1. ILP formulations and solution techniques For Optical network design problems Supervised by Dr. Abd ElKarim Shaban Omr Professor, Faculty of Engineering, Cairo University Dr. Khaled Mohamed Fouad Elsayed Professor, Faculty of Engineering, Cairo University By Zein ElAbedin Mohamed Wali

2. Agenda Optical Networks (why?) Routing and Wavelength Assignment (what?) Solution approaches (how?) Proposal

3. Agenda Optical Networks (why?) Need for new network solution Optical Networks Advantages Multiplexing techniques WRON’s Lightpath Routing and Wavelength Assignment (what?) Solution approaches (how?) Proposal

4. Optical Networks (Need for new network solution) The need for new network solution emerges from the following reasons: More users More bandwidth-intensive networking applications (voice, video, ….) New generation networks involving HD-TV, Video mail, …etc

5. Optical Networks (Cont.) (Optical Networks Advantages) Based on fibers, Optical networks can be best suited for the above demands: 1. huge bandwidth (nearly 50 terabits per second (Tbps) 2. low signal attenuation (as low as 0.2 dB/km) 3. low signal distortion (immune to electromagnetic interference) 4. low power requirement 5. low material usage 6. small space requirement, and 7. low cost.

6. Optical Networks (Cont.) (Multiplexing techniques) Different Multiplexing techniques may be used to efficiently utilize the huge bandwidth provided by optical networks: Space-division multiplexing (SDM) Frequency/Wavelength-division multiplexing (FDM/WDM) Time-division multiplexing (TDM) Code-division multiplexing (CDM)

7. Optical Networks (Cont.) (WRON’s) WDM Routed Optical Networks WRON’s: (Fiber bandwidth is divided between several independent logical channels each carried on different wavelength) Fiber Tx Rx

8. Example WRON: Optical Networks (Cont.) (WRON’s)

9. Example WRON (OXC structure)

10. Optical Networks (Cont.) (Lightpaths) A lightpath is the basic mechanism of communication in WRON. lightpath (also referred to as -channel), is a clear optical path –alternatively referred to as an all-optical communication channel -between two edge nodes, it bypasses electronic packet processing at intermediate nodes. It is realized by finding a physical path and allocating a free wavelength on each link of that path

11. Agenda Optical Networks (why?) Routing and Wavelength Assignment (what?) Problem statement Wavelength conversion Classification Solution approaches (how?) Proposal

12. Routing and Wavelength Assignment (RWA) (Problem statement) Problem statement: Given: – Set of lightpaths demands that need to be established. – A constraint on the number of wavelengths. Required: – To determine the routes over which these lightpaths should be set up. – Also to determine the wavelengths that should be assigned.

13. RWA (Cont.) (Problem statement) Example:

14. RWA (Cont.) (Problem statement) Constraints: 1. Wavelength continuity constraint: A lightpath must use the same wavelength on all the links along its path from source to destination edge node 2. Distinct wavelength constraint: All lightpaths using the same link (fiber) must be allocated distinct wavelengths

15. RWA (Cont.) (Problem statement) Illustration (wavelength continuity):

16. RWA (Cont.) (Wavelength Conversion) The OXCs may be equipped with wavelength converters. If all the OXC have such capability, the wavelength continuity constraint is relaxed, and the RWA problem is reduced to classical routing problem (in Circuit-switched networks)

17. RWA (Cont.) (Wavelength Conversion) Illustration: B D C A E 2 Wavelength converter 1 2 1 1 Lightpath

18. RWA (Cont.) (Classification) Classification: Traffic type: Static Incremental Dynamic Wavelength-conversion capability: Full-wavelength conversion Sparse wavelength conversion No wavelength conversion Objective function: Min-RWA Max-RWA

19. RWA (Cont.) (Classification) Fiber multiplicity Requests multiplicity formulation structure: Link-Based Path-Based

20. Agenda Optical Networks (why?) Routing and Wavelength Assignment (what?) Solution approaches (how?) Proposal

21. Solution approaches(1) Min-RWA, link-based, no conversion, unique requests, single fiber: Problem decomposition into: – Routing sub-problem – Wavelength Assignment sub-problem

22. Solution approaches(1) Routing:

23. Solution approaches(1) Wavelength Assignment: using Graph Coloring

24. Solution approaches(2) Min-RWA, link-based, no conversion, multiple requests, single fiber (routing)

25. Solution approaches(3) Min-RWA, link-based, full-wavelength conversion, unique requests, single fiber This case reduces the RWA problem to the classical routing problem once lightpaths has been established, any wavelength available on any link may be used not of much commercial importance, since in most cases full wavelength conversion in the network is not preferred and not even necessary due to high costs and limited performance gains.

26. Solution approaches(4) Max-RWA, path-based, no conversion, multiple requests, single-fiber (Selection & WA)

27. Solution approaches(4) Illustration: P(sd 1 ) P(sd 2 ) P(sd R ) SD 1 SD 2 SD R Connection requests Candidate pathsLinks Capacity constraints are applied for each link, such that each wavelength is used at most once A Matrix B Matrix

28. Solution approaches(5) Max-RWA, path-based, no conversion, multiple requests, single-fiber

29. Solution approaches(5) Illustration: P(sd 1 ) P(sd 2 ) P(sd R ) SD 1 SD 2 SD R Connection requests Candidate paths A Matrix W1 Set of path-flow variables Set of wavelengths W2 WwWw f1 f2 fRfR D Matrix f Vector

30. Solution approaches(6) Max-RWA, link-based, no conversion, multiple requests, single-fiber (Routing & WA)

31. Solution approaches(7) Max-RWA, link-based, no conversion, multiple requests, single-fiber (Routing & WA)

32. Solution approaches(8) Max-RWA, path-based, no conversion, multiple requests, mutli-fiber (Selection & WA)

33. Solution approaches(8) Applied Heuristic Start End All connections satisfied? No. of used Wavelengths = No. of used Wavelengths +1 No Yes Report solutio n Call Greedy Algorithm for maximum coverage No. of used Wavelengths = 0 Assign the paths for the satisfied connection the current wavelength

34. Solution approaches(9) Greedy Heuristic Approach Maximum Edge Disjoint Paths problem: Given: a graph and a set of source- destination pairs are given and the requirement is to find Edge disjoint paths for as many of the pairs as possible Start End All connections satisfied? No. of used Wavelengths = No. of used Wavelengths +1 No Yes Report solution Call Greedy Algorithm for EDP No. of used Wavelengths = 0 Assign the paths for the satisfied connection the current wavelength

35. Solution approaches(10) Min-RWA, path-based, full conversion, unique requests, single-fiber (Selection & WA)

36. Solution approaches(10) Objective function used The cost function of every link is convex, monotonically increasing, and piecewise linear. The breakpoints of each piecewise linear link cost function occur at the integer points The cost for flow larger than W is , thereby imposing a link capacity constraint.

37. Solution approaches(11) Min-RWA, path-based, no conversion, unique requests, single-fiber (Selection & WA)

38. Solution approaches(12) Min-RWA, path-based, sparse conversion, unique requests, single-fiber (Selection & WA) W Converter No W Converter

39. Solution approaches(12) Approach:

40. Solution approaches(13) Min-RWA, path-based, sparse conversion, multiple requests, multi-fiber (Selection & WA)

41. Solution approaches(13) Min-RWA, path-based, sparse conversion, multiple requests, multi-fiber (Selection & WA)

42. Solution approaches(14) Tabu Search Heuristic Approach

43. Agenda Optical Networks (why?) Routing and Wavelength Assignment (what?) Solution approaches (how?) Proposal Motivation Proposed Model Network growing problem TU-Based solution technique (in progress)

44. Proposal (Motivation) Motivation: – Only few models addressed the Min-RWA problem. – Mostly all the approaches presented ILP models, but relied on approximation or heuristic algorithms to solve the problem especially for large size networks. – No model addressed the Min-RWA problem with multi-fiber links case.

45. Proposal (Proposed Model) Min-RWA, Path-based, no conversion, multiple requests, Multiple-fiber Handling multiple-fibers: Network is modeled to an undirected multi- graph instead of a simple undirected graph 102 102

46. Proposal (Cont.) (Proposed Model) ILP formulation (Selection & WA)

47. Proposal (Cont.) (Proposed Model) Weights selection: Lemma 1: At optimality, the traffic demand must be satisfied at equality. Moreover, using any monotonically increasing weights for the increasing index wavelengths will ensure that the minimum number of wavelengths is used.

48. Proposal (Cont.) (Proposed Model) Proof: ( By contradiction) The traffic demand constraint: The capacity constraint:

49. Proposal (Cont.) (Network Growing Problem) Given: – Set of lightpaths demands that need to be established. – A constraint on the number of wavelengths. When the current network topology and resources does not satisfy the demanded requests, it is required to obtain the minimum set of modifications (in terms of additional resources) to satisfy the connection requests. Our assumption: the suggested modifications are only the addition of fibers to already existing links.

50. Proposal (Cont.) (Network Growing Problem) Read input data from file End Feasible? Build new model with worst case no. of wavelengths Solve the model No Yes Report solution Calculate modifications Solve the model Build the LP model Start /*Values obtained from the 2nd run */ W = the number of available wavelengths per link. W(L) = the needed number of wavelengths on link L For each node pairs (i,j) For each link Lij (between the nodes (i,j) If ( W (Lij) < W ) freeWaves = freeWaves + W- W(Lij) EndFor For each link Lij (between the nodes (i,j) If (( W(Lij) > W ) && ( freeWaves < W(Lij) – W) ) Fibers to add = ceil ((W(lij)-W-freeWaves)/W) EndFor Solution approach:

51. References 1. Biswanath. Mukherjee, "Optical communication networks", McGraw-Hill Publishers, 1997 2. D. Banerjee, and B. Mukherjee, “A practical approach for routing and wavelength assignment in large wavelength-routed optical networks," IEEE Journal on Selected Areas in Communications, Vol. 14 No. 5, 1996 3. R. Ramaswami and K. Sivarajan, “Routing and wavelength assignment in all- optical networks”, IEEE/ACM Trans. Networking, vol. 3, October 1995. 4. R.M. Krishnaswamy, K.N. Sivarajan, “Algorithms for Routing and Wavelength Assignment Based on Solutions of the LP-Relaxation”, IEEE Communications Letters, vol. 5, no. 10, October 2001. 5. Mohamed Saad, Zhi-Quan Luo, "On the Routing and Wavelength Assignment in Multifiber WDM Networks", IEEE Journal on Selected Areas in Communications (special series on optical communications and networking), vol. 22, no. 9, November 2004. 6. A.E. Ozdaglar, D.P. Bertsekas, “Routing and Wavelength Assignment in Optical Networks”, IEEE/ACM Transactions on Networking, vol. 11, no. 2, April 2003.

52. References 7. Steven S. W. Lee, Maria C. Yuang, Po-Lung Tien, and Shih-Hsun Lin, "A Lagrangean Relaxation-Based Approach for Routing and Wavelength Assignment in Multigranularity Optical WDM Networks", IEEE Journal on Selected Areas in Communications (special series on optical communications and networking), vol. 22, no. 9, November 2004. 8. Christiane Dzongang, Philippe Galinier, and Samuel Pierre, "A Tabu Search Heuristic for the Routing and Wavelength Assignment Problem in Optical Networks", IEEE Communications letters, Vol. 9, No. 5, May 2005.

53. Thank You!