Blocking probability minimization in WDM with optimal placement of wavelength converters using ETGA

JOURNAL OF TELECOMMUNICATIONS, VOLUME 30, ISSUE 1, APRIL 2015 1

Blocking probability minimization in WDM with optimal placement of wavelength converters using ETGA

Ramya.S and Dr Indumathi T.S

Abstract Wavelength division multiplexing technology has offered to exploit the wide bandwidth available in optical fibres, but also introduced new complexities in the routing problem. In this context, the wavelength converter allocation problem has become a key factor to minimize blocking probability. In this research we have given attention to minimizing blocking probability for given number of converters by providing its optimal placement in network. This work proposes a variation in conventional genetic algorithm by providing the elitism in tournament selection process. Extensive simulations show promising results in the sense that our algorithm generates the trade-off curve between blocking and the number of converters needed and outperforms conventional genetic algorithm approach.

Index Terms optical network, wavelength division multiplexing, wavelength converter, Genetic algorithm, Elitism.

!

1 INTRODUCTION Wavelength division multiplexing (WDM) is a mature technology that has solved the electronic bottleneck problem. In this context, WDM networks provide a larger bandwidth at the expense of a higher technological complexity. WDM networks have several critical issues such as the routing and wavelength assignment (RWA) problem and the WDM network design problem, areas of active research. The RWA approach aims to calculate the optimal lightpath, which is conformed by optical fibres and assigned wavelengths. The main objective of a WDM network design is to minimize request blocking with the minimum investment and management costs. Typically, a WDM network imposes the use of just one wavelength in the whole lightpath. This is known as the wavelength continuity constraint problem, which is the main issue that causes the blocking problem this is, the incapability of assigning a lightpath to a request. To overcome the blocking generated by this constraint it is necessary to add wavelength converters into optical routers. A wavelength converter is a device that changes a wavelength into another wavelength. Deciding how many and where to locate these wavelength converters is a particular design problem known as the wavelength converter allocation (WCA) problem, which is an NP-hard problem when dealing with irregular network topologies . The WCA problem treated as a mono-objective optimization problem. More specifically, there are three possible approaches can be applied reported

Associate professor, K.S.Institute of Technology,Bengaluru, Karnataka.

Professor&PG coordinator,VisvesvarayaTechnological University, Muddenahalli, Chickaballapur, Karnataka

( a) minimize the number of wavelength converters subject to a given blocking probability bound (a) Minimize the number of wavelength converters subject to a given blocking probability bound and (b) minimize the blocking probability subject to a given number of wavelength converters (c) simultaneous taking care of both to get optimum solution in terms of blocking probability and utilized number of wavelength converters.

2 RELATED WORKS In literature the problem of wavelength converter placement has got attention by number of researchers as it is addressed in many studies [2-13]. There are two traffic scenarios considered: static [5][7], [9], [10] and dynamic [3], [4], [8], [11][13] traffic demands. In all these approaches, researchers typically use heuristic algorithms to place wavelength converters, such as abstracting technique in [7], tabu search in [9], particle swarm optimization (PSO) in [10] or adaptive traffic-load based in [12]. Some analytical models were also introduced. [3], [11] and [13] use binary linear program to maximize the utilization of wavelength converter, maximize the average of end-to-end success probability and minimize network-wide blocking probability, respectively. In [14] authors have considered a converter placement problem of minimizing the wavelength conversion cost (WCC) to meet the constraint on the blocking probability. A analytical model accounting for the two sources of call blocking in wavelength conversion: a range blocking from the limited conversion range of a wavelength converter; and a capacity blocking from the

2015 JOT www.journaloftelecommunications.co.uk

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limited number of wavelength converters has also presented. Authors in [15] has study the impact of wavelength conversion capability on wavelength routing WDM networks with fixed shortest-path routing. In [16] authors have proposed multistage wavelength conversion by sharing limited range wavelength converters in wavelength division multiplexed (WDM) all-optical packet switching networks. In [17] authors have analyzed the Sparse-Partial Wavelength Conversion network architecture and demonstrate that it can significantly save the number of wavelength converters, yet achieving excellent blocking performance. In [18] silicon-on-insulator device used for conversions between polarization division multiplexing (PDM) and mode division multiplexing (MDM) signals is proposed and experimentally demonstrated by utilizing a structure combining the improved two-dimensional grating coupler and two-mode multiplexer. Blocking performance optimization for convertible routers in WDM optical networks are examined using simulation has given in [19].

3 WAVELENGTH ROUTED OPT ICAL NETWORKS Wavelength Division Multiplexing (WDM), transmitting signals on different wavelength channels simultaneously through an optical fiber, is rapidly becoming a technology-of- choice to meet the tremendous bandwidth demand of the next generation wide-area networks. In these networks, transmission and switching are both implemented by optical technology without using intermediate optical-to-electrical conversions. A connection between source and destination nodes is similar to the one in a circuit-switched network. This can be realized by determining a path between the two nodes and allocating a free wavelength on all links of the path. Such an optical path is commonly referred to as lightpath or wavelength path. In simple WDM networks, a lightpath must use the same wavelength on all links along the path. This is known as wavelength continuity constraint and results in high blocking probability. The restriction imposed by wavelength continuity constraint can be avoided by the use of wavelength converters. A wavelength converter is a device that is able to convert the data arriving on one wavelength along a link into another wavelength at an intermediate node and forward it along the next link. Therefore, with the help of wavelength converters, optical links of a lightpath can be assigned different wavelengths. Many studies have shown that wavelength converters can improve the performance of large mesh networks, where a path consists of many hops due to the increasing amount of wavelength reuse (10 to 40%).An optical node can connect to several optical links that have many wavelengths multiplexed. However, the conversion capacity of a converter can be much smaller than the number of wavelengths connecting to a node. A converter usually has a limited number of in-coming/out-going ports, which represent the number of wavelengths that can be converted. Moreover, in reality; a converter might not be able to convert a wavelength to any existing wavelengths but only to some in a range. For example, a converter can convert wavelength ! to another wavelength in the adjacent range (! !R ; ! +R) with R being conversion range. This refers to limited-range wavelength converters. Several architectures

with conversion capability have been proposed. A scheme of shared converters has been considered in this work. Shared schemes are efficient because they have converters that can be used by all input channels. In particular, this paper considers a node architecture where converters are shared by all input channels. This architecture shown in Figure 1 is known as Share-per-node wavelength converter router (SNWCR). It is composed of F input ports and F output ports, F de-multiplexers and F multiplexers, m wavelength converters and one optical switch. When using a set of wavelengths ! , the optical switch is made of (F* ! + m) input and output ports. Currently, wavelength converters are still very expensive. Therefore, it is not cost-effective to equip all nodes with wavelength converters. Moreover, the blocking probability does not decrease linearly with the number of converters. The rate of performance improvement decreases with the increasing conversion density. Hence sparse wavelength converter placement can achieve almost as good performance as full wavelength converter placement. This motivates us to study the wavelength converter placement problem.

Fig. 1. Wavelength convertible switch architecture

4 GENETIC ALGORITHM AND ITS VARIANTS ETGA Evolutionary computing, also called evolutionary computation, is the field of research that draws ideas from evolutionary biology in order to develop search and optimization techniques for solving complex problems. Most evolutionary algorithms are rooted on evolutionary biology, which basically states that a population of individuals capable of reproducing and subjected to genetic variation followed by selection results in new populations of individuals increasingly fitter to their environment. The computational abstraction of these procedures resulted in the so-called evolutionary algorithms. The basic idea of Evolutionary computing has been to make use of the powerful process of natural evolution as a problem-solving paradigm, usually by simulating it on a computer. A standard genetic algorithm can thus be proposed as follows:1)A population: of individuals that reproduce with inheritance. Each individual represents or encodes a point in a search

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space of potential solutions to a problem. These individuals are allowed to reproduce, generating offspring that inherit some traits from their parents. These inherited traits cause the offspring to present resemblance with theirprogenitors.2)Genetic variation: Offspring are prone to genetic variation through mutation, which alters their genetic makeup. Mutation allows the appearance of new traits in the offspring and, thus, the exploration of new regions of the search space.3)Natural selection: The evaluation of individuals in their environment results in a measure of adaptability, or fitness value to be assigned to them. A comparison of individual fitness will lead to a competition for survival and reproduction in the environment, and there will be a selective advantage for those individuals with higher fitness.

5 ELITISM BASED TOURNAM ENT SELECTION IN GA (ETGA)

Selection is an important part of an evolutionary algorithm. Without selection directing the algorithm towards fitter solutions there would be no progress. Selection must favour fitter candidates over weaker candidates but beyond that there are no fixed rules. Furthermore, there is no one strategy that is best for all problems. Some strategies result in fast convergence, others will tend to produce a more thorough exploration of the search space. An evolutionary algorithm that appears ineffective with one selection strategy may be transformed by switching to a strategy with different characteristics.

The detail pseudo code for ETGA has shown in Fig.2. The detail pseudo code for ETGA has shown in Fig.2.

Fig.2 ETGA pseudo code . In the elitism-based immigrants scheme, the elite from the

previous generation is retrieved to replace the worst individuals in the current population. This way for both, the schemes, not only the diversity be maintained, but it is done more efficiently to adapt GAs to the changing environment. The detail pseudo code for ETGA has shown in Fig.2.

6 APPLIED SYSTEM MODEL We assume that a node can be equipped with either one full range converter, or none. We are also considering a shortest path routing and random wavelength assignment in the network. Hence, the model can be formulated as a binary programming problem and expresses the overall system success probability as a polynomial function of binary variables under a linear constraint. The network is modeled as an undirected graph G = (V, E). The network nodes are then numbered 1, 2. . . n. The following variables are taken: ! !" ! Directed link from node i to node j; F! Number of wavelengths on each link; k! Number of wavelength converters. We will assume one converter per node; therefore variable k also represents the number of nodes to be equipped with conversion. ! !" !End -to-end traffic rate from node s to node t. It is the arrival probability of a call from s to t. T! Traffic matrix of the network !! !"

!" ! Amount of traffic ! !" going through link ! !" ! !" !Load per wavelength over link ! !" ! !" ! is the probability that a given wavelength on link ! !" is occupied, which is called the blocking probability on ! !" . The traffic model can be computed by Eq.1

! !" !! !"

!"! !"

! (1)

Under the condition that!!!! !"

!" is small such that ! !" < 1. (x1, x2. . . xn) is the state vector, indicating the placement of converters. xi is defined as:

! =1

0

By using variables ! where (i = 1, 2, . . . , n), and the given traffic matrix T and k converters, we can determine the values in (x1, x2, . . . , xn), such that the overall blocking probability of the network is minimized. Mathematical representation of success probability in terms of geometric average in the system can be defined as it given in Eq.2.

!"# !! !" !" ! ! !"! !! !!

! !"! !! !! (2)

s.t ! !

!! ! ! ! !

! ! ! ! !! , i=1, 2.3.n By using variables ! ! where (i = 1, 2, . . . , n), and the given traffic matrix T and k converters, we can determine the values in (x1, x2, . . . , xn), such that the overall blocking probability of the network is minimized. Mathematical representation of success probability in terms of geometric average in the system can be defined as it given in Eq.2.

t:=0 and initializ population P(0) randomly For k" 1:N 1. pr" define two parents randomly; 2. crp" generate two random number U[1,dm-1]; 3. tmp1" assign first parent ; 4. tmp2" assign second parent 5. crp1" extract crossover position information from 1st parent 6. crp2" extract crossover position information from 2nd parent 7. offspr1=tmp1[crp ]" assign crp2 in crossover position 8. offspr2=tmp2[crp ]" assign crp1in crossover position 9. rm=generate dm random number U[0 ,1]; 10.for i=1:2 if i=1 offspr1 selected for mutation else offspr2 is selected for mutation end psm= rm

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7 EXPERIMENTAL RESULTS A test case network consist of bi-directional graph with five nodes (D = 5) is shown in Fig.3. It is assumed that a fiber link (F) consists of five channels, and ! !" = 0.05 for any node pair (i, j) where 1 ! i ! D and 1 ! j ! D. The shortest paths for each node pair are defined in table1. The traffic load on each link ! !" as shown in table2 and the end-to-end success probability S(Pst) of any node pair Sij are obtained shown in table3. We can formulate the converter placement problem as a linear function of variable xi for 1 ! i ! 5 since the number of hops in this example is two (i.e., d ! 2).

Fig.3 Bidirectional mesh network topology

Table1: Route table

Table2: Link load

Table3: Success probability S(Pst)between pair of nodes

1 2 3 4 5

1 * ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !

2 ! ! * ! ! ! ! ! ! ! ! ! ! ! ! ! ! !

3 ! ! ! ! * ! ! ! !

4 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! * ! !

5 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! *

Where ! ! ! ! ! ! !!"

! ;! ! ! ! ! ! .!" ! ;! ! ! ! ! ! !!! ! ; ! ! ! ! ! ! !!!!"

! ;! ! ! ! ! ! !!!!"!

We have developed the whole solution environment in MATLAB platform. Various different experiments have done under genetic algorithms and its variant ETGA like (i) effects of one point crossover and two point crossover and comparison in their performance (ii)effects of different population size like in one case it is 10 and another case it 20 over performances (iii) how better elitism based tournament selection based GA(ETGA) in comparison with tournament selection based GA (TGA).in all experimental cases mutation probability is taken as 0.1 and 20 generations have allowed to evolve the solution.in all cases to get the more detail understanding 100 independent trails have applied and performances are evaluated in terms of mean, best, worst and standard deviation available in all 100 trails. Whole experiments have developed for all possible value of converters like: 0, 1,2,3,4 and 5.under all cases the mean performances have also observed in graphs to get their convergence characteristics comparatively. In Fig.4 to Fig.8 performances for all different cases have shown .2PCR represent the 2 point crossover while 1PCR represent 1 point crossover has applied in algorithm while P10 and p20 represent the size of population has taken as 10 and 20.with observation for these figure it is clear that there is a better and faster convergence with 2 point crossover and with larger population size i.e with 20. In Table 4 to Table 10 all the performances in numeric figure have presented. To get the benefit of proposed ETGA over TGA, we have applied the comparison of their convergence characteristics as it shown in Fig.9 to Fig.12.It is clear with all the graphs proposed solution has outperformed the conventional GA.

Fig.4. Maximization characteristics of success probability with 1

converter in ETGA

0 2 4 6 8 10 12 14 16 18 20

-1.78

-1.76

-1.74

-1.72

-1.7

Generation

log(

SP

)

2PCR-P102PCR-P201PCR-P101PCR-P20

1 2 3 4 5 * 12 13 134 135 2 21 * 23 24 245 3 31 32 * 34 35 4 421 42 43 * 45 5 531 542 53 54 *

1 2 3 4 5 1 * 0.01 0.03 * * 2 0.02 * 0.01 0.02 * 3 0.02 0.01 * 0.02 0.02 4 * 0.03 0.01 * 0.02 5 * * 0.02 0.02 *

5

Fig.5 Maximization characteristics of success probability with 2

converter in ETGA


converter in ETGA


converter in ETGA

Fig8. Maximization characteristics of success probability with 5

converter in ETGA

Fig.9. Comparison of success probability with 1 converter in ETGA

and TGA

Fig.10. Comparison of success probability with 2 converter in ETGA and TGA

Fig.11. Comparison of success probability with 3 converter in

ETGA and TGA

Fig.12. Comparison of success probability with 4 converter in

ETGA and TGA

0 2 4 6 8 10 12 14 16 18 20-1.68

-1.66

-1.64

-1.62

-1.6

-1.58

-1.56

-1.54

Generation

log(S

P)


0 2 4 6 8 10 12 14 16 18 20-1.6

-1.55

-1.5

-1.45

Generation

log(

SP)


0 2 4 6 8 10 12 14 16 18 20-1.58

-1.56

-1.54

-1.52

-1.5

-1.48

-1.46

-1.44

Generation

log(

SP)


0 2 4 6 8 10 12 14 16 18 20-1.53

-1.52

-1.51

-1.5

-1.49

-1.48

-1.47

-1.46

Generation

log(

SP)


0 2 4 6 8 10 12 14 16 18 20-1.78

-1.77

-1.76

-1.75

-1.74

-1.73

-1.72

-1.71

-1.7

-1.69

Generation

log(S

P)

ETGATGA

0 2 4 6 8 10 12 14 16 18 20-1.62

-1.61

-1.6

-1.59

-1.58

-1.57

-1.56

-1.55

-1.54

Generation

log(S

P)

ETGATGA

0 2 4 6 8 10 12 14 16 18 20-1.54

-1.53

-1.52

-1.51

-1.5

-1.49

-1.48

-1.47

-1.46

Generation

log(

SP)

ETGATGA

0 2 4 6 8 10 12 14 16 18 20-1.51

-1.505

-1.5

-1.495

-1.49

-1.485

-1.48

-1.475

Generation

log(

SP)

ETGATGA

6

Table4: performance of ETGA with 1 convertor for 100 independent trails

Table5: performance of ETGA with 2 convertor for 100

independent trails

Table6: performance of ETGA with 3 convertor for 100

independent trails

Table7: perfromance of TGA with 1 convertor for 100

independent trails

Table8: performance of TGA with 2 convertor for 100

Independent trails

Table9: performance of TGA with 3 convertor for 100 independent trails

Table10: performance of TGA with 4 convertor for 100

independent trails

Fig.13. Effects of converters over success rate

In the Fig.13 we have given the performance variation observed with increasing the number of converters. it is clear that till inclusion of 3 converter there is improved in success rate observed but again not in linear manner fact is that there is decrement in slope of success rate no improvement has observed with 4 and 5 converters which supports the fact that rather than applying converters to all nodes, sparse placement of converters are better choice. 8 CONCLUSION

In WDM all-optical networks, the use of wavelength converters can increase the wavelength resource efficiency and reduce the blocking probability. However, all-optical wavelength converters are likely to remain costly devices. Moreover, the blocking probability does not decrease linearly with the number of converters. Hence, it is desirable that just a limited amount of wavelength converters are used in the whole network. Optimal converter placement in WDM all-optical networks has proposed in this paper. We have proposed a variation of conventional genetic algorithm which is based on providing elitism at stage of tournament selection. With various experiments we have shown that elitism has delivered the faster and optimal convergence.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 514

15

16

17

18

19

20

21

22

23

No. of Wavelength Convertor

(%) S

ucce

ss R

ate

2PCR-P10ETGA

2PCR-P20ETGA

1PCR-P10ETGA

1PCR-P20ETGA

Mean

(1CN) -1.7065 -1.7065 -1.7073 -1.7065

Best -1.7065 -1.7065 -1.7065 -1.7065 Worst -1.7065 -1.7065 -1.7821 -1.7065 Std.Dev 2.45e-015 2.45e-015 7.55e-003 2.45e-015

2PCR-P10ETGA

2PCR-P20ETGA

1PCR-P10ETGA

1PCR-P20ETGA

Mean

(2CN) -1.5545 -1.5545 -1.5553 -1.5545


2PCR-P10ETGA

2PCR-P20ETGA

1PCR-P10ETGA

1PCR-P20ETGA

Mean

(3CN) -1.4790 -1.4790 -1.4790 -1.4790


2PCR-P10TGA

2PCR-P20TGA

1PCR-P10TGA

1PCR-P20TGA

Mean

(1CN) -1.7156 -1.7065 -1.7164 -1.7065


2PCR- P10TGA

2PCR- P20TGA

1PCR- P10TGA

1PCR- P20TGA

Mean

(2CN) -1.5606 -1.5545 -1.5621 -1.5545

Best -1.5545 -1.5545 -1.5545 -1.5545

Worst -1.7065 -1.5545 -1.7065 -1.5545

Std.Dev 2.58e-002 1.11e-015 2.96e-002 1.11e-015

2PCR- P10TGA

2PCR- P20TGA

1PCR- P10TGA

1PCR- P20TGA

Mean

(3CN) -1.4895 -1.4790 -1.4895 -1.4790


2PCR-P10TGA

2PCR-P20TGA

1PCR-P10TGA

1PCR-P20TGA

Mean

(4CN) -1.4797 -1.4790 -1.4797 -1.4790


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[18] Mengyuan Y, On-chip multiplexing conversion between wavelength division multiplexingpolarization division multiplexing and wavelength division multiplexingmode division multiplexing, OPTICS LETTERS / Vol. 39, No. 4 / February 15, 2014

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Blocking probability minimization in WDM with optimal placement of wavelength converters using ETGA