QOS MULTICAST ROUTING DESIGN USING NEURAL

NETWORK

Ming Huang and Shang Ming Zhu

Department of Computer Science, East China University of Science and Technology, 200237 ShangHai, China

Keywords: Quality of service, Hopfield neural network, Multicast routing.

Abstract: In this paper, an algorithm based on Hopfield neural network for solving the problem of determining

minimum cost paths to multiple destination nodes satisfying QoS requirements is proposed. The schema of

constructing the multicast tree with HNN is emphasized after the analysis of the attributes of the multicast

tree. At last, the emulation explores the feasibility of this algorithm.

1 INTRODUCTION

With the rapid emergency of the multimedia

applications on networks, especially for video

conferences, the need for multicast QoS routing

mechanism to satisfy the multimedia transmission

requirements among conference participants is

urgently rising.

Wang and Crowcroft have proved QoS routing

with multi-constraint to be a NP-complete problem

(Wang et al., 1996). Neural networks have often

been formulated to solve NP-complete optimization

problems. Tank and Hopfield (Tank et al., 1986)

proposed the first neural approach applied in the

TSP problem. The advantage of the Hopfield NN is

the rapid computational capablility of solving the

combinatorial optimization problem. Ahn and

Ramakrishna (Ahn et al., 2001) proposed a near-

optimal routing algorithm employing a modified

Hopfield NN. In this paper, a new Hopfield NN

model is proposed to speed up the convergence

whilst improving the optimality of the multicast tree

constructed under multi-constraint

2 PROBLEM FORMULATION

As far as multicast routing is concerned, a network

is usually represented as a weighted directed graph

G=(V, E), where V, the set of vertexes, denotes the

set of nodes, and E, the set of directed edges,

corresponds to the set of links connecting the nodes.

Suppose the number of nodes is n, refer to the ith

node as i for short, then the adjacency matrix O

describing the initial state of the focused network

can be defined as: O

ij

=1, if the link from i to j exists;

elsewise, O

ij

=0.

We also appoint a node s

∈

V to denote the

source node of a multicast request. The source node

acts as the root of the multicast tree to be build

which has only out-degree. Correspondingly, let

d={d

1

,…,d

m

} ⊂ (V-{s}) denotes the set of the

destination nodes with only in-degree. Then the

constructed multicast tree, denoted by T and shown

in Fig.1, should satisfy:

1) T is a subgraph of G;

2) The equal undirected graph T’ is a tree;

3) s is the root of T’;

4) d

∈

T and every leaf of T’ is in d;

5) Every vertex in T except s can be accessed

from s.

Figure 1: Indicating diagram of multicast tree.

213

Huang M. and Ming Zhu S. (2008).

QOS MULTICAST ROUTING DESIGN USING NEURAL NETWORK.

In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - SPSMC, pages 213-216

DOI: 10.5220/0001476002130216

Copyright

c

SciTePress

Let the adjacency matrix A describing the

constructed subgraph G’ of G after multicast routing

is defined as: A

ij

=1, if the link from i to j is in G’;

elsewise, A

ij

=0. Then let’s prove the theorems

below:

Theorem 1. In a multicast tree T, there will be

one and only one path from s to v (v

∈

T and v≠s).

Proof: Existence. According to attribute 5) of T,

v can be accessed from s, so there is at least one path

from from s to d

i

(i=1,…,m);

Uniqueness. If there are two different paths from

s to v in T, then there will be at least two dis-

coincident sectors composed of directed edges in the

two paths. Combined with the joint vertexes, the two

sectors form a circle in the equal undirected graph of

T. Refer to attribute 2) of multicast tree, the

existence of the circle contradict the acyclic attribute

of a tree. So there is only one path from s to v in T;

Theorem 2. Supposing

s, d

∈

G’ and the in-

degree of s is 0, G’ is a multicast tree T if and only

if:

()

1

1

=

⎟

⎠

⎞

⎜

⎝

⎛

∑

=

sj

n

k

k

A

, where j

∈

G’ and j≠s

(1)

()

01

2

'

2

1

=

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

−

∏

∑∑

∈

∈=

d

AA

d

Gj

dj

id

n

k

k

,

where i

∉

d or

0

'

>

∑

∈Gj

ij

A

(2)

Proof: Necessity. Based on the accessible theory

in graph theory, Eq.1 denotes the number of paths

from s to j within a length of k. Refer to Theorem 1,

Eq.1 is obviously tenable. If I

∈

T, then i must

locate at a branch of T except i is a leaf destination

node itself. Suppose the branch ends at a leaf θ.

According to Theorem 1, there is one and only one

path from s to θ and i is in the path. Due to attribute

4 of multicast tree, θ

∈

d, therefore Eq.2 is got.

Sufficiency. Obviously, attribute 1 of multicast

tree is qualified. Because of Eq.1, attributes 5 is

qualified. Considering the in-degree of s is 0, G’ is a

tree with s as the root, i.e. attributes 2 and 3 is

qualified. When Eq.2 is satisfied, for I

∈

G’, except

i is a leaf destination node itself , there will be at

least one leaf θ

∈

d which can be accessed from i by

one and only one path. So attribute 4 is qualified.

Therefore, G’ is a multicast tree.

3 NEURAL NETWORK MODEL

The Hopfield NN model for multicast QoS routing,

which consists of

nn

×

neurons connected with

each other, is mapped from the corresponding

directed graph G of the aimed network system with

n nodes.

ij

V

ij

V

ij

V

ij

ijij

V

E

U

dt

dU

∂

∂

−−=

τ

Figure 2: Model of Hopfield neural network.

The output of the neuron at the position (i,j) is

denoted by V

ij

, where V

ij

=1, if the link from i to j

exists; otherwise, V

ij

=0. Obviously, the output

matrix V=[V

ij

]

n×n

is equal to the adjacency matrix A

of G. Let U

ij

denotes the input of neuron (i,j), and

define the gain function g of the neuron as:

()

1

1

=

⎟

⎠

⎞

⎜

⎝

⎛

∑

=

sj

n

k

k

A

, where j

∈

G’ and j≠s

(3)

ij

ijij

V

E

U

dt

dU

∂

∂

−−=

τ

(4)

Define several link state matrix as: W=[W

ij

]

n×n

,

B=[B

ij

]

n×n

, D=[D

ij

]

n×n

and L=[L

ij

]

n×n

, where W

ij

is the

cost of the link from i to j, B

ij

is the bandwidth of the

link from i to j, D

ij

is the delay of the link from i to j

and L

ij

is the parcket loss rate of the link from i to j.

The QoS constraints is denoted with B

w

, D

w

and L

w

where B

w

is the minimal available bandwidth of each

selected link, D

w

is the maximal available delay of

each selected path and L

w

is the maximal available

packet loss rate of each selected path.

As shown in Fig.2, the dynamic Eq.4 governs

the dynamics of the network. The design of the

energy function should reflect the attributes of the

selected multi-path below:

1) There is no non-existing link in the selected

multi-path;

2) There is no input to the source node in the

selected multi-path;

ICINCO 2008 - International Conference on Informatics in Control, Automation and Robotics

214

3) All destination nodes is in the selected multi-

path;

4) According to Theorem 2, the two equations

should be satisfied;

5) Satisfy the QoS constraints.

6) The total cost of the selected multi-path must

be as low as possible;

To fit the constraints above, we design the

suitable energy function as:

665544

332211

EEE

EEEE

μμμ

μ

μ

μ

+++

++=

(5)

()()

2

11

1

1

∑∑

==

−=

n

i

n

j

ijijij

VOVE

(6)

()

∑

=

=

n

i

is

VE

1

2

2

(7)

()

∑∑

∈=

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−

⎟

⎠

⎞

⎜

⎝

⎛

=

d

V

d

sd

n

k

k

E

2

1

3

1

(8)

()

()

⎟

⎟

⎟

⎠

⎞

⎟

⎟

⎠

⎞

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎜

⎜

⎜

⎝

⎛

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

−

+

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−

⎟

⎠

⎞

⎜

⎝

⎛

=

∑

∑

∏

∑

∑∑

∈

>

∑

∉

≠

∈

∈

=

≠

∈=

∈

2

0or

'

2

1

'

2

1

4

1

1

Vj

dj

i

si

Gi

d

id

n

k

k

sj

Gj

sj

n

k

k

Vj

ij

E

V

V

V

Ad

d

(9)

()

(

)

3215

zHzHzE ++=

(10)

() () ()

⎩

⎨

⎧

>

==

∫

e, otherwis

z, if z

zhdzzhzH

z

0

0

,

0

(11)

()

∑∑

=

≠

=

−=

n

i

n

ij

j

wijij

BVBHz

11

1

(12)

∑∑ ∑

=

≠

==

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

−=

n

i

n

ij

j

n

k

jkijijw

VDVmDHz

11 1

2

(13)

()

())

w

n

i

n

ij

j

n

k

jkijij

Lm

VLVHz

−−

⎜

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

−=

∑∑ ∑

=

≠

==

1

1

11 1

3

(14)

()

∑∑

=

≠

=

=

n

i

n

ij

j

ijij

VWE

11

2

6

(15)

Obviously, E

1

, E

2

and E

3

refer to constraints 1, 2

and 3 respectively. According to Theorem 2, when

E

4

get minimal (i.e. zero), the constraint 4 is

attained. E

5

represents the integration of QoS

constraints on bandwidth, delay and loss rate. As z

1

,

z

2

and z

3

represents the deviation of the QoS

constraints and the minus value is meaningless, so

we filter the minus value with an integral

computation in E

5

. With z

1

, z

2

and z

3

, conditions of

links near root will influence the deviation more

severely.

4 EMULATION

Fig.3 shows the topology of the delegating network

system. The source node which promotes the routing

request and four destination nodes have already been

signed out in the graph. Each link in the network is

labeled with a link status vector consists of cost W,

bandwidth B(MB), delay D(ms) and loss rate L. The

QoS constraints are: B

w

=2MB, D

w

=8ms, L

w

=10

-3

.

In this case, we set coefficient μ

1

=80000, μ

2

=40000, μ

3

=160000, μ

4

=500, μ

5

=400, μ

6

=400,

λ=1, and Δt = 2×10

-8

. By emulation, we could obtain

the global optimal solution shown in Fig.3.

5 CONCLUSIONS

In this paper, we propose a new multicast tree

selection algorithm to simultaneously optimize

multiple QoS parameters which is based on Hopfield

neural network. The result of emulation shows that

the utilization of Hopfield neural network is an

available method to solve QoS routing problems.

Furthermore, by the massive parallel computation of

neural network, it can find near optimal route

quickly, so the real-time requirement of routing in

high-speed network system could be satisfied.

Figure 3: Topology of network system with parameters

and selected multi-path.

QOS MULTICAST ROUTING DESIGN USING NEURAL NETWORK

215

REFERENCES

Wang Z, Crowcroft J, 1996. Quality of service for

supporting multimedia applications. 14th. IEEE JSAC.

Tank, D.W., Hopfield, J.J, 1986. Simple neural

optimization networks: an A/D converter, signal

decision network, and a linear programming circuit.

33th. IEEE Transactions on Circuits and Systems.

Ahn, C.W., Ramakrishna, R.S., Kang, C.G., Choi, I.C.,

2001. Shortest Path Routing Algorithm Using Hopfield

Neural Network. 37th. Electronics Letters.

B.M. Waxman, 1988. Routing of multipoint connections.

Vol.9. IEEE TSAC.

S.Chen, K.Nahrstedt, Y.Shavitt, 2000. A QoS-aware

multicast routing protocol. Vol.18. IEEE Journal on

Selected Areas in Communications.

Q.Sun, 1999. A genetic algorithm for delay-constrained

minimumcost multicasting. Technical Report. IBR. TU

Braunschweig. Braunschweig. Germany.

ICINCO 2008 - International Conference on Informatics in Control, Automation and Robotics

216