topology control in heterogeneous wireless networks

8/2/2019 Topology Control in Heterogeneous Wireless Networks

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Topology Control in HeterogeneousWireless Networks: Problem and Solution

Ning Li and Jennifer C.HouDepartment of Computer Science

University of Illinous at Urbana-Champaign

08.03.29

System Software LaboratoryMyung-Ho Kim TeamDae-Woong JO

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Contents

Introduction

Network Model

Related Work and Why They Cannot Be DirectlyApplied To Heterogeneous Networks

DRNG and DLMST

Properties Of DRNG and DLMST

Simulation Study

Conclusions

References

System Software Laboratory 2


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Introduction

Energy efficiency and Network capacity Reducing Energy consumption and improving network capacity

Two localized topology control algorithms

DRNG Directed Relative Neighborhood Graph

DLMST Directed Local Minimum Spanning Tree

Be able to prove

1) Derived under both DRNG and DLMST

2) DLMST is bounded, DRNG may be unbounded.

3) DRNG and DLMST preservers network bi-directionality



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Introduction (cont.)

Simulation results indicate Compared with the other known topology control algorithms

Have smaller average node degree (both logical and physical)

Have smaller average link length.

In Section 2 Network model

In Section 3 Summarize previous work on topology control

In Section 4 DRNG and DLMST algorithms

In Section 5 Prove several of their useful properties

In Section 6 Evaluate the performance of the proposed algorithms

In Section 7 conclude



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Network Model

V = {v1, v2, . . . , vn}, random distrivuted in the 2-Dplane.

Let rvi Maximal transmission range of vi

Heterogeneous network All nodes may not be the same.

rmin= minv

V {rv} rmax= maxvV {rv}

d(u,v) is distance between node u and node v



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Network Model (cont.)

Simple directed graph G = (V(G),E(G)) V(G) = randomly distributed in the 2-D plane E(G) = {(u,v) : d(u,v) w(u2, v2)

d(u1, v1) > d(u2, v2)

or (d(u1, v1) = d(u2, v2)

&&max{id(u1), id(v1)} > max{id(u2), id(v2)})

or (d(u1, v1) = d(u2, v2)&&max{id(u1), id(v1)} = max{id(u2), id(v2)}

&&min{id(u1), id(v1)} > min{id(u2), id(v2)}).

Definition 3 (Neighbor Set ) Algorithm A, denoted u

A v

NA(u) = {vV (G) : uA

v }.



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Definition 4 Topology

Directed graph GA = (E(GA),V(GA)) Where V (GA) = V (G), E(GA) = {(u, v) : u

A v , u, vV (GA)}.

Definition 5

Radius The radius, ru, of node u is defined

Definition 6 Connectivity

Topology generated by an algorithm A Node u is connected to node v (denoted uv)

If there exists a path(p0 =u, p1,,pm-1,pm= v) It follows that u => v if u = > p and p = > v for some pV(GA)

Definition 7 Bi-Directionality

Any two nodes u,v V (GA), uNA(v) implies vNA(u).



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Definition 8 Bi-Directional Connectivity

Bi-directionally connected to node v (denoted uv) If there exists a path p0 = u, p1,pm-1, pm = v) It follows that u u if u p and p v for some p V(GA)

Definition 9

Addition and Removal

Addition operation

extra edge (v, u) E(GA)

Removal operation delete any edge (u, v) E(GA)



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RELATED WORK AND WHY THEY CANNOT BEDIRECTLY APPLIED TO HETEROGENEOUS NETWORKS

System Software Laboratory

Ramanathan et al. [5] Two distrubuted heuristics for mobile networks

Require global information

Cannot be directly deployed

Borbash and Jennings [8] Proposed to use RNG

(Relative Neighborhood Graph)

Topology initialization of wireless networks

Good overall performance

Low interference, and reliablity

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RELATED WORK AND WHY THEY CANNOT BEDIRECTLY APPLIED TO HETEROGENEOUS NETWORKS


Definition 10 ( Neighbor Relation in RNG) u

RNG v if and only if there does not exist a third

node p such thatw(u, p) < w(u, v) and w(p, v) < w(u, v).

Or equivalently, there is no node

inside the shaded area


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RELATED WORK AND WHY THEY CANNOT BEDIRECTLY APPLIED TO HETEROGENEOUS NETWORKS (cont.)

System Software Laboratory

CBTC() [6] Proved to preserve network connectivity

In [10] Proposed LMST(Local Minimum Spanning Tree)

Topology control in homogeneous wireless multihop- networks

Proved thatLMST preserves the network connectivity

The node degree of any node

Can be transformed into one with bi-directional links

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RELATED WORK AND WHY THEY CANNOT BEDIRECTLY APPLIED TO HETEROGENEOUS NETWORKS (cont.)



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DRNG and DLMST

Propose two localized topology control algorithms DRNG (Directed Relative Neighborhood Grpah)

DLMST (Directed Local Minimum Spanning Tree)

Both algorithms are composed of three pahses Information Collection

Topology Construction

Construction of Topology with only Bi-Directional Links



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DRNG and DLMST (cont.)

Definition 12 Neighbor Relation in DRNG

uDRNG

v if andonly if d(u, v) ruand there does not exist a third node p

such that w(u, p) < w(u, v) and w(p, v) < w(u, v), d(p, v) rp



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DRNG and DLMST (cont.)

Definition 13 Neighbor Relation in DLMST

Directed Local Minimum Spanning TreeGraph (DLMST)

uDLMST

v if and only if (u, v) E(Tu), where Tu is thedirected local MSTrooted at u that spans N

R

u.

each node u computes a directed MST that spans NR

uand takes on-tree

nodes that are one hop away as its neighbors



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Properties of DRNG and DLMST

Discuss the connectivity, bi-directionality anddegree bound of DLMST and DRNG

Connectivity

Theorem 1 (Connectivity of DLMST) If G is strongly connected, then G DLMST is also strongly connected.

Proof For any two nodes u, vV (G), there existsa unique global MST T

rooted at u since G is stronglyconnected. Since E(T) E(GDLMST)by Lemma 2, thereis a path from u to v in GDLMST.

Lemma 2 : Let T be the global directed MST of G rooted at any node w V(G) ,then E(T) E(Gdlmst)



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Properties of DRNG and DLMST

Theorem 2 (Connectivity of DRNG) If G is strongly connected, then G DRNG is also strongly connected.

Proof For any two nodes u, vV (G), since G is strongly connected, there

exists a path (p0 = u, p1, p2, . . . , pm1, pm = v) from u to v, such

that(pi, pi+1) E(G), i = 0, 1, . . .,m 1. Thus pipi+1 in GDRNGbyLemma 3. Therefore, uv in GDRNG. Hencewe can conclude thatGDRNGis strongly connected.

Lemma 3: For any edge (u,v) E(G), we have u => v in Gdrng



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Properties of DRNG and DLMST (Cont.)

Bi-directionality Theorem 3

If the original topology G is strongly connected and bi-directional,then G DLMST and G DRNG are also strongly connected and bi-directional

Proof For any two nodes u, vV (G), there exists atleast one path p =

(w0 = u,w1, w2, , wm1, wm = v)from u to v, where (wi, wi+1) E(G), i = 0, 1, ,m 1. Since wiwi+1 in GDLMSTby Lemma 5,we have uvin GDLMST. Therefore, wiwi+1 in GDRNG, whichmeans uv in GDRNG. The same results still hold after Addition or

Removal

Lemma 5 : If the original topology G is strongly connected and bi-directional, then any edge (u,v) E(G) satisfies that u v in Gdlmst



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Properties of DRNG and DLMST(Cont.)

Degree Bound Theorem 4

For any node uV (GDLMST), the numberof neighbors in GDLMSTthat are inside Disk(u, rmin) is atmost 6.

Theorem 5 The out degree of node in GDLMST is boundedby a constant that

depends only on rmaxand rmin.



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Simulation Study

Evaluate the performance R&M, DRNG and DLMST by simulations.

Preserve network connectvity in heterogeneousnetworks

First simulation 50 nodes are uniformly distributed

1000m x 1000m region

R&M, DRNG and LMST all reduce

Average node degree, while maintaining network connectivity

DRNG and DLMST outperforms R&M



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Simulation Study (cont.)



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Simulation Study(cont.)

Second simulation Vary the number of nodes in the region

80 to 300

Average of 100 simulation runs

Each data point Nodes are uniformly distributed in [10m,250m]

Average radius and the average edge length

NONE(no topology control)

R&M, DRNG, and DLMST

DLMST outperforms the others

Better spatial reuse and use less energy



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Compare the out degree The topologies by different algorithms

The result of NONE is not shown

Langer than under R&M, DRNG, DLMST

Out degrees increase linearly

Shows the average logical/physical

Derived by R&M, DRNG, DLMST

Under R&M and DRNG increase

Under DLMST actually decrease



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Conclusions

Proposed two local topology control algorithms DRNG, DLMST

Heterogeneous wireless multi-hop networks

Have different transmission ranges

Show that

Most existing topology control algorithms

Have different transmission ranges

Disconnected network topology

Directly applied to heterogeneous networks.



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Conclusions(cont.)

DRNG and DLMST prove1) Preserve network connectivity

2) Preserve network bi-directionality

3) Bounded in the topology under DLMST ,Unbounded

under DRNG

Future research

Different maximal transmission power

Density of nodes, distribution of the transmission ranges

MAC-level interference affect network

Connectivity and bi-directionality



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References (cont.)

[8] S. A. Borbash and E. H. Jennings, Distributed topology control algorithm for multihop wireless

networks, in Proc. 2002 World Congress onComputational Intelligence (WCCI 2002), Honolulu, Hawaii, US, May2002.

[9] X.-Y. Li, G. Calinescu, and P.-J. Wan, Distributed construction of planar

spanner and routing for ad hoc networks, in Proc. IEEE INFOCOM

2002, New York, New York, US, June 2002.

[10] N. Li, J. C. Hou, and L. Sha, Design and analysis of an MSTbasedtopology control algorithm, in Proc. IEEE INFOCOM 2003, San

Francisco, California, US, Apr. 2003.

topology control in heterogeneous wireless networks

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