S. K. S. Gupta, Arizona State Univ On Maximizing Lifetime of Multicast Trees in Wireless Ad hoc Networks Bin Wang and Sandeep K. S. Gupta Computer Science

S. K. S. Gupta, Arizona State Univ

On Maximizing Lifetime of Multicast Trees in Wireless Ad hoc

Networks

Bin Wang and Sandeep K. S. GuptaComputer Science and Engineering Department

Arizona State UniversityTempe, AZ, USA

{Bin.Wang,Sandeep.Gupta}@asu.edu


Outline• Multicasting in Wireless Network• Node Metric• Problem Statement• Current State of Art• L-REMiT Algorithm• Performance Results• Conclusions


Multicasting• Allow one entity to send messages to multiple

entities residing in a subset of the nodes in the network

• Why multi-destination delivery in a single message?– Transparency; Efficiency; Concurrency

• Applications – distributed database, distributed games,

teleconferencing


Why Multicasting is different in Wireless Networks?

• Wireless medium is broadcast medium (Wireless multicast Advantage)– One time local transmission can possibly reach

all the neighbors

i k

j

m pi ,mpi , j

pi , k

mikijimikijimkji ppppppp ,,,,,,),,( of instead },,,max{


• Power control allows a node to determine who are its neighbors.

• More power used – more interference– Reduces # simultaneous transmissions (thrput)– Consumes energy at a faster rate

node can die faster leading to disconnections.

Why Multicasting is different in wireless network?


Why Not Single-Hop Multicast?

• Single source multicast: reach a subset of nodes from a given source s– s increases its transmission range to such an

extent that it can reach all the group members• Increased interference and power wastage• source may have limited transmission range


Multi-hop Approach• Multi-hop Solution Problem of

constructing multicast tree1. What is a link?

• Depends on power level• Using maximum transmission power results in too

many links 2. link weight? 1. & 2. Link-based view not appropriate!– Node-based view: construct tree with

“minimum/maximum summation of node cost”


Node Cost?• Depends upon the optimization goals:

–Minimizing total energy consumption [Gupta, Globcom2003]

1

23

./8 ,/10 ,/6 And.002 are 3 and 1,2 nodeat energy battery Remaing Assume

node. source theis 1 Node

3,23,12,1 pckJouleEpckJouleEpckJouleEJoule

packets2010200 tree theof Lifetime

Joule/pck 10 Tree theofCost Energy


Lifetime Node Cost

– Maximizing multicast tree’s lifetime (#packets transmitted before the first node dies)

packets258

200 tree theof Lifetime

Joule/pck 14 86 Tree theofCost Energy

1

23

./8 ,/10 ,/6 And.002 are 3 and 1,2 nodeat energy battery Remaing Assume


3,23,12,1 pckJouleEpckJouleEpckJouleEJoule


Node’s Multicast Lifetime Metric Node i’s multicast lifetime: maximum number of

multicast packets that may be forwarded by the node i:

• T: source-based multicast tree• Ri : remaining battery energy of node i, • E(T,i): forwarding energy cost of node i

,),(

),(iTE

RiTLT i


Node’s Forwarding Energy Cost

node. source not thebut noode, leaf a is i if

node; source or the leaf aneither is i if

;node source theis i if

i)(T,

recv

recvielec

ielec

EEKdE

KdE

E

• Energy consumed (per bit) at node i in a Source-based Tree T

where and are energy cost (per bit) of transmission processing and reception processing, is length of the link between node i and i’s farthest children. is propagation loss exponent, K is a constant dependent upon the antenna.

elecEid

recvE


Lifetime of Multicast Tree• The lifetime of a multicast tree T is the minimum lifetime of

any node in T:

• The maximum lifetime multicast tree T* is:

where TG is the set of all possible multicast trees for the multicast group G in a given graph o.

• Maximizing multicast tree lifetime maximizing the lifetime of tree’s bottleneck node

),()},({min)( bottleneckTLTiTLTTLTTi

}),(

min{maxarg)}({maxarg*

iTERTLTT i

TiTTTT GG


REMiT Approach

• Refinement-based- (Take an initial solution and make it better) ?– Needed anyways because of dynamic changes

in the network• Battery level• interference

• Distributed?– Sensor networks may have millions of nodes– High overhead to obtain global knowledge


Challenges to Distributed Tree Construction?

• NP-complete problem [Li, LCN2001], [Singh, PIMRC99], heuristic algorithm is needed

• How to distribute the computation?


Refinement Operation: Change• Increase the lifetime of the multicast tree by moving

the farthest child (say node i) of bottleneck node x to another node (say node j)

(Tree T) (Tree T' )

x

ji

x

ji

jxiChange ,


Refinement Criterionjx

ijx

i Changeg ,, by gain lifetime theis

i

x

j

),()},'(),,'(),,'(min{, xTLTxTLTjTLTiTLTg jxi

}max{arg where, node Findneighbor si'

,

k

kxigjj


Oscillation & Disconnection Avoidance

• Lemma 1: Nodes j and x are the only nodes in the multicast tree whose multicast lifetime may be affected by Changei

x,j

• Lemma 2: If j is not in the sub-tree of i, then the tree remains connected after Changei

x,j. x

j

i


L-REMiT Algorithm• Two phases

– First Phase: Build a MST [Gallager, TPLS1983].– Second Phase:

1. Bottleneck node election, say node x.2. Identify the farthest child of node x, say node i.3. Select the new parent for node i with the highest lifetime

gain, say node j. If the highest lifetime is not positive, go to step 5.

4. Node i changes its parent from x to j, then go to Step 1.5. Terminate L-REMiT algorithm.


Example of L-REMiT Algorithm

1

23

4Initial MST

3

1) Bottleneck node election: node 2 2) Farthest child of node 2 is node 4.3) Moving 4 to node 3 results in the the highest

positive lifetime gain.4) Node 4 changes its parent from node 2 to 3.5) New bottleneck node election. Node 1 6) Farthest child of node 1 is node 3.7) Moving 3 to node 2 results in the highest

lifetime gain, however, gain is negative. 8) Terminate

1

2

4

L-REMiT Tree


Related Work: BIP/MIP

– BIP/MIP [Wieselthier, CN2002]); Dist-BIP-A, Dist-BIP-G [Wieselthier, Milcom2002]. The node metric is :

Limitations:• Even =1, Ci is not node i’s lifetime metric. • As increases, it will choose those nodes with higher remaining

battery level as the relay nodes, 0<<2.

,))()0((

tRREC

i

iii

energy.battery initial theis (0) andfactor weighting theis where

iR


Example of BIP/MIP Algorithm

.0 and 0,/5 ,/8 ,/5.100(t)R,80(t)R,80(t)R ,100(0)R Assume


3,23,12,1

321i

recvelec EEpckJouleEpckJouleEpckJouleEJouleJouleJouleJoule

1 MIP/BIP

1

23

treeMulticast Lifetime Maximum

1

23

packets108

80 tree theof Lifetime packets165

80 tree theof Lifetime


Related Work: Refinement– Refine a minimum spanning tree (MST) to

conserve energy consumption• EWMA, Dist-EWMA[Cagalij, Mobicom2002]

i

j

k


Performance Results

nodes. groupmulticast are nodes 100% and 0recvE

0.50.550.60.650.70.750.80.850.90.951

10 40 70 100number of nodes in graph

EWMA-DistMSTL-REMiTMIP(β=0)MIP(β=1)

,0,1,10,2when Lifetime, normalized ofMean max elecEKr


Performance Results

nodes. groupmulticast are nodes 50% and 0recvE

0.550.60.650.70.750.80.850.90.951

10 40 70 100number of nodes in graph

EWMA-DistMSTL-REMiTMIP(β=0)MIP(β=1)



Performance Results

nodes. groupmulticast are nodes 50% and )(1.0 maxKrErecv

0.60.650.70.750.80.850.90.951

10 40 70 100

number of nodes in graph

EWMA-Dist

MST

L-REMiT

MIP(β=0)

MIP(β=1)



Performance Results),(4,1,10,2when Lifetime, normalized ofMean maxmax

KrEKr elec

nodes. groupmulticast are nodes 100% and )(3.0 maxKrErecv

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10 40 70 100

number of nodes in graph

EWMA-Dist

MST

L-REMiT

MIP(β=0)

MIP(β=1)


Conclusions

• L-REMiT is a distributed algorithm to extend the lifetime of source-based multicast tree.

• L-REMiT performs better than BIP/MIP, L-MIP, EWMA-Dist algorithms.


Future Work

• Lifetime extension for group-shared multicast trees

• Other schemes for maximizing lifetime of multicast tree– Directional antenna– Scheduling sleep mode among the nodes


Reference[1] J. E. Wieselthier, G. D. Nguyen, and A. Ephremides, Resource management inenergy-limited, bandwidth-limited, transceiver-limited wireless networks for session-based multicasting. Computer Networks, 39(2):113–131, 2002.[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] B. Wang and S. K. S. Gupta. S-REMiT: An algorithm for enhancing energy-efficiency of multicast trees in wireless ad hoc networks. In Proceedings of IEEE GlobleCOM, San Francisco, CA, Dec. 2003.[7] S. Singh, C. S. Raghavendra and J. Stepanek. Power-Aware Broadcasting in Mobile Ad Hoc Networks. In Proceedings of PIMRC, pages 22 – 31, Osaka, Japan, September, 1999.

Documents

S. K. S. Gupta, Arizona State Univ On Maximizing Lifetime of Multicast Trees in Wireless Ad hoc Networks Bin Wang and Sandeep K. S. Gupta Computer Science