Is it a Good Idea to Is it a Good Idea to Design WDM Networks to Design WDM Networks to Minimize The Number of Minimize The Number of

Wavelengths Used?Wavelengths Used?Cavendish, D.; Kolarov, A.; Sengupta, B.Cavendish, D.; Kolarov, A.; Sengupta, B.

From : 2004 IEEE ICC on Volume 4, 20-24 From : 2004 IEEE ICC on Volume 4, 20-24 June 2004 Page(s):2097 - 2101 Vol.4 June 2004 Page(s):2097 - 2101 Vol.4

Reporter : Chia-Nung WanReporter : Chia-Nung Wangg

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OutlineOutline IntroductionIntroduction Problem StatementProblem Statement Minimizing the number of Minimizing the number of

wavelength conversions.wavelength conversions. Minimizing the number of Minimizing the number of

wavelength used.wavelength used. Performance analysisPerformance analysis ConclusionsConclusions

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IntroductionIntroduction

Design the system to direct minimize Design the system to direct minimize the blocking probability is quite difficult.the blocking probability is quite difficult.

This paper focus on two different This paper focus on two different optimization criteria.optimization criteria.

(1)Minimizing the number of (1)Minimizing the number of wavelength conversions.wavelength conversions.

(2) Minimizing the number of (2) Minimizing the number of wavelength used.wavelength used.

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Introduction (cont.1)Introduction (cont.1) The RWA problem takes two flavors:The RWA problem takes two flavors: (1)Off-line:(1)Off-line: All connection requests are know in All connection requests are know in

advance.advance. A routing decision can be made based on A routing decision can be made based on

the complete knowledge of the traffic. the complete knowledge of the traffic. (2)On-line:(2)On-line: A connection request must be routed A connection request must be routed

and wavelengths assigned independently and wavelengths assigned independently of other connection.of other connection.

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Introduction (cont.2)Introduction (cont.2)

Finding a globally optimal solution for Finding a globally optimal solution for the off-line problem is NP-hard.the off-line problem is NP-hard.

In this paper, we will seen a sub-In this paper, we will seen a sub-optimal but computationally efficient optimal but computationally efficient method.method.

The work presented in this paper The work presented in this paper differs from others:differs from others:

(1) The limitation on wavelength (1) The limitation on wavelength conversion capabilities. conversion capabilities.

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Introduction (cont.3)Introduction (cont.3)

The work presented in this paper The work presented in this paper differs from others (cont.):differs from others (cont.):

(2) Formulating problems with (2) Formulating problems with different objectives, whereas most of different objectives, whereas most of previous work has focus on single previous work has focus on single objective. objective.

(3) For each of the objectives, (3) For each of the objectives, authors develop a sequential authors develop a sequential algorithm. algorithm.

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Problem StatementProblem Statement

Model as a undirected graph G(Model as a undirected graph G(υυ,,εε), ), where |where |υυ|=N, ||=N, |εε |=J.|=J.

A wavelength set A wavelength set ΛΛ={0,1,2,…..,K-1} of ={0,1,2,…..,K-1} of size |size |ΛΛ|=K.|=K.

κκ jj is maximum number of wavelengt is maximum number of wavelengths which can be converted at node j. hs which can be converted at node j.

ρρjj denotes the wavelength conversion denotes the wavelength conversion capability still left at node j.capability still left at node j.

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Problem Statement Problem Statement (cont.1)(cont.1)

R is request set and LR is request set and Lii is a lightpath i. is a lightpath i. NNkk is the cost of using wavelength k on is the cost of using wavelength k on

any link. any link. βk is a factor , if the wavelength has bβk is a factor , if the wavelength has b

een used then the value is 0.een used then the value is 0. Define Define ααnmnm(k) = 1, if wavelength k is a(k) = 1, if wavelength k is a

vailable for use on that link.vailable for use on that link. The coloring of lightpath L is defined aThe coloring of lightpath L is defined a

s the assignment of wavelength labels.s the assignment of wavelength labels.

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Problem Statement Problem Statement (cont.2)(cont.2)

A valid coloring must fulfill the following cA valid coloring must fulfill the following conditions:onditions:

(1)Every link belonging to each lightpath m(1)Every link belonging to each lightpath must be colored.ust be colored.

(2)If two consecutive links colored with diff(2)If two consecutive links colored with different colors, there must be a wavelength coerent colors, there must be a wavelength conversion happened. nversion happened.

(3)No two distinct lightpaths with a commo(3)No two distinct lightpaths with a common link and in the same direction, can use thn link and in the same direction, can use the same wavelength at the common link. e same wavelength at the common link.

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Minimizing the number of Minimizing the number of wavelength conversions wavelength conversions

Base on Dijkstra algorithm.Base on Dijkstra algorithm. If there are multiple way, the method If there are multiple way, the method

minimize the length of lightpath. minimize the length of lightpath. On-line algorithm begin:On-line algorithm begin:

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Minimizing the number of Minimizing the number of wavelength conversions wavelength conversions

(cont.1)(cont.1)

Then find the minimizes value of Then find the minimizes value of ( j, k ), denote that (μ,ν).

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Minimizing the number of Minimizing the number of wavelength conversions wavelength conversions

(cont.2)(cont.2) If If μ=N-1 then go to step5, otherwise

continue. For all j ∈ A(μ) and k ∈ Λ:

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Minimizing the number of Minimizing the number of wavelength conversions wavelength conversions

(cont.3)(cont.3) Step 5: Let m = 1, ξm = μ and Φm = ν.

If f(ξm, Φm) = ∞ then stop.

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Minimizing the number of Minimizing the number of wavelength conversions wavelength conversions

(cont.4)(cont.4) The optimal lightpath consists of m no

des and equals (ξm, ξm−1, · · · , ξ1). ξm = 0 and ξ1 = N − 1. The number of wavelength conversion

s needed is the total of ∆(φi−1, φi) for i=2~m-1.

The variable βk is 0 if wavelength k has been used.

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Minimizing the number of Minimizing the number of wavelength conversions wavelength conversions

(cont.4)(cont.4) Off-line algorithm:Off-line algorithm: Step 1: First, find the shortest paths for

all elements of the request set, then order them.

Step 2: Sequentially process all ordered requests by the on-line algorithm. (No W.C capability)

Step 3: Use the on-line algorithm to process all requests which are blocked in Step 2. (With W.C capability)

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Minimizing the number of Minimizing the number of wavelength usedwavelength used

The method of solving the problem is identical to the one presented before, except.

The step 3 should be changed to:

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Performance analysisPerformance analysis

The two RWA strategies used are:The two RWA strategies used are: (1)MinConv: minimizes the number of (1)MinConv: minimizes the number of

wavelength conversions on one request wavelength conversions on one request at a time.at a time.

(2)MinWav: minimize the number of (2)MinWav: minimize the number of wavelengths used.wavelengths used.

In this simulation we set N=32 and In this simulation we set N=32 and J=45 bidirectional link.J=45 bidirectional link.

Each link has a capacity of 16 wavelengths in each direction (K =16).

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Performance analysis Performance analysis (cont.1)(cont.1)

We simulated two traffic types, based on the uniform and Zipf distributions.

varying the number of requests: |R| ={200, 300, 400, 500, 600}.

We will analysis the results as blocking probability, average number of hops and average number of OEO conversions.

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Performance analysis Performance analysis (cont.2)(cont.2)

Focus on blocking Focus on blocking probabilityprobability

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Focus on blocking Focus on blocking probability (2)probability (2)

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Performance analysis Performance analysis (cont.2)(cont.2)

Focus on Focus on average number of hops

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Performance analysis Performance analysis (cont.2)(cont.2)

Focus on Focus on average number of OEO conversions

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ConclusionConclusion

Author solved the routing and wavelength assignment sub-problems as a single problem.

The algorithm which minimizes the number of wavelength conversions (MinConv) is better the one which minimizes the number of wavelengths used.

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Thanks for listening !Thanks for listening !