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

1. Is it a Good Idea to Design WDM Networks to Minimize The Number of Wavelengths Used? Cavendish, D.; Kolarov, A.; Sengupta, B. From : 2004 IEEE ICC on Volume 4, 20-24 June 2004 Page(s):2097 - 2101 Vol.4 Reporter : Chia-Nung Wang

2. Outline • Introduction • Problem Statement • Minimizing the number of wavelength conversions. • Minimizing the number of wavelength used. • Performance analysis • Conclusions

3. Introduction • Design the system to direct minimize the blocking probability is quite difficult. • This paper focus on two different optimization criteria. (1)Minimizing the number of wavelength conversions. (2) Minimizing the number of wavelength used.

4. Introduction (cont.1) • The RWA problem takes two flavors: (1)Off-line: All connection requests are know in advance. A routing decision can be made based on the complete knowledge of the traffic. (2)On-line: A connection request must be routed and wavelengths assigned independently of other connection.

5. Introduction (cont.2) • Finding a globally optimal solution for the off-line problem is NP-hard. • In this paper, we will seen a sub-optimal but computationally efficient method. • The work presented in this paper differs from others: (1) The limitation on wavelength conversion capabilities.

6. Introduction (cont.3) • The work presented in this paper differs from others (cont.): (2) Formulating problems with different objectives, whereas most of previous work has focus on single objective. (3) For each of the objectives, authors develop a sequential algorithm.

7. Problem Statement • Model as a undirected graph G(υ,ε), where |υ|=N, |ε|=J. • A wavelength set Λ={0,1,2,…..,K-1} of size |Λ|=K. • κj is maximum number of wavelengths which can be converted at node j. • ρj denotes the wavelength conversion capability still left at node j.

8. Problem Statement (cont.1) • R is request set and Li is a lightpath i. • Nk is the cost of using wavelength k on any link. • βk is a factor , if the wavelength has been used then the value is 0. • Define αnm(k) = 1, if wavelength k is available for use on that link. • The coloring of lightpath L is defined as the assignment of wavelength labels.

9. Problem Statement (cont.2) • A valid coloring must fulfill the following conditions: (1)Every link belonging to each lightpath must be colored. (2)If two consecutive links colored with different colors, there must be a wavelength conversion happened. (3)No two distinct lightpaths with a common link and in the same direction, can use the same wavelength at the common link.

10. Minimizing the number of wavelength conversions • Base on Dijkstra algorithm. • If there are multiple way, the method minimize the length of lightpath. • On-line algorithm begin:

11. Minimizing the number of wavelength conversions (cont.1) • Then find the minimizes value of ( j, k ), denote that (μ,ν).

12. Minimizing the number of wavelength conversions (cont.2) • If μ=N-1 thengo to step5, otherwise continue. For all j ∈ A(μ) and k ∈ Λ:

13. Minimizing the number of wavelength conversions (cont.3) • Step 5: Let m = 1, ξm = μ and Φm = ν. If f(ξm, Φm) = ∞ then stop.

14. Minimizing the number of wavelength conversions (cont.4) • The optimal lightpath consists of m nodes and equals (ξm, ξm−1, ··· , ξ1). • ξm = 0 and ξ1 = N − 1. • The number of wavelength conversions needed is the total of ∆(φi−1, φi) for i=2~m-1. • The variable βk is 0 if wavelength k has been used.

15. Minimizing the number of wavelength conversions (cont.4) • 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)

16. Minimizing the number of wavelength used • The method of solving the problem is identical to the one presented before, except. • The step 3 should be changed to:

17. Performance analysis • The two RWA strategies used are: (1)MinConv: minimizes the number of wavelength conversions on one request at a time. (2)MinWav: minimize the number of wavelengths used. • In this simulation we set N=32 and J=45 bidirectional link. • Each link has a capacity of 16 wavelengths in each direction (K =16).

18. Performance analysis (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.

19. Performance analysis (cont.2)Focus on blocking probability

20. Focus on blocking probability (2)

21. Performance analysis (cont.2)Focus on average number of hops

22. Performance analysis (cont.2)Focus on average number of OEO conversions

23. Conclusion • 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.

24. Thanks for listening !