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![Page 1: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/1.jpg)
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
![Page 2: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/2.jpg)
S. K. S. Gupta, Arizona State Univ
Outline• Multicasting in Wireless Network• Node Metric• Problem Statement• Current State of Art• L-REMiT Algorithm• Performance Results• Conclusions
![Page 3: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/3.jpg)
S. K. S. Gupta, Arizona State Univ
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
![Page 4: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/4.jpg)
S. K. S. Gupta, Arizona State Univ
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{
![Page 5: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/5.jpg)
S. K. S. Gupta, Arizona State Univ
• 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?
![Page 6: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/6.jpg)
S. K. S. Gupta, Arizona State Univ
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
![Page 7: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/7.jpg)
S. K. S. Gupta, Arizona State Univ
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”
![Page 8: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/8.jpg)
S. K. S. Gupta, Arizona State Univ
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
![Page 9: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/9.jpg)
S. K. S. Gupta, Arizona State Univ
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
node. source theis 1 Node
3,23,12,1 pckJouleEpckJouleEpckJouleEJoule
![Page 10: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/10.jpg)
S. K. S. Gupta, Arizona State Univ
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
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S. K. S. Gupta, Arizona State Univ
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
![Page 12: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/12.jpg)
S. K. S. Gupta, Arizona State Univ
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
![Page 13: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/13.jpg)
S. K. S. Gupta, Arizona State Univ
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
![Page 14: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/14.jpg)
S. K. S. Gupta, Arizona State Univ
Challenges to Distributed Tree Construction?
• NP-complete problem [Li, LCN2001], [Singh, PIMRC99], heuristic algorithm is needed
• How to distribute the computation?
![Page 15: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/15.jpg)
S. K. S. Gupta, Arizona State Univ
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 ,
![Page 16: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/16.jpg)
S. K. S. Gupta, Arizona State Univ
Refinement Criterionjx
ijx
i Changeg ,, by gain lifetime theis
i
x
j
),()},'(),,'(),,'(min{, xTLTxTLTjTLTiTLTg jxi
}max{arg where, node Findneighbor si'
,
k
kxigjj
![Page 17: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/17.jpg)
S. K. S. Gupta, Arizona State Univ
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
![Page 18: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/18.jpg)
S. K. S. Gupta, Arizona State Univ
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.
![Page 19: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/19.jpg)
S. K. S. Gupta, Arizona State Univ
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
![Page 20: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/20.jpg)
S. K. S. Gupta, Arizona State Univ
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
![Page 21: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/21.jpg)
S. K. S. Gupta, Arizona State Univ
Example of BIP/MIP Algorithm
.0 and 0,/5 ,/8 ,/5.100(t)R,80(t)R,80(t)R ,100(0)R Assume
node. source theis 1 Node
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
![Page 22: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/22.jpg)
S. K. S. Gupta, Arizona State Univ
Related Work: Refinement– Refine a minimum spanning tree (MST) to
conserve energy consumption• EWMA, Dist-EWMA[Cagalij, Mobicom2002]
i
j
k
![Page 23: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/23.jpg)
S. K. S. Gupta, Arizona State Univ
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
![Page 24: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/24.jpg)
S. K. S. Gupta, Arizona State Univ
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)
,0,1,10,2when Lifetime, normalized ofMean max elecEKr
![Page 25: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/25.jpg)
S. K. S. Gupta, Arizona State Univ
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)
,0,1,10,2when Lifetime, normalized ofMean max elecEKr
![Page 26: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/26.jpg)
S. K. S. Gupta, Arizona State Univ
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)
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S. K. S. Gupta, Arizona State Univ
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.
![Page 28: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070605/5a4d1ad57f8b9ab059972ddd/html5/thumbnails/28.jpg)
S. K. S. Gupta, Arizona State Univ
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
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S. K. S. Gupta, Arizona State Univ
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.