LIGHT TRAIL MINIMIZATION IN ALL-OPTICAL NETWORK USING ...

INADYUTI DUTT* et al. ISSN: 2250–3676

[IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-2, Issue-5, 1327 – 1337

IJESAT | Sep-Oct 2012

Available online @ http://www.ijesat.org 1327

LIGHT TRAIL MINIMIZATION IN ALL-OPTICAL NETWORK USING

CONNECTION MATRIX AND GENETIC ALGORITHM AND THEIR

COMPARISONS WITH THE ALGORITHM ADOPTED BY INTEGER

LINEAR PROGRAMMING

Inadyuti Dutt1, Soumya Paul

2

1Asst. Professor, Dept of Computer Application, B. P.Poddar Institute of Management & Technology, West Bengal

University of Technology BF-142, Salt Lake City, Sector-II, Kolkata, West Bengal-700052, India ,[email protected] 2Assoc. Professor, Dept of Computer Application, B. P.Poddar Institute of Management & Technology West Bengal

University of Technology, KolkatA, West Bengal-700052, India , [email protected]

Abstract Recently a new architecture called “light trail” has been proposed for carrying data traffic in optical networks and has emerged as a

promising candidate for enabling IP over WDM networks. Optimizing the number of light trails that must be setup to service

connection requests as they arrive is an important light trail design problem. Most of the existing light-trail assignment algorithms

adopt ILP (Integer Linear Programming) approach. Due to high complexity such algorithms are not scalable. In this paper, a

heuristic approach with Connection Matrix (CM) and Genetic Algorithm (GA) is proposed for reducing the number of light trails for

given a graph (network) and a number of connection requests, while using minimum network resources that need to be setup in a

survivable optical network. The results are also compared with light trail algorithm adopted by ILP.

Index Terms: Heuristic; Internet Protocol (IP); Wavelength Division Multiplexing (WDM), Lightpath; Light-trail;

Integer Linear Programming (ILP); Genetic Algorithm (GA).

----------------------------------------------------------------------***------------------------------------------------------------------------

1. INTRODUCTION

In an all-optical network (AON), all network-to-network

interfaces are based on optical transmission, all user-to-

network interfaces use optical transmission on the network side

of the interface and all switching and routing within AON

network nodes is performed optically. Optical networks are

high-capacity telecommunications networks based on optical

technologies and components that provide routing, grooming,

and restoration at the wavelength level as well as wavelength-

based services. In a wavelength routed optical network, data

transfer between clients requires setting up a unidirectional

lightpath (channel) in the optical layer. Such a channel allows

source-to-destination transfer optically throughout the course

of the lightpath. This requires that an appropriate path (route)

and a free wavelength on this path be determined such that this

lightpath connects the sending and receiving clients optically.

The process of lightpath determination may be repeated till

either a connection is established or all the options have been

exhausted. Normally it is required that the same wavelength be

allocated on all the fiber links in the lightpath. This is known as

the “wavelength continuity constraint”.

This lightpath approach does not yield good bandwidth usage

due to the burst nature of data traffic and the fact that most

users generate relatively lower bit rate traffic compared to the

bandwidth of the lightpath. A light trail is a unidirectional

optical bus between a convener node (i.e. light-trail head) and

an end node. It is implemented using a wavelength, and allows

the intermediate nodes to share the bandwidth by adding and

dropping traffic, provided that the total traffic load carried is

not more than the bandwidth of the wavelength. At each

intermediate node, this is achieved by splitting a percentage of

transponder. Meanwhile, the rest of the optical signals continue

to propagate along the light-trail. Thus a light trail is similar to

a lightpath, yet it is different in the sense that intermediate

nodes can also access the unidirectional connection for data

transfer, resulting in better source utilization.





One of the light trail design problem is to minimize the number

of light trails needed to serve a given number of connection

requests. The proposed heuristic finds a set of light-trails to

cover the given requests in survivable optical networks such

that the total number of light-trails required is minimized using

Genetic Algorithm, Integer Linear Programming.

2. SURVEY STUDY OF EXISTING ALGORITHMS

Ashwin Gumaste and Imrich Chlamtac [1] propose the concept

of light-trails to alleviate the problems in sustaining IP centric

communication at the optical layer. With the principle of

access to the all-optical path at any node, a light-trail offers to

provide full unidirectional optical connectivity, while avoiding

the need for dynamic, burst type, optical paths establishment.

For setting up light-trails as well as signaling purposes within

light-trails an out of band communication channel called

optical service channel (OSC) exists which is dropped and

processed at each node.

Michael T. Frederick, Nathan A. VanderHom and Arun K.

Somani [4] discuss the advantage of light-trail over MPLS

(Multiprotocol Level Switching), OBS (Optical Burst

Switching) and OPS (Optical Packet Switching) as solutions to

realizing an all-optical network. Proposed solutions for all-

optical networks such as MPLS and OBS monopolize a

wavelength throughout connection duration and do not take

advantage of switches that are already configured. An OPS is a

technology that is not mature and most likely will not be in the

near future. Light trail technology attempts to address the

shortcomings of these various technologies by allowing

intermediate connection nodes to also use the unidirectional

bus, as well as maximize the reuse of already configured

optical switches.

Ashwin Gumaste, Gabriel Kuper and Imrich Chlamtac [5] used

the concept of clustered light-trail (CLT). While ring networks,

due to the fact that their nodal degree is 2, can support only

linear light-trails, mesh networks, on the other hand can

support tree shaped light-trails which are called clustered light-

trails (CLT). A Clustered Light-trail is a tree rooted at a node

called the convener. The end nodes of the branches may be

distinct, and so the CLT can have multiple end nodes.

Wensheng He, Jing Fang, Arun K. Somani [6] focus on the

optimal design of survivable light trail optical network. Two

protection schemes, namely connection based protection and

link based protection, that can achieve 100% protection against

single link failure are proposed and compared. Connection

based protection scheme is more practical for light trail

architecture where the hop-length is limited due to power loss.

Jing Fang, Wensheng He, Arun K. Somani [7] present light-

trail architecture and its optimal design. A two-step approach

for solving the light trail design problem -the first step is called

traffic matrix preprocessing; it divides single longhop paths

into several shorter paths that satisfy the hop-length constraint.

In the second step, the light trail design problem is formulated

as an integer linear programming (ILP) optimization problem.

Bin Wu and Kwan L. Yeung [9] introduce an efficient heuristic

algorithm to solve static light-trail assignment problem. The

problem is solved based on three key factors. These factors

include the request discreteness, the shortest path length of

each request, and the flow volume. The importances of the

three factors are ranked in the same order as they are

mentioned. This algorithm also adopts a reference node

mechanism to address the request discreteness issues.

Weiyi Zhan, Guoliang Xue, Jian Tang, Krishanaiyan

Thulasiraman [10] considers the dynamic light-trail routing

problem where the connection request comes and leaves

dynamically. For each dynamically arriving connection request

a light-trail is found to carry it with the objective of consuming

a minimum number of free wavelengths. Protection issues in

light-trail routing in WDM networks with dynamic traffic also

has been considered.

Akhil Lodha, Ashwin Gumaste, Paresh Bafna and Nasir Ghani

[12] consider an optimization technique; the uncertain nature of

traffic is called stochastic optimization. Stochastic optimization

is based on a multi-stage model reducible to a two-stage model.

The stages involve computation of an optimal solution

followed by estimation and recourse taking future uncertainties

into consideration.

Arun K. Somani [11] discusses an important problem in optical

networks with wavelength-division multiplexing is that of

traffic grooming. Traffic grooming is a technique for

multiplexing different sub wavelength capacity traffic

requirements onto a single wavelength so that the wavelength

and hence the capacity requirements of the whole network are

minimized.

Dzmitry Kliazovich, Fabrizio Granelli, Hagen Woesner and

Imrich Chlamtac [16] present a novel solution of bidirectional

high speed communications for IP traffic transport over WDM

networks. Bidirectional light-trail (BDLT) is an organization of

two separate light-trails connecting a set of nodes in two

directions (downlink and uplink) allowing bidirectional

communication. Broadcasting and multicasting in BDLT

architecture is performed by simultaneous transmission in both

directions for any node of the light-trail.





3. PROPOSED HEURISTIC IN SURVIVABLE

OPTICAL NETWORK

3.1 Problem Definition

Given a graph (network) and a number of connection requests,

the problem is to find a set of light-trails to cover the given

requests, such that the total number of light-trails required is

minimized. Additionally the blocking problem of the network

has been considered. Number of blocked links or connections

has been reduced with minimized light-trails and the

percentage of reduction of blocking is calculated here.

3.2 Problem Description

Consider G (V, E) is a graph (unidirectional or bidirectional)

which represents a topology, where V represents the set of n

nodes and E represents the set of m links. The maximum length

(in hop) of a light-trail is denoted by Lmax. The set of existing

request for the network is taken in a request matrix which is

denoted by rqst_mtrx and the set of connections among the

nodes of the network is represented by another matrix denoted

by connectivity matrix or shortly cntv_mtrx. As G is a directed

graph, so connections among the nodes do not only indicate the

links among those nodes but their directions also. Each request

in rqst_mtrx is served by only one light-trail and one light-trail

is used to serve only one request. So, here the number of light-

trail is equal to the number of existing request in rqst_mtrx. So,

the set of light-trails denoted by LT is actually the set of

existing requests in rqst_mtrx.

3.2.1 Assumptions

1. Traffic-matrix Preprocessing: Normally due to power losses,

there is a limit on the maximum hop length of a connection.

The hop length is generally restricted to a maximum of 5. Thus

if the number of hops in the shortest path between a pair of

nodes exceeds this limit, then a connection request between

them must be broken down into two or more connection

requests. The algorithm that preprocesses the connection

request is discussed in [6]. It was not implemented as the part

of the work.

2. Assignment constraint: each request is assigned to one and

only one light-trail.

3. Light Trail Capacity Constraint: The aggregated request

capacity on a light trail should not exceed the full wavelength

capacity.

4. Link-disjoint Light trail Constraint: In order to provide

connection based protection, primary and backup connection

request should be accepted and maintained as link-disjoined

light trails.

3.3 Algorithm

3.3.1 Light-trail implementation with Connection

Matrix (CM)

INPUT: Graph G (V, E); the set of existing light-trails LT

from request matrix rqst_mtrx; connectivity matrix cntv_mtrx;

the maximum hop-length of a light-trail Lmax.

OUTPUT: The set of light-trails (final_lt) that cover the given

requests having following properties:

1. The length of each light-trail is no longer than Lmax.

2. Total number of light-trails required is minimized.

Step1: Checking of blocking

1. If, any light-trail of rqst_mtrx is blocked, keep it in

blocked_lt.

else, keep the light-trail in nonblocked_lt.

2. Split each link of each light-trail of blocked_lt.

3. Check, whether these links are covered by the light-trails of

nonblocked_lt either directly or via nodes.

if not, the links are kept in blocked_links.

Step2: Minimization of light-trails of nonblocked_lt with CM.

1. Determine the hop-length of each light-trail of

nonblocked_lt.

2. Compare the hop-length of each light-trail with Lmax.

(i) if hop-length < Lmax, select the corresponding light-trail.

(ii) else if hop-length ==Lmax, add the corresponding light-

trail to temp1.

3. Concatenate the light-trails selected from step2 (i) with each

other and store the result in temp2.

4. Each node of the light-trails of temp2 are checked.

If, two consecutive nodes are same (same node

number), consider them as one node (uniqueness).

5. Again count the hop-length of each light-trail of temp2.

6. Compare the hop-length of each light-trail of temp2 with

Lmax.

(i) if hop-length > Lmax, cancel out the

corresponding light-trail.

(ii) else, the remaining light-trails are kept in temp3.

7. Check the connection of each light-trail of temp3 by

cntv_mtrx.

(i) if the connection of light-trail is not valid

according to cntv_mtrx, cancel out the light-trails.

(ii) else, keep it in temp4.

8. Check uniqueness of the light-trails of temp4.

If, two or more light-trails are same consider them as

one unique light-trail.

9. Selection of proper light-trails from temp4 and kept in

temp5.

(i) Check for the requests which are served by only

one light-trail, select the light-trails first.





(ii) Find out other requests which are also served by

theses selected light-trails and cancel out the other light-trails

which serve only these requests.

(iii) Now if any request is left that is served by two or

more light-trails select any one from them.

10. Match each light–trail of temp5 with each light-trail of

temp1.

(i) if a match is found the corresponding light-trail is

cancel out from temp5.

(ii) else keep the light-trail of temp5 in new_lt.

11. Check whether all the requests in the rqst_mtrx are served

by the light-trails of new_lt.

If not, then the request is added to the final_lt.

12. Add temp1 and new_lt and also blocked light-trails to

final_lt.

13. Return final_lt.

Step3: Reduction of blocking with minimized light-trail.

1. Check whether the links of blocked_links are covered by

the light-trails of new_lt either directly or via nodes.

if not, the links are kept in finally_blocked.

2. Calculate the percentage of reduction of blocking using the

following equation.

Consider, total number of links of blocked_links = bl

total number of links of finally_blocked =fb

So, reduction of blocking (%) =

3.3.2 Example Illustrating Proposed Heuristic with

CM

The directed (unidirectional) graph G, representing mesh

topology is depicted in figure1. The request matrix denoted by

rqst_mtrx containing all the requests and the connectivity

matrix denoted by cntv_mtrx representing all the connections

between the nodes of network G are given as:

Here, the size of the rqst _mtrx is 8x4. So, at the beginning the

total number of light-trails needed to serve all the requests is 8.

Now consider the first two light-trail of rqst_mtrx are blocked.

So each link of these two light-trails is blocked.

The rest of the light-trails of rqst_mtrx are kept in

nonblocked_lt. The links of blocked light-trails which are not

covered by the light-trails of nonblocked_lt (either directly or

via nodes) are considered as blocked_links. Here, [2 3] is

covered by 2nd light-trail of nonblocked_lt.

(bl - fb)

bl X 100

Fig: 1.Unidirectional graph G representing mesh topology





In this example, the value of Lmax is considered 3. The first two

light-trails (that served first four requests) having Lmax=3, will

be a part of final result. But the rest four having hop-length <3,

will be concatenated with each other. The steps are shown

below:

Now request 3-1-5 is only served by the light-trail 0-3-1-5. So

this light-trail is considered first. 0-3 and 1-5 are also served by

this light-trail. So, we don‟t need to consider the light-trail 1-5-

0-3 anymore. Now 2-4 can be served by both 1-5-2-4 and 2-4-

1-5. So, any one of them can be selected. The minimized light-

trails are kept in new_lt.

So, in this example finally the total number light-trails required

to serve all the requests is reduced from 8 to 6.

Now [0 1] link of the blocked_links is covered by 1st

light-trail

of new_lt through node 3 and [1 2] link of the blocked_links is

covered by 2nd

light-trail of new_lt through node 5.

finally_blocked will contain the links of blocked_links which is

not covered by new_lt. So, finally_blocked = 4 1

Total number of links of blocked_links (bl) =3; Total number

of links of finally_blocked (fb) =1. So, reduction of blocking

(%) = ((3 -1)/3)*100=66.67%

Similarly another example is given for NSF network shown in

figure2. Hence also the value of Lmax is 3.

Fig 2.NSF network

The request matrix rqst_mtrx and the connectivity matrix

cntv_mtrx of this network are given below:

So, finally_blocked =

Total number of links of blocked links (bl) =4; Total number

of links of finally blocked (fb) =2

So, reduction of blocking (%) = ((4 -2)/4)*100=50%

3.4 Light-trail Minimization Using Genetic Algorithm

Step1 and step 3 are same as previous algorithm. So, they are

not mentioned here. Only step 2 is implemented using GA.

Step2: Minimization of light-trails of nonblocked_lt with

Genetic Algorithm.

(i) Set generation number t 0; Set maximum generation

max_gen 10; Set string length xlen (Lmax +1); Set

crossover probability pcross 0.98; Set mutation probability

pmut 0.001; Set crossover site xsite2;

0 3 1 5 1 5 2 4

new_lt =





(ii) Initial population:

(a) Calculate the value of WL for each light-trail in

rqst_mtrx,

where WL= 𝑊𝑖𝑗Lmax +1𝑗=𝑖+1

Lmax𝑖=1

and 𝑊𝑖𝑗 =

(b) The light-trail which satisfy WL<Lmax, is considered as a

string Si.

(c) ini_pop {S1, S2,…….,Spop_size} as initial population,

where pop_size denotes total number of strings.

(d) Keep the rest of light-trail of nonblocked_lt in temp1.

(iii) Compute fit (Si) for each string Si (1≤ i≤pop_size) of

initial population, where fitness function

fit (Si) = | Lmax + WL|

(iv) Selection or Reproduction:

The selection operation described below on the string of

ini_pop, generate a mating pool mate_pool of size pop_size.

(a) Calculate the probability Pi of selection of Si

(1≤i≤pop_size)

Pi = fit (Si) / ∑ fit ( Si)

(b) Calculate the expected number of copy E.C.

(expected count) of Si (1≤i≤pop_size).

E.C=

where,

(c) Generate a random number rj from [0,1] for

j=[1,2,………,pop_size] and compute actual number of copies

(actual count) of Si(1≤i≤pp_size).

if rj > (1- fractional remainder of E.C.), then the additional copy

is awarded to the ith

string.

(v) Crossover:

The crossover operation is described below on the strings of

mate_pool and obtains a population of temp_pop of size

pop_size.

(a) Randomly select two strings as pair from mate_pool

such that the total number of each string is equal to the

corresponding actual count and form (pop_size/2) number of

paires.

(b) Generate a random number rk from [0, 1] for k= [1, 2,

(pop_size/2)] for each pair such that, if rk ≤pcross, the

crossover will undergoes at the cut point xsite.

(vi) Mutation:

Mutation operation is described below on the string of

temp_pop and obtains a population new_pop of size pop_size.

Generate a random number rm from [0, 1] for m= [1,

2...pop_size X xlen] for each node nj (1≤j≤xlen) of each string

Si (1≤i≤pop_size) of temp_pop such that,

if rm ≤pmut, exchange node nj of Si with any other

randomly selected node nk of Si where 1≤k≤xlen and k ≠ j.

(vii) Compute fit(Si) for each string Si (1≤i≤pop_size) of

new_pop.

if, fit (Si)=2Lmax, then Si is kept in new_lt.

(viii) Check, whether the requests, served by the light-

trails of ini_pop are now all served by the light-trails of new_lt.

if, yes, then

(a) Light-trails of temp1 and new_lt are kept in

final_lt. The blocked light-trails of blocked_lt are also added to

the final_lt.

(b) Return final_lt.

else

if t< max_gen,

(a) Set tt+1; (b) Rename new_pop as ini_pop; (c) Go to

step (iii).

3.4.1 Example Illustrating Proposed Heuristic with

GA:

WL values of each light-trail of nonblocked_lt of 1st example

(fig.1.) are shown in table1. The last four light-trails having

WL<Lmax (i.e WL<3 as Lmax=3) forms the initial population.

Table2. Computes fitness value of each string.

Table 1: Evaluating

WL value of each

light-trail

Initial Population

rq no. Rqst_mtrx W(Li)

1. 4 1 2 3 3

2. 5 2 3 1 3

3. 3 1 5 - 2

4. 0 3 - - 1

5. 1 5 - - 1

6. 2 4 - - 1

pop_size =

1, if there exists a unidirectional link from node i to node j 0, otherwise

Initial

population





Table 2: Evaluating fitness value of each string

The considerations are:

(i) Population size (pop_size) = 4; (ii) Maximum number of

generation (max_gen) = 10; (iii) String length = 4; (iv)

Crossover probability (pcross) = 0.98; (v) Mutation

probability (pmut) =0.001; (vi) Crossover site (xsite) = 2.

Selection procedure of individual string is referred in Table 3.

Crossover and offspring generation is shown in table4. Here,

fitness value of each offspring is evaluated.

Table 3. Selection procedure of individual string is being

Table 4: Generating new population

Strings of new population having fitness value equal to 2Lmax

(here Lmax=3, so 2Lmax=6) are considered as light-trails of

new_lt. Now the light-trails of new_lt have served all the

requests which were served by the light-trails of ini_pop. So,

we don‟t need to go in the next generation. The total number of

light-trails required to serve all the requests in the ini-pop is

reduced from 4 to 2. So, total number of light-trail in rqst_mtrx

is minimized from 8 to 6.

Similarly this concept is also applied on NSF network (fig2)

with same rqst_mtrx.

rq

no.

rqst_mtrx fit(Si)

1. 3 1 5 - 5

2. 0 3 - - 4

3. 1 5 - - 4

4. 2 4 - - 4

Strin

g no.

Initial

populatio

n

fit(Si

)

Selection

probabilit

y

Expecte

d count

Rando

m

Actua

l

count

1. 3 1 5

-

5 0.295 1.18 0.67 1

2. 0 3 -

-

4 0.235 0.94 0.28 1

3. 1 5 -

-

4 0.235 0.94 0.55 1

4. 2 4 -

-

4 0.235 0.94 0.98 1

Parents

(with xsite=2)

New population

(Offspring)

fit(Si) New_lt

- 3 1 5

0 3 - -

1 5 - -

- - 2 4

0 3 1 5

- 3 - -

1 5 2 4

- - - -

6

3

6

3

0 3 1

5

1 5 2 4

Sum 17 1.000 4.00 4

Average 4.25 0.25 1.00 1





Table 5: Evaluating WL value of each light-trail

Table 6: Evaluating fitness value of each string

Table 7: Evaluating Sum and Average fit (Si), Selection

Probability, Expected Count and Actual Count

Sum 25 1.0 6.00

6

Average 4.17 0.167 1.00

1

Table 8: Generating new population

Now the light-trails of new_lt have served all the requests

which was served by the light-trails of initial population. The

total number of light-trails required to serve all the requests in

the ini-pop is reduced from 6 to 3. So, total number of light-

trail in rqst_mtrx is minimized from 14 to 11.

rq

no.

rqst_mtrx W(Li)

1. 0 1 3 4 3

2. 3 4 6 8 3

3. 5 12 11 9 3

4. 13 9 11 12 3

5. 9 8 6 4 3

6. 4 3 1 0 3

7. 3 10 13 - 2

8. 4 5 - - 1

9. 7 9 - - 1

10. 13 12 - - 1

11. 0 8 - - 1

12. 9 13 - - 1

Parents

(with

xsite=2)

New

population

(Offspring)

fit(Si) New_lt

3 10 13

-

- - 13

12

4 5 -

-

- - 7

9

0 8 -

-

- - 9

13

3 10 13 12

- - 13 -

4 5 7 9

- - - -

0 8 9

13

- - - -

6

3

6

3

6

3

3 10

13 12

4 5 7

9

0 8 9

13

rq

no.

rqst_mtrx fit(Si)

1. 3 10 13 - 5

2. 4 5 - - 4

3. 7 9 - - 4

4. 13 12 - - 4

5. 0 8 - - 4

6. 9 13 - - 4

String no.

Initial population

Fit (Si)

Selection probabilit

y

Expected count

Random

Actual count

1. 3 10 13

-

5 0.2 1.2 0.67 1

2. 4 5 -

-

4 0.16 0.96 0.28 1

3. 7 9 -

-

4 0.16 0.96 0.55 1

4. 13 12 -

-

4 0.16 0.96 0.98 1

5. 0 8 -

-

4 0.16 0.96 0.47 1

6. 9 13 -

-

4 0.16 0.96 0.71 1

Initial

population

Sum 25 1.0 6.00 6

Average 4.17 0.167 1.00 1





4. SIMULATION AND RESULT

As most of the existing light-trail minimization algorithms

adopt ILP (Integer Linear Programming) approach. To

compare the performance of the proposed heuristics with ILP,

consider the example shown in fig1.(mesh topology) and

fig2.(NSF network).

4.1 ILP Formulation

Variables:

µlsd: Binary variable, route indicator, takes value of 1 if request

(s, d) takes light trail l; zero otherwise. This also implies that

node s and d are on trail l and s is d‟s upstream node.

δl: Binary variable, light trail usage indicator takes value of 1 if

trail l is used by any request; zero otherwise.

Wij: Binary variable, link indicator, takes value of 1 if there

exists a link from node i to node j. Here i is upstream node of j.

hl: Hop-length of each light-trail l.

tsd: Traffic flow between node s and node d.

C: Full-wavelength capacity.

Objective: Minimum number of light-trails those are required

in the network.

Subject to following constraints:

1. 1. Hop-length constraint: The hop-length of each light-

2. trail should not exceed the value of Lmax.

hl ≤ Lmax , ⍱l

3. Connectivity constraint: The connections with in a

light-trail l should satisfy the connection matrix.

∑ ∑ Wij = hl

4. Assignment constraint: Each request is assigned to one

and only one light-trail.

5. Light-trail capacity constraint: The aggregated request

capacity on a light-trail should not exceed the full-wavelength

capacity.

6. Light-trail usage constraint: If any of the s-d pair is

assigned on light-trail l, δl is set to 1, otherwise if none of the s-

d pairs picked light-trail l, then δl = 0.

δl ≥ µlsd ⍱ (s,d): tsd єT, δl є {0,1}

We assume Lmax =3 and C=40. Traffic matrix of Fig.1. and

Fig2. are shown in table1. and table3. respectively. The ILP

solutions of these two examples are given in Table 10 and

Table 11 respectively.

Table9.

Traffic

matrix

(TN×N) for

6-node

network

(fig.1)

Table 10. ILP Solution: Resulting Light-trails with Lmax=3, C=40

Table11. ILP Solution: Resulting Light-trails with Lmax=3, C=40

No. Light-

trail

Accommodated s-d pairs Capacity

1. 0-1-3-

4

(0,1)(0,3)(0,4)(1,3)(1,4)(3,4) 38

2. 1-2-5-

7

(1,2)(1,5)(1,7)(2,5)(2,7) 32

3. 3-4-6-

8

(3,6)(3,8)(4,6)(4,8)(6,8) 36

4. 8-9-

11-12

(8,9)(811)(8,12)(9,11)(9,12) 37

5. 5-12-

11-9

(5,9)(5,11)(5,12)(11,9)(12,9)(12,11) 39

6. 13-9-

11-12

(11,12)(13,9)(13,11) 39

7. 9-8-6-

4

(6,4)(8,4)(8,6)(9,4)(9,6)(9,8) 35

8. 4-3-1- (1,0)(3,0)(3,1)(4,0)(4,1)(4,3) 38

0 1 2 3 4 5

0 0 5 15 13 0 18

1 0 0 12 7 12 10

2 0 7 0 14 17 0

3 6 13 4 0 4 8

4 18 5 12 5 0 3

5 9 5 5 7 9 0

No Light-trail Accommodated s-d pair capacity

1. 0-1-2-3 (0,1)(0,2)(1,2)(1,3) 39

2. 3-4-5-0 (3,0)(3,4)(4,0)(4,5)(5,0) 40

3. 4-1-2-3 (2,3)(4,1)(4,2)(4,3) 36

4. 5-2-3-1 (2,1)(3,1)(5,1)(5,2)(5,3) 37

5. 0-3-1-5 (0,3)(0,5)(1,5)(3,5) 39

6. 1-5-2-4 (1,4)(2,4)(5,4) 38

δl

µlsd =1 ⍱(s,d), tsd єT, tsd>0

µlsd tsd ≤ C





0

9. 3-10-

13-12

(3,10)(3,12)(3,13)(10,13)(13,12) 40

10. 4-5-7-

9

(4,5)(4,7)(4,9)(5,7)(7,9) 39

11. 0-8-9-

13

(0,8)(0,9)(0,13)(8,13)(9,13) 38

Using ILP, we can see that the 1st example (Fig.1.mesh

topology) needs 6 light-trails and the 2nd

example (Fig.2.NSF

network) needs 11 light-trails to serve all the requests.

Table 12. Traffic matrix (TN×N) for 14-node NSF network(Fig.2)

Table.9 summarizes the result. The 1st, 2nd and 3rd rows give the

number of light-trails required by the Proposed Heuristic with CM and

GA and ILP respectively.

Algorithm

(Fig. 1) N=6 (Fig. 2)

N=14

(Unidirectional)

Biderectional)

Connection Matrix 6 11

Genetic Algorithm 6 11

Integer Linear Programming 6 11

Though all generate same result, but there is no certainty that

the middle approach (GA) will always produce an optimal

solution. Here reduction of blocking is also similar as both

yield same minimized light-trails for a given set of requests for

same blocked light-trails. Complexity of the proposed heuristic

is O(n.k), where n is the number of light-trails assigned to the

network to serve the requests and k is the number of nodes

between source and destination of each light-trail or request,

whereas the complexity of second approach is slightly

increases due to formulation of initial population. But light-

trail implementation with ILP is a NP-Hard problem.

5. CONCLUSION

A heuristic approach with connection matrix and Genetic

Algorithm is proposed for minimizing the number of light trails

for given a graph (network) and a number of connection

requests. Here, mesh topology assuming it as unidirectional

and NSF network which is bidirectional are considered to

illustrate the proposed heuristics. Both the approaches can

solve it in polynomial time, whereas ILP needs exponential

time. Above all, we have tried to develop an algorithm of light-

trail optimization problem which is very efficient and user

friendly such that it will always return an optimal or a sub-

optimal solution with having reasonable lower complexity than

other existing algorithms.

REFERENCES

1. Ashwin Gumaste and Imrich Chlamtac, „Light-trails:

A Novel Conceptual Framework for Conducting

OpticalCommunications‟,Proceedings of HPSR 2003 Torino

Italy, June 2003.

2. Michael T. Frederick, Nathan A. VanderHom and

Arun K. Somani, „Light Trails: A Sub-Wavelength Solution for

Optical Networking‟, HPSR‟2004,pp. 175-179.

3. Ashwin Gumaste, Gabriel Kuper and Imrich Chlamtac,

„Optimizing Light-trail Assignment to WDM Networks for

Dynamic IP Centric Traffic‟, IEEE LANMAN 2004, Apr.

2004,pp 113-118.

4. Wensheng He, Jing Fang, Arun K. Somani, „On Survivable

Design in Light Trail Optical Networks‟, proceeding of 8th

IFIP

Working Conference on Optical Network Design and

Modeling, Feb,2004.

0 1 2 3 4 5 6 7 8 9 10 11 12 13

0 0 5 0 11 8 0 0 0 13 4 0 0 0 8

1 4 0 6 6 2 0 0 9 0 0 0 0 0 0

2 0 0 0 0 0 2 0 8 0 0 0 0 0 0

3 9 4 0 0 6 0 7 0 9 0 3 0 8 10

4 10 9 0 2 0 8 4 6 3 2 0 0 0 0

5 0 0 0 0 0 0 0 12 0 10 0 9 7 0

6 0 0 0 0 4 0 0 0 13 0 0 0 0 0

7 0 0 0 0 0 0 0 0 0 11 0 0 0 0

8 0 0 0 0 7 0 9 0 0 9 0 7 6 5

9 0 0 0 0 8 0 5 0 2 0 0 9 6 8

10 0 0 0 0 0 0 0 0 0 0 0 0 0 7

11 0 0 0 0 0 0 0 0 0 3 0 0 11 0

12 0 0 0 0 0 0 0 0 0 4 0 6 0 0

13 0 0 0 0 0 0 0 0 0 13 0 15 12 0





5. Jing Fang, Wensheng He, Arun K. Somani, „Optimal

Light Trail Design in WDM Optical Networks‟, IEEE Intl Conf

on Commun (ICC) 2004 Paris.

6. Bin Wu nad Kwan L. Yeung, „Light-trail assignment in

WDM optical networks‟, IEEE Proc of Globecom 2006 San

Francisco CA.

7. Weiyi Zhan, Guoliang Xue, Jian Tang, Krishanaiyan

Thulasiraman, „Dynamic light-trail routing and protection issue

in WDM optical network‟, IEEE Globecom 2005, vol. 4, pp

1963-1967.

8. Akhil Lodha, Ashwin Gumaste, Paresh Bafna and Nasir

Ghani, „Stochastic Optimization of Light-trail WDM Ring

Networks using Bender‟s Decomposition‟, Indian Institute of

Technology, Bombay, India,Tennessee Technological

University Cookeville USA.

9. Arun K. Somani, „Survivability and Traffic

Grooming inWDM Optical Networks‟, Cambridge

University press.

10. Dzmitry Kliazovich and Fabrizio Granelli, „Bidirectional

Light-Trails for Synchronous Communications in WDM

Networks‟, IEEE Globecom 2005.

BIOGRAPHIES

Inadyuti Dutt, has been in the field of

academics and research for more than ten

years and is currently the Assistant Professor

in the Department of Computer Application

of B. P. Poddar Institute of Management &

Technology, Kolkata, West Bengal, India.

.Earlier, she held several technical positions

in National Informatics Centre, Kolkata and Semaphore

Computing Networks Pvt. Ltd. respectively. She has Master‟s

Degree in Computer Application and currently pursuing her

research in Computer Science and Engineering. She is Student

Branch Co-ordinator of CSI Student Branch, B.P.Poddar

Institute of Management & Technology. She has more than 20

publications to her laurels and her research interest is

specifically in the field of Optical Networking, Security and

Neural Networks. She has also been the Technical Reviewer ,

Member, Editorial Board in several journal publications like

International Journal of Software Engineering Research

International Journal of Engineering & Advanced Technology.

Soumya Paul, Associate Professor and

Head, Department of Computer

Application in B. P. Poddar Institute of

Management & Technology, Kolkata,

India, has been in teaching and research

for over 12 years. He holds a Master‟s

Degree in Technology, Computer Application as well as in

Mathematics and has gathered vast experiences in the same. He

received his M.Sc. (Mathematics) from Visva Bharati

University and stood 1st class 1

st. He received MCA from

National Institute of Technology, Rourkela and M. Tech (CSE)

from AAI-Deemed University and pursuing Ph. D in Computer

Science and Engineering. He served as a faculty member and

visiting faculty member in various Institutes and Universities

like RCCIIT, Visva Bharati University, University of Calcutta,

Bardhaman University, West Bengal University of Technology

etc. He is a member of Board of Study of MCA, BCA of West

Bengal University and Technology. He has delivered numerous

lectures across India in the field of his research interest,

Network Security and Genetic Algorithms. He is an author/co-

author of several published articles in International Journals

and International Conferences. He has chaired an International

Conference technically supported by IEEE communication. He

has more than 20 research publications and currently Reviewer

and Member, Editorial Board in many conferences and journals

like International Journal of Data Modeling and Knowledge

Management, International Journal of Advanced Research in

Computer Science and Electronic Engineering.

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