1. 1 The Optimal Multiple Multicast Problem on WDM Ring 演講者 : 丁德榮 弘光科技大學 資訊管理系助理教授 兼電算中心主任 Mail: deron@sunrise.hk.edu.tw

2. 2 Outline Introduction Multicast Problem on WDM Multiple Multicast Problem on WDM Ring Solution Methods Results Conclusion and Further Research Topics

3. 3 What is WDM Wavelength Division Multiplexing (WDM) –Each wavelength is an independent communication channel –Multiple wavelengths channels can be multiplexed into one fiber

4. 4 Why WDM? Provide huge bandwidth using fiber –Fiber has about 50 terabits per second –Multiple WDM channels provide huge aggregate bandwidth in a single fiber Avoid the bottleneck of increasing baud rate –Current peak rate is about only 10 Gbps –Implementation of higher bit rate using fiber for long- distance transmission is more difficult –Multiple WDM channels with peak rate can achieve huge capacity Upgrade network capacity without fiber re- deployment

5. 5 Optical Components in WDM Networking Optical Transmitter –Tunable transmitter –Fixed transmitter Transmit at a fixed wavelength Optical Receivers (Filters) –Tunable receiver –Fixed receiver Filter out one or multiple wavelengths from

6. 6 Optical Components in WDM Networking Wavelength multiplexer & demultiplexer 1, 2,…, n 1 2 n 1 2 n Multiplexer Demultiplexer

7. 7 Optical Components in WDM Networking Wavelength router

8. 8 Optical Components in WDM Networking Wavelength converter –Main function: convert the input wavelength from one to another –Used to raise wavelength utilization and reduce call blocking rate Wavelength Converter s c s = 1,2,…,N c = 1,2,…,N

9. 9 Two Kinds of WDM-based LAN Single-hop systems –The source node’s transmitter and the destination node’s receiver always tune to the same wavelength. –Direct transmission without store-and-forward by intermediate nodes. –Transmission coordination is necessary to avoid channel collision and receiver collision. Multi-hop systems –Only some pair of nodes have direct transmission. –Traffic between two nodes may be stored-and-forwarded via intermediate nodes. –Wavelength converter is need

10. 10 Wavelength-Routed Network Light-path: the all-optical communication channel between two nodes.

11. 11 Wavelength-Routed Network Constraints –Wavelength continuity A light-path is required to be on the same wavelength throughout its path. Wavelength converter can be used to change the wavelength in one light-path. –Different light-paths traversing the same fiber must be on different wavelengths

12. 12 Research Problems Virtual topology embedding Topological optimization Virtual topology reconfiguration Routing and wavelength assignment (RWA) Optimization problems due to using wavelength converters Multicast problem Placement Problem

13. 13 Multicast Problem on WDM Multicast is a point to multipoint communication, by which a source node sends messages to multiple destination nodes. A light-tree, as a point to multipoint extension of a light-path, is a tree in the physical topology and occupies the same wavelength in all fiber links in the tree. Definition: given an multicast request in a WDM network system, compute a set of routing trees and assign wavelengths to them such the cost is minimized.

14. 14 Multiple Multicast Problem on WDM Ring WDM Model –Single-hop WDM network –All Optical Network –Ring –Multicast Capability (light-splitting capability) –Static Traffic

15. 15 Problem Definition Ring network G(V,E) –V: the set of nodes –E: the set of links –bi-directional link –W wavelengths per link 。

16. 16 Problem Definition r groups of multicasts ， –M i ={s i, D i } ， i=1, 2, …, r, 1 ≦ k i ≦ n ； where –D i ={d 1i, d 2i, …, d kii } be the destination –s i :source –For each multicast M i ={s i, D i } ， a multicast tree MT i is need –Construct a multicast forest MF=U i=1,2,…r MT i 。 –Construct MF with wavelength continuity constraint, such the number of used wavelengths is minimized 。

17. 17 OMMP Optimal multiple multicast problem, OMMP 給定一個 WDM 網路與 r 個多點傳送的需求所成的 集合 M={Mi={si, Di} ， i=1, 2, …, r, 1 ≦ ki ≦ n} ，建 立一個多點傳送樹林，並決定每一個多點傳送樹 之波長通道指派，使的所需求的波長通道為最少。 OMMP is a NP-hard problem Since RWA(NP-hard) is a special case of OMMP RWA on Ring is a NP-hard problem.

18. 18 Example

19. 19 Possible Assignment of Example

20. 20 Observation Each MT i can be constructed by ： – 建立一個順時針方向的路徑： P c (s i, d l-1i ) – 建立一個逆時針方向的路徑： P r (s i, d l+1i ) – 建立兩個路徑，一個順時針與逆時針之路徑 P r (s i, d l’i ) 與 P c (s i, d l’i ) ，對某一個 l’  D 。

21. 21 Model

22. 22 Solution Methods Heuristic Algorithms Genetic Algorithms

23. 23 Heuristic Algorithms Two phases –Routing Phase: R1: Maximal-gap Routing R2: Minimal Load Routing –Assignment Phase: A1: Greedy Method A2: Approximation Method: 7/4-approximation algorithm

24. 24 Maximal Gap Routing

25. 25 Greedy Method

26. 26 Genetic Algorithm

27. 27 Genetic Algorithm Chromosome Encoding Objective Function Penalty Function Crossover Mutation Selection

28. 28 Chromosome Encoding routing gene MG i ={mg i k, i=1,...,r; k=1,2} AG i ={ag i k, i=1,...,r; k=1,2} r: number of connections. r=4 7127...38122234

29. 29 Example of chromosome encoding 1 2 3 4 5 8 7 6

30. 30 Wavelength gene

31. 31 Objective Function Objective function The assignment represented by the connection may not constraint-satisfy, thus, a penalty function should be included in objective function.

32. 32 Penalty Function Assume both connections c 1 =(1,2) and c2=(1,4) are assigned to wavelength 1 with clockwise direction, then conflict occurred. Penalty should be defined. How to detect the conflict in a connection gene? A conflict-detection algorithm should be developed. O(M 2 ) pairs of connections should be examined. The conflict between two connections can be detected in constant time O(1).

33. 33 Conflict-detection Algorithm Construct four bipartite graph AA, AB, BA, BB, Node: connection Edge: conflict occurred –A: clockwise direction –B: counter-clockwise direction

34. 34 Experiments Run on PC with a Pentium III 1GHz CPU and 512MB RAM. For nodes n=100, 200, 300 Two sets of multicast requests are randomly generated. –Specific –Random MAXM={5, 10} : the maximal number destinations in D.

35. 35 Specific Set Ranges A i = { j | n*(i-1)/5+1 ≦ j ≦ n*i/5 } The source and destination nodes of multicast M i, i=1,2,...,r are randomly selected from nodes in A i and two of which are n*(i-1)/5+1 and n*i/5. The lower bound of the minimal used wavelengths of the set M specific is n/5.

36. 36 Specific n=100 (MAXM =5 or 10)

37. 37 Specific n=200 (MAXM =5 or 10)

38. 38 Specific n=300 (MAXM =5 or 10)

39. 39

40. 40 Random n=100 (MAXM =5 or 10)

41. 41 Random n=200 (MAXM =5 or 10)

42. 42 Random n=300 (MAXM =5 or 10)

43. 43

44. 44 More Improvement

45. 45 More Improvement

46. 46 Conclusion and Further Research Proposed –Mathematic Model for multiple multicast problem on WDM ring –Several Heuristic Algorithms –Genetic Algorithms Further Research in the problem –Lower bound proof –CPLEX package to found optimal solution –Other Soft-computing method Simulated Annealing, Tabu search, Ant algorithm, Scatter search

47. 47 Further Extension Dynamic traffic case: minimize blocking probability Allow dynamic joining and leaving multicast group Different WDM Model –Multi-hop WDM –Partial Multicast Capacity –Different Network Topology: Mesh, General Network Other research problem –Group Communication Problem