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G-REMiT: An Algorithm for Building Energy Efficient Multicast Trees in Wireless Ad Hoc Networks

Bin Wang and Sandeep K. S. Gupta

Computer Science and Engineering Department

Arizona State University

Tempe, AZ, USA{Bin.Wang,Sandeep.Gupta}@asu.edu

2

Outline

• Problem Statement• Challenges• Background and Related Work• System Model & Assumptions• Node’s Energy Consumption Metric• G-REMiT Algorithm & Performance Results• Conclusions

3

Problem Statement

• Given a set of nodes with– wireless transceiver and – power control ability

• Find– a group-shared multicast tree such that the total

energy consumption of all the nodes is minimized

4

Difference of Wired & Wireless Network

Wired Network Graph Wireless Network Graph

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Challenges

• Transmission Power determines– The total amount of energy consumed on the

link– Feasible of the link– Network topology

6

Background and Current State of Art

• Multicasting– What is?

• Allow one entity to communicate efficiently with multiple entities residing in a subset of the nodes in the network

– Why multi-destination delivery in a single message?

• Transparency; Efficiency; Concurrency

– Applications (e.g, distributed database, distributed games, teleconferencing)

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Background and Current State of Art

i k

j

pi , j

pi , k

m

pi , m

Wireless Multicast Advantage

},,max{ ,,,),,(, mikijimkji pppp

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Background and Current State of Art

• Building energy-efficient broadcast/ multicast tree– Optimal solution is NP-hard problem [Li LCN2001],

heuristic algorithm is needed– Distributed Solution vs. Centralized Solution

• High overhead to obtain global knowledge

• Dynamic of wireless link and data traffic

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Background and Current State of Art

• Current heuristic algorithms for building energy efficient broadcast/multicast tree– Minimize cost metric increment for adding a node in the

source-based tree. • Using cost metric with energy cost (BIP/MIP, BLU/MLU,

BLiMST/MLiMST [Wieselthier Infocom2000]); Dist-BIP-A, Dist-BIP-G [Wieselthier Milcom2002]

– Refine a minimum spanning tree (MST) by cover as more downstream node as possible in source-based tree

• EWMA, Dist-EWMA [Cagalj Mobicom2002]

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System Model & Assumptions

• Static Wireless Ad hoc Network• Each node knows the distance between itself and

its neighbor nodes• Every node knows the number of nodes in the

multicast group• Group message generation rate (in term of bit/s) at

every node follow Poisson distribution. And all of these message generation rates are independent random variables

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Wireless Communication Model

• The minimum power needed for link between nodes i and j for a packet transmission is:

)( ,, jielecji rKEp

)(4 , jielec rKE

So is not negligibleelecE

• For short range radio,

where is energy cost of transmission processing, is Euclidean distance between i and j, is propagation loss exponent, K is a constant dependent upon the antenna.

elecE jir ,

[Feeney Infocom2001]

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Node’s Energy consumption in different multicast sessions

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m

k

i l

m

k

jj

di[1]

di[1]

di[2]

di[2]

eleci

kii

Ed

pEC

])2[(

,

eleci

jii

Ed

pEC

])1[(

,

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A Group-shared Tree Example

elecsumAB

elecAelecB

AB

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EdEd

ppP

])1[(])2[(

]])1[[(]])2[[(

10]1[10]1[

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;104321]1[10 A 11875]1[10

B

]1[]1[ 1010 BAsum 4]1[; 10 w (because )}11,8,7,5{]1[10 B

2

109

4

1

3

d [2]10

10d [1]

6

8

57

11

B [1]10

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Node’s energy cost metric in Group-shared Tree)

• Energy consumed at node i is

• If we introduce , then

• Node’s Relative Energy Cost Metric

eleciiiii EGdwGdwR ||])1[])(1[(|])2[](1[

elecsumiAiBi EddPii

])1[(])2[( ]1[]1[

}||])1[])(1[|(|])2[](1[{ eleciiiii EGdwGdwP

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G-REMiT Algorithm

• Idea: a node changes its connected tree neighbor to minimize the total energy consumption of tree.

(Tree 1) (Tree 2)

x

j

i

x

j

i

jxiChange ,

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Example of Refinement at a node for minimizing energy consumption of the Tree

88.7)'''()(

88.1)'''()(

Similary,

49.4)'''()(

:by obtianed gain The

8928928,9

2

1092109210,9

2

6926926,9

2

6,92

6,92

RRRRRRg

RRRRRRg

RRRRRRg

Changeg

has the largest positive value. So node 2 select node 6 as its new connection tree neighbor. And make .

6,92g

6,92Change

2

109

4

1

3

6

8

57

11

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Tree’s Energy Consumption Oscillation Avoidance

R10 may be affected by , because may be changed.

6,92Change ]1[10w

• Lemma 1 : Nodes that are on tree pathj,i are the only nodes in the multicast tree that may be affected by Changei

x,j 2

109

4

1

3

6

8

57

11

10d [1]

10d [2]

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Disconnection Refinement

• Lemma 2: If i is not on tree pathj,x the tree remains

connected after Changeix,j

x

j

i

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G-REMiT Algorithm Description

• Two phases (Core-Based Tree)– First Phase: using distributed algorithm to build

MST [Gallager TPLS1983].– Second Phase: organized by rounds. Each

round is leaded by the core node. It terminates G-REMiT algorithm where there is no gains by switching any node in the multicast tree.

• In each round, a depth-first search algorithm is used to pass G-REMiT token to the nodes one by one.

)'''()(,xjixji

jxi RRRRRRg

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Second Phase of G-REMiT

Step 1: node x sel ecti on

Step 2: node j sel ecti on

Step 3: tree path Expl ori ngj , i

Path_Expl ori ng(path_gai n)

. . .

i xkj

Udpate path_gai n i n msg

Step 4: Make jxiChange ,

J oi n_REQ(j )

J oi n_REP(j )

l eave(x)Nei ghbor I nfo Udpate

j , i

Nei ghbor I nfo Udpate

Nei ghbor I nfo UdpateStep 5: tree path Updati ng

and Nei ghbor Noti fi cati on

. . .

. . .. . .

Path Updati ng wi th jxiChange ,

Local broadcast to nei ghborsabout jx

iChange ,

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Performance Results

Normalized TPC when 50% nodes are multicast group nodes

2,10,1,)(*1.0 maxmax rKrKEelec

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Performance Results (Cont.)

Normalized TPC for a graph with 100 nodes

2,10,1,)(*1.0 maxmax rKrKEelec

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Conclusions

• Energy consumption metric for evaluating energy-efficiency of multicast protocol in WANET

• G-REMiT is a distributed algorithm to construct an energy-efficient multicast tree.

• G-REMiT Perform better than BIP/MIP Dist-BIP-G, and Dist-BIP-A algorithms for long range radios.

• All of the algorithms have similar performance for short range radios.

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Future Work

• Energy efficient multicast in mobile ad hoc network

• Multicast tree lifetime extension

• Other schemes for energy efficient multicast of short range radios– Directional antenna– Scheduling sleep mode among the nodes

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Reference[1] J.E. Wieselthier, G.D. Nguyen, and A. Ephremides. On the construction of energy-efficient broadcast and multicast tree in wireless networks. In Proceedings of the IEEE INFOCOM 2000, pages 585–594, Tel Aviv, ISRAEL, March 2000.[2] J. E. Wieselthier, G. D. Nguyen, and A. Ephremides, Distributed algorithms for energy-efficient broadcasting in ad hoc networks, Proceedings of MilCom, Anaheim, CA, Oct. 2002.[3] M. Cagalj, J.P. Hubaux, and C. Enz. Minimum-energy broadcast in All-wireless networks: NP-completeness and distribution issues. In Proceedings of ACM MobiCom 2002, pages 172 – 182, Atlanta, Georgia, September 2002.[4] F. Li and I. Nikolaidis. On minimum-energy broadcasting in all-wireless networks. In Proceedings of the 26th Annual IEEE Conference on Local Computer Networks (LCN 2001), pages 193–202, Tampa, Florida, November 2001.[5] R.G. Gallager, P. A. Humblet, and P. M. Spira. A distributed algorithm for minimum weight spanning trees. ACM Transactions on Programming Languages and Systems, 5(1):66–77, January 1983.[6] L. M. Feeney and M. Nilsson. Investigating the energy consumption of a wireless network interface in an ad hoc networking environment. In Proceedings of IEEE INFOCOM, Anchorage, pages 1548 –1557, AK, April 2001.