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

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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

Outline

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

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

Challenges

- Transmission Power determines
- The total amount of energy consumed on the link
- Feasible of the link
- Network topology

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)

Background and Current State of Art

Wireless Multicast Advantage

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

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]

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

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.

Wireless Communication Model- The minimum power needed for link between nodes i and j for a packet transmission is:

- For short range radio,

[Feeney Infocom2001]

So is not negligible

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

G-REMiT Algorithm

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

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

Example of Refinement at a node for minimizing energy consumption of the TreeR10 may be affected by , because

may be changed.

Tree’s Energy Consumption Oscillation Avoidance- Lemma 1 : Nodes that are on tree pathj,i are the only nodes in the multicast tree that may be affected by Changeix,j

Disconnection Refinement

- Lemma 2: If i is not on tree pathj,x the tree remains connected after Changeix,j

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.

Performance Results

Normalized TPC when 50% nodes are multicast group nodes

Performance Results (Cont.)

Normalized TPC for a graph with 100 nodes

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.

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

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.

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