COSC 5341 High-Performance Computer Networks

Presentationfor

By Linghai ZhangID:205715354

Sanjiv Kapoor, Srivatsan RaghavanGlobal Telecommunications conference, 2000, G

LOBECOM’00

Improved Multicast Routing with Delay and

Delay Variation Constrains

Outline

Graph ModelProblem descriptionProposed algorithmAnalysis of the algorithmPerformance evaluationConclusion

Graph ModelDirected Graph G(V,E) V: the entire set of nodes in

the multicast.E: the set of edges in the

graph.Delay Function D and Cost

Function C: E -> R+Source Node: sDestination Node Set:

sVzzS k ,1

Example of the graph

V={s,a,b,c,d,e,f}

E={(s,a),(s,b),(c,a),(b,c),(b,f),(c,d),(c,e)}

S={a,c,d,f}

The red number stands for the delay of the edge and the green number represents the cost.

7,5 [s]

(c)

b

(d)

(f)

e

1,3 6,2

2,2

4,6

4,2

3,1

(a)

Problem Description

Given a delay bound Δ, a variation bound δ, find a multicast tree T such that:

and

Then try to minimize the total cost

SzlD izsPl i

,

jijizsPlzsPl

zzSzzlDlDji

,,,,,

SzzsPlC iizsP

Sizi

,,,

Example of a Multicast Tree

[s] (c)

b

(d)

(f)

1,3

2,2

4,6

4,2

3,1

(a)

The delay of longest path is equal to 10 and the delay variation between different destinations is less than 9 while the total cost of the tree is 14.

The proposed algorithm 1

Find a multicast tree satisfied above requirement is proved to be a NP-Complete problem. The proposed algorithm is a heuristic algorithm.

Let the minimum cost path from s to j with delay exactly equal to t. The following recurrence is used.

tg j

The proposed algorithm 1(Cont’d)

Analysis of the algorithm 1

The algorithm correctly generates minimum cost paths to the multicast nodes if they exist within the delay bound Δand variation bound δ. The overall time complexity is

And examples show that the algorithm can finds paths with variation bounds which are not found by DVMA (Delay Variation Bounded Multicast Algorithm) as well as cases where the overall cost of the paths is less than that found by DVMA.

SEO

The proposed algorithm 2

Analysis of the algorithm 2

Approximation schemes

Approximation Schemes (Cont’d)

Performance Evaluation

The figure show that we can find paths with variances an order of magnitude lower than that founded by DVMA

Performance Evaluation (Cont’d)

The execution times of both the approaches were also much less as compared to that of the DVMA algorithm.

Performance Evaluation (Cont’d)

DPDVB gives competitive results in terms of the cost of the paths compared to DVMA whereas DPDVBC expectedly does much better.

Performance Evaluation (Cont’d)

Performance Evaluation (Cont’d)

Conclusion

This paper focused on the problem of Multicast Routing with delay boundedness and delay variation boundedness as constraints.

A routing protocol is proposed and compared with previous schemes DVMA. The results show that the scheme proposed improves over the DVMA in the variation bounds achieved and is comparatively far more efficient.

any QUESTIONS?

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