Multicast in Wireless Mesh Network

transcript

Xuan (William) Zhang

Xun Shi

2006/11/07 2

Outline

Introduction to multicast in WMNs Defining the cost of multicast tree Ruiz’s MNT protocol Chou’s MDM protocol Conclusion

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Outline

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What is Multicast?

“Point-to-multipoint" or "multipoint-to-multipoint“

Different from broadcast and unicast

(a) Broadcast (b) Multicast (c) Unicast

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Advantages of Multicast

Delivery to destinations simultaneously Deliver the messages over each link of the

network only once Only create copies when the links to the

destinations split

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Wireless Mesh Networks

Mesh routers are generally stationary Multi-hop forwarding High speed Reliable power supply

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Internet multicast protocols

Feature Wired / Powerful / Reliable Maintain a large and fixed topology

Shortest path algorithms simpler to implement simpler to support frequent joins/leaves lowest delay

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Drawbacks of Internet multicast in WMNs Routing metrics do not aim at minimizing the

cost of multicast tree Not using broadcast nature

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MANET multicast protocols

Feature Maintaining a smaller and mobility network

topology Relying on flooding mechanism

On-demand routing protocols Suitable for mobility Low power consumption

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Drawbacks of MANET multicast in WMNs Complexity of computation

High mobility High Power consumption

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Multicast protocols in WMNs

WMNs multicast is between Internet and MANET multicast Fixed topology Broadcast nature Mobility and power are not problems

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Outline

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Traditional definition of cost

Measured by hops, delays, etc. Minimum Steiner tree problem

NP-complete Heuristic algorithms – polynomial time

Shortest path tree Sub-optimal shared tree MST algorithm: 2*optimal approximation Zelikovsky algorithm: 11/6*optimal approximation

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Define the cost in WMNs

Cost: number of transmissions Minimize the number of transmissions Maximize the forwarding nodes which are shared

by sender-receiver paths

This problem is NP-complete

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Problem with Steiner Tree

Steiner Tree: minimum edge cost Broadcast: node can send neighbors data in one

transmission

Our goal: minimizing the number of transmissions!!

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Outline

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Ruiz’s Algorithm

Purpose: find minimal data overhead tree Contributions:

Theorem 1: Prove Steiner tree is not optimal in WMNs with respect to the number of transmissions

Theorem 2: Prove minimal data overhead tree is NP-Complete

Proposed heuristics to compute trees with minimizing the number of transmissions

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Problem statement

Define t is multicast delivery tree Define Ct(t) is the number of transmissions

required to deliver a message from sender s to receiver set R

Problem statement: Minimize the Ct(t) Ct(t)=1+|Ft| Minimize the number of forwarding nodes

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Theorem 1: Steiner tree not minimal Steiner multicast tree (minimal edge cost) is

not the minimal data-overhead multicast tree. Proof by example:

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Theorem 2: NP-Complete

Proof by including a particular case Special case: R=V-{s}, find the smallest

forwarding nodes covers the rest of nodes in V-{s}

Vertex cover problem – NP-complete

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Heuristic Algorithm

Goal: approximate minimal data overhead multicast tree Reduce the number of forwarding nodes While increase the number of leaf nodes

Centralized greedy-based heuristic algorithm Distributed heuristic algorithm

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Greedy minimal data overhead Alg. Centralized WMNs Greedily build cost-effective sub-trees

A node v is selected a forwarding node only if it covers two or more nodes

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Greedy minimal data overhead Alg. cont.

Steps Construct a cost-

efficient sub-trees Build a Steiner

tree among the roots of the sub-trees

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Initialize

V=V-{s}

aux=R-Con(s)+{s}

Alg Demo

MF (multicast forward node list)

M1, R1, R2, R3, R4, R5, R6

V (unvisited nodes)

aux (nodes to cover list)

M2, M3, M1, R1, R2, R3, R4, R5, R6M2

S, R5, R6, M2

R4R5 M2M1

S, M2, M3

M2, M3

MF=MF+{v}

aux=aux-Cov(v)+{v}

M3, M1, R1, R2, R3, R4, R5, R6

S, R2, R3, R4, R5, R6,

R4R5 M2M1

Stop!! All nodes in V now only cover at most 1 receiver

R4R5 M2M1

MST heuristics to build Steiner tree

R4R5 M2M1

minimal data overhead tree!Hehe!!

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Performance Evaluation

Compared Algs SPT: source path tree Alg MST: Steiner tree Alg MNT: centralized proposed Alg MNT2: distributed proposed Alg

Simulations Number of Tx required Mean number of hops Number of Tx with density

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Performance Evaluation cont. Number of transmissions required

The total number of packets transmitted either by the source or any relay node in path.

MNT, MNT2

Theorem 2, Steiner tree is not minimum data-overhead.Do not aim at minimize the cost of the tree.

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Performance Evaluation cont. Mean path length (Mean number of hops)

The number of multicast hopsfrom a receiver to the source averaged over the totalnumber of receivers.

MNT, MNT2MSTSPT

Aim at minimize the length of the tree.

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Performance Evaluation cont. Number of transmissions with density

Examine reduction of Tx numbers when increase the density.

Proposed heuristic MNT, MNT2 reduced more than SPT and MST!

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Summary of Ruiz’s Algorithm

Steiner tree does not suitable in WMNs The proposed Algorithm is NP-complete Heuristic Algorithm

Centralized Algorithm Distributed Algorithm

Evaluation the higher the density, the higher are the Heuristic

Alg performance

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Outline

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Resilient Forwarding Mesh

Makes multicast robust to node or link failure 2 paths Increases PDR and throughput

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Resilient Forwarding Mesh Example

(a) Network topology (b) Optimal solution (c) Suboptimal solution

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Node-Disjoint Paths

Parallel routes that connect the source and the destination

Do not have any node in common except the source and destination

Deliver packets simultaneously

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Optimal Resilient Forwarding Mesh Each source-destination pair is connected by

two node-disjoint paths Total number of broadcast transmissions is

minimized Minimizing the number of broadcast

transmissions is NP-complete Use heuristic algorithms to obtain

approximate solutions

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Heuristic Approximation Algorithms Tree-based

Node-Disjoint Tree Algorithm (NDT) Revised Node-Disjoint Tree Algorithm (RNDT)

Path-based Shared Disjoint Mesh Algorithm (SDM) Minimal Disjoint Mesh Algorithm (MDM)

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Node-Disjoint Tree Algorithm (NDT) Build a multicast tree PT with minimal number

of transmissions using the MNT Remove all intermediate nodes of PT from

node set V Find a new minimal multicast tree BT in the

new V Add all intermediate nodes of PT and BT to

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NDT ExampleS

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NDT ExampleS

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Shared Disjoint Mesh Algorithm Find a shortest path P Remove all intermediate nodes of P from V,

and find another shortest path B which is node-disjoint to P

Update out-flow links of all intermediate nodes to zero

Add all intermediate nodes of PT and BT to RFM

Repeat above steps for all receivers

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SDM ExampleS

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Minimal Disjoint Mesh Algorithm Improves SDM in the way of building the nod

e-disjoint path pair Use Suurballe’s algorithm to find node-disjoin

t path pair with minimal cost at the same time

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Suurballe’s Algorithm Example S

M1 M3M2

10 1 100

M1 M3M2

10 1 100

Cost = 3 + 101 Cost = 11 + 12

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Comparison of the 4 Protocols Simulated in QualNet Manually calculate optimal solution up to

session size of 10 Performance is measured by the number of

transmissions as a function of multicast session size

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Performance Comparison

NDTRNDTSDMMDM

Multicast Session Size

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Summary

NDT and RNDT are tree-based heuristic algorithms

SDM and MDM are mesh-based heuristic algorithms

MDM used Suurballe’s algorithm to find node-disjoint path pair with minimal cost

Total Number of transmissions: MDM<SDM<RNDT<NDT

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Compare MNT with MDM

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Compare MNT with MDM cont. MDM needs additional transmissions to

provide resilience MDM needs more transmissions when

session size is small When session size increases, the MDM is

more likely to find the disjoint paths that share more common intermediate nodes

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Outline

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Lecture Summary

Ruiz’s The MNT is NP-complete Heuristic Algorithm

Centralized Algorithm Distributed Algorithm

Chou’s Tree-based: NDT and RNDT Path-based: SDM and MDM Total number of transmissions:

MDM<SDM<RNDT<NDT

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References

Heuristic algorithms for minimum bandwidth consumption multicast routing in wireless mesh networks, P. M. Ruiz, and A. F. Gomez-Skarmeta, Proceedings of ADHOC-NOW, 2005.

Protecting Multicast Sessions in Wireless Mesh Networks, X. Zhou, J. Guo, C.T. Chou, and S. Jha, IEEE Conference on Local Computer Networks, 2006.

Simulation Study of Diverse Routing and Protection Algorithm in Mesh WDM Network, X. Yao, and C. Chen, 2004.

A Performance Comparison Study of Ad Hoc Wireless Multicast Protocols, S.J. Lee, W. Su, J. Hsu, M. Gerla, and R. Bagrodia, Proceedings of IEEE INFOCOM, 2000.

A Fast Algorithm for Steiner Trees, L. Kou, G. Markowsky, and L. Berman, Acta Informatica, No. 15, vol. 2, 1981, pp.141-145.

Multicast in Wireless Mesh Network

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