ai(t) - aj(t) aTH, for all clusterhead neighbors j < i, and

- ai(t) - aj(t) aTH, for all clusterhead neighbors j > i.

j

ajijjiii THAwlwv ,,,

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Unified Clustering Algorithm Clustering Criteria (contd.]

The ith node decides at time (t+t) to assume the role of regular node in all other cases.

j

ajijjiij

jijjiij

jijjiii THAwlvAwlwAvlvttw ,,,0,,,0,,, )(

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Unified Clustering Mechanism

Model

ain

aic

aiq

fq

qi

fn

fcci

fa

ai

wi (t+t)

aj from other nodes

wi to other nodes

Block diagram for node i

hq

i

wj from other nodes

ai to other nodes

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Research Objectives

• Unification of clustering mechanisms

• Is the unified clustering mechanism Is the unified clustering mechanism stable?stable?

• Propose new performance measures for clustering mechanisms

• Performance analysis of clustering mechanisms

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Discrete Linear Control System

• Definition

• Unified clustering mechanism

– x[kT] is clusterhead state, wi(t)– u[kT] is the link status, li,j (t)Unified Clustering Mechanism is Non-Linear!

,...2,1,0);(u)(B)(x)(A)1(x kkTTkTTTk

,...2,1,0);(u)(D)(x)(Cy kkTTkTTkT

j

ajijjiij

jijjiij

jijjiii THAwlvAwlwAvlvttw ,,,0,,,0,,, )(

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Discrete Non-Linear Control SystemDefinition

• Stability in the sense of Liapunov Consider a region in the state space enclosing an equilibrium point

x0. This equilibrium point is stable provided that there is a region (),

which is contained within , such that any trajectory starting in the region does not leave the region . This permits the existence of a continuous oscillation about the equilibrium point.

• Asymptotic stability An equilibrium point is asymptotically stable if, in addition to being

stable in the sense of Liapunov, all trajectories approach the equilibrium point. This is the stability definition usually used in control-system design.

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Unified Clustering MechanismStability in different scenarios

• Case: Node-id or Connectivity based For a given u, there will be a unique set of availability factor a. Thus

we will get a unique output w. Therefore, such a system will be stable.

• Case: Clusterhead-time based For a given (fixed) u, the equilibrium point will change from time to

time. The output w will follow the trajectory w(t1), w(t2), w(t3), and so

on, in the state space. But for each equilibrium point w(tk), the system

is designed such that it approaches equilibrium. Thus, the system is still stable.

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Research Objectives

• Unification of clustering mechanisms

• Is the unified clustering mechanism stable?

• Propose new performance measures for Propose new performance measures for clustering mechanismsclustering mechanisms

• Performance analysis of clustering mechanisms

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Proposed Clustering Performance Measures

• Clusterhead GranularityFraction of nodes which are clusterhead.

• Clusterhead Load distributionDistribution of clusterhead role among nodes.

• Clusterhead StabilityFrequency of changes in clusterheads.

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Clustering PerformanceClusterhead Granularity

Let G(t) be the granularity of clusterheads of the system as defined below:

1)(0 ;)(1

)(1

tGtqN

tGN

jj

Tn

ui

Ti tutw

ntq

1

)(1

)(

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Clustering PerformanceClusterhead Load Distribution

Let D(t) be the clusterhead load distribution of the system as defined below:

1)(0 ;)()()(

11)(

1

2 tDtGtq

tCHtD

N

j jav

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Clustering PerformanceClusterhead Stability

Let S(t) be the clusterhead stability of the system as defined below:

1)(0 ;)(1

)(1

tStsN

tSN

jj

)()( tzi

iets

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Clustering PerformanceExamples

System G S D

N-clusterhead 1 1 1

1-clusterhead non-hopping

1/N 1 <<1

1-clusterhead slow hopping

1/N 1

1-clusterhead fast hopping

1/N 1

1e

60e

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Research Objectives

• Unification of clustering mechanisms

• Is the unified clustering mechanism stable?

• Propose new performance measures for clustering mechanisms

• Performance analysis of clustering Performance analysis of clustering mechanismsmechanisms

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D and G Relationship

• Assumptions– Static nodes (wireless connection but no

movements)– Node-id or Connectivity based clustering

• Result

GD 11

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Impact of Availability Factor Threshold

• The purpose of availability factor threshold is to limit frequent changes in clusterheads.

• The availability factor threshold introduces a hysteresis, thus favoring a node to remain clusterhead once it becomes clusterhead.

• The larger the availability factor threshold the higher will be the clusterhead stability of the system.

• As a consequence it may also result in reduced clusterhead load distribution.

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Clusterhead-time based clustering

State Transitions – affect of threshold

Static nodes with wireless links

TT

T

a

1.0

t

aTH

t1 t2 t3t0

x1 x3

x4x5

x2

ttrans

x6

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• The number of clusterhead changes ( ) is proportional to

The larger the availability factor threshold the higher will be the stability of the system.

• The larger the availability factor threshold the smaller the

clusterhead load distribution.

Clusterhead-time based clustering

Performance (Static Network)

1/ if ,1 GaD TH

)(tzi

THaG /

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Clustering PerformanceSimulation Parameters

• Network:• Number of mobile nodes, N = 20

• Service area, A = 1 km2 (1000m x 1000 m)

• Maximum coverage radius, R = 250 m

• Various average speeds 0-5 m/s

• Mobility:• Two patterns

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Clustering PerformanceSimulation Protocols

• Clustering:• Link Information Broadcast (LIB) • Link Information Unicast (LIU) • Member Link Info (MLI) • System Info (SYS) • Beacon (BEA)

• Routing:• Routing Request (RRQ) • Routing Response (RRP)

• Application:• Data Request (DRQ) • Data Response (DRP)

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Clustering PerformanceSimulation Results – node-id based

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0.700

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0.900

1.000

0 1 2 3 4 5

Average Mobility (m/s)

S

G

D

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Clustering PerformanceSimulation Results – connectivity

based

0.000

0.100

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0.900

1.000

0 1 2 3 4 5

Average Mobility (m/s)

S

G

D

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Clustering PerformanceSimulation Results – CH-time based

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 1 2 3 4 5

Average Mobility (m/s)

S

G

D

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Performance of CH-time based Clustering

Average Mobility 3m/s

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0.1

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0.9

1

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Availability factor threshold

Perfo

rman

ce c

hara

cter

istic

s G

S

D

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ADDITIONAL EXPIREMENTS

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Additional Work• Clustering based on the mobility of the nodes is added to

the unified mechanism. Experiments show that it improves the clusterhead stability.

• Many simulations are performed with various combinations of the clustering mechanisms (e.g. connectivity + clusterhead-time based). Results show performance trade-offs.

• Impact of clustering gap on unserviced index is studied using simulations. Results show that larger clustering gap results in larger unserviced index.

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SUMMARY

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Summary• Defined unified clustering mechanism using generic availability factor.

• Clusterhead-time based mechanism helps improve the clusterhead load distribution.

• Mathematical/matrix formulation of clustering algorithm.

• Application of Non-linear Control Systems Stability theory shows that the unified clustering mechanism is stable.

• Defined clustering performance measures to be used with unified clustering mechanism.

• Unified clustering mechanism is useful in comparing various clustering mechanisms. It also makes it easy to introduce a new clustering (based on some new parameter) in future.

• Change in the availability factor threshold affects the Clusterhead Stability and Clusterhead Load Distribution.

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FUTURE ENHANCEMENTS

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Clusterhead Granularity is ½ if N is even,

(N+1)/2N if N is odd.

2

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5 1

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Clustering PerformanceWorst Case Analysis – Granularity

Maximum degree = 2

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Clustering PerformanceWorst Case Analysis – Granularity

Maximum degree = 3

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Clustering PerformanceWorst Case Analysis – Granularity

Maximum degree = 3

Level Nodes per

level

Total nodes

Number of clusterheads

Clusterhead granularity

1 1 1 1 1

2 3 4 1 1/4=0.25

3 6 10 7 7/10=0.7

4 9 19 7 7/19=0.368

5 12 31 19 19/31=0.613

6 15 46 19 19/46=0.413

7 18 64 37 37/64=0.578

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Clustering PerformanceWorst Case Analysis – Granularity

Maximum degree = 4

1

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5

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7

89

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Clustering PerformanceWorst Case Analysis – Granularity

Maximum degree = 4

Level Nodes per

level

Total nodes

Number of clusterheads

Clusterhead granularity

1 1 1 1 1

2 4 5 1 1/5=0.2

3 8 13 9 9/13=0.692

4 12 25 9 9/25=0.36

5 16 41 25 25/41=0.61

6 20 61 25 25/61=0.41

7 24 85 49 49/85=0.576

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Future Work• Mathematical relationship between

Clusterhead Stability and Clusterhead Load Distribution.

• Further analysis of worst case scenarios.

• Theoretical analysis for the feasibility of combining/mixing various clustering mechanisms.

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Key Words

• Ad Hoc

• Multihop

• Cluster

• Modeling

• Performance

• Routing

• Sensor