Andrea Fumagalli, Isabella Cerutti, Marco Tacca, Member of IEEE Presented by Shaun Chang

1. Optimal Design of Survivable Mesh Networks Based on Line Switched WDM Self-Healing RingsIEEE/ACM Transactions on Networking, Vol 11, NO.3, June,2003 Andrea Fumagalli, Isabella Cerutti, Marco Tacca, Member of IEEE Presented by Shaun Chang

2. Outline • Introduction • Mesh network with WDM bidirectional shared-line ring protection • Ubiquitous wavelength conversion availability case: ILP formulation • Limited wavelength conversion availability • Numerical Results • Summary

3. Introduction • Wavelength division multiplexing (WDM) offers a viable solution to the increasing need for higher bandwidth. • A network is considered survivable when it provides some ability to restored disrupted traffic demands due to network a component failure, such as a cable cut.

4. Introduction (cont’d) • Protection switching is currently implemented at higher layers, such as SONET/SDH, ATM and IP. • The recent availability of OADM and OXC offers a new dimension of make high-speed connections survivable. • A lightpath is a path of light between a source and a destination node. • SHRs/WDM : shared-line WDM self-healing rings

5. Introduction (cont’d) • Upon failure of a ring line, only the two nodes immediately adjacent to the faulted line need to perform rerouting of the interrupted traffic demands. • The problem of designing a mesh (arbitrary) topology by superposing multiple SHRs/WDM has been marginally studied. • The potential design constraints due to software and hardware complexity are not taken into account.

6. Introduction (cont’d) • This paper takes into account the following design constraints: • The maximum number of SHRs/WDM sharing line is bounded. • The maximum number of SHRs/WDM sharing a node is bounded. • The SHR/WDM maximum size (number of nodes is bounded.

7. Introduction (cont’d) • WDM self-healing rings with line protection problem consists of three subproblems: • WL subproblem : for every traffic demand, route the working lightpaths • RC subproblem : for every line carrying at least one working lightpath, identify the ring(s) covering the line and protecting the traffic • SW subproblem: for every ring in the cover, provision the spare wavelengths that are necessary to protect the working lightpaths.

8. Introduction (cont’d) • Objective • Minimize the total (working and protection) wavelength mileage required in a given network topology. • Limit the use of wavelength converters • Converter-free OADMs • Only OXCs support wavelength conversion

9. Outline • Introduction • Mesh network with WDM bidirectional shared-line ring protection • Ubiquitous wavelength conversion availability case: ILP formulation • Limited wavelength conversion availability • Numerical Results • Summary

10. Mesh network with WDM bidirectional shared-line ring protection • Working lightpaths are established between node pairs to support traffic demands. • A lightpath can rely upon multiple rings if necessary. • Optical crossconnect capabilities are required only at nodes where working lightpaths hop from one protection ring to another

11. Mesh network with WDM bidirectional shared-line ring protection • In case of a line fault, the two nodes immediately adjacent to the fault stop transmitting on the faulted line and reroute the interrupted working lightpaths along the provisioned counter rotating spare wavelengths.

12. Mesh network with WDM bidirectional shared-line ring protection

14. Mesh network with WDM bidirectional shared-line ring protection • ubiquitous wavelength conversion • wavelength conversion is available in both OADMs and OXCs • limited wavelength conversion • wavelength conversion is available only in the OXCs, i.e., the wavelength of a lightpath can be changed only when crossconnecting from one ring to another

15. Outline • Introduction • Mesh network with WDM bidirectional shared-line ring protection • Ubiquitous wavelength conversion availability case: ILP formulation • Limited wavelength conversion availability • Numerical Results • Summary

16. Ubiquitous wavelength conversion • solved with the objective of minimizing the total (working and protection) wavelength mileage

17. Ubiquitous wavelength conversion • Assumptions:

18. Definition : Input parameters

19. Definition : Input parameters

20. Definition : Constants

21. Definition : Variables

22. Objective Function

23. Subject to: WL subproblem

24. Subject to: RC & SW subproblem

25. Integrality constraints

26. Pruning the search space • Shortest Ring (SR) algorithm • The minimum total wavelength mileage for a single traffic demand is achieved by selecting the shortest ring that connects both source and destination • Set R is further augmented by adding the minimum weight rings that complete the covering of all lines

27. Pruning the search space • Shortest Ring (SR) algorithm • The minimum total wavelength mileage for a single traffic demand is achieved by selecting the shortest ring that connects both source and destination • Set R is further augmented by adding the minimum weight rings that complete the covering of all lines

28. Pruning the search space • Minimum Ring Distance Path (MRDP) algorithm • Based on the conjecture that a candidate path must rely upon the minimum number of rings • The size of set Psd is further reduced to k paths, where k is a varying parameter that can be used to control the complexity of the ILP formulation.

29. Auxiliary graph

30. Outline • Introduction • Mesh network with WDM bidirectional shared-line ring protection • Ubiquitous wavelength conversion availability case: ILP formulation • Limited wavelength conversion availability • Numerical Results • Summary

31. Limited wavelength conversion availability • wavelength converters are present only in OXC nodes. • The objective is to keep the number of required wavelength converters as minimal as possible. • This is equivalent to minimizing the number of rings that are required to protect a lightpath. • In many cases the two cost functions, i.e., wavelength mileage and number of converters, have conflicting objectives.

32. Ring assignment

33. Heuristic 1: Minimize the Number of Wavelength Converters First • Step1: • Minimize the number of rings assigned to each working lightpath given both the ring cover R0 and the set of working lightpaths P0 . For each lightpath, the ring assignment problem is solved by selecting the ring sequence with the smallest number of rings. The sequence is found by applying a shortest path algorithm [23] to the auxiliary graph.

34. Heuristic 1: Minimize the Number of Wavelength Converters First • Step2: • Minimize the wavelength mileage of each ring without changing the working lightpath-ring assignments found in Step 1. Based on the result of Step 1, the capacity of each ring to ensure 100% protection against any single line fault is determined.

35. Heuristic 2: Minimize the Wavelength mileage First • Step 1: • Minimize the number of rings assigned to each working lightpath. For each lightpath, two integer values are derived: • rd: the smallest number of rings required to protect the entire lightpath; • RD: the largest number of rings required to protect the entire lightpath • Subsequently, the lightpaths are sorted according to the nondecreasing difference ( RD-rd ) .

36. Heuristic 2: Minimize the Wavelength mileage First

37. Outline • Introduction • Mesh network with WDM bidirectional shared-line ring protection • Ubiquitous wavelength conversion availability case: ILP formulation • Limited wavelength conversion availability • Numerical Results • Summary

38. Numerical Results • A. Seven-Node Benchmark Network

39. Seven-Node Benchmark Network • N = 7 nodes • L = 22 unidirectional lines • The weight (length in miles) of the lines is shown in the figure

40. Seven-Node Benchmark Network

41. European Network

42. European Network • N = 19 nodes • L = 78 unidirectional lines • Total number of requested lightpaths = 1352

43. Total wavelength mileage

44. Average number of wavelength converter

45. Total wavelength mileage

46. Summary • This paper addressed the problem of optimally designing WDM networks with arbitrary topologies using self-healing WDM rings (SHRs/WDM), referred to as the WRL problem. • The proposed approach to designing survivable WDM networks is therefore close to optimal, relatively large networks with dozens of nodes can be designed the worst case recovery time of the SHR/WDM can be determined by limiting the maximum size of the rings, and node hardware and network management complexity can be limited by bounding the maximum number of rings that may share the same node and the same line.

47. Overall Gain of a SFG • The general problem in network analysis of finding the relation between response (output) to stimulus (input) signals is equivalent to finding the overall gain of that network. • In SFG analysis, this can be done by two general methods: • Node Absorption (Elimination) method. In this method, the overall gain of SFG from a source node to a sink node may be obtained by eliminating the intermediate nodes. • Mason's rule method.

48. Mason's rule is a general gain formula can be used to determine the transfer functions directly. (i.e., relates the output to the input for a SFG. ) Mason's Rule Thus the general formula for any SFG is given by : Where, Pi : the total gains of the ith forward path D = 1 - (  of all individual loop gains) + (  of loop gains of all possible non-touching loops taken two at a time) - (  of loop gains of all possible non-touching loops taken three at a time) + … Di = the value of D evaluated with all gain loops touching Piare eliminated. Notice: In case, all loops are touching with forward paths (Pi) , Di = 1

49. V5(s) Touching loops: Loops with one or more nodes in common are called touching. A loop and a path are touching when they have a common node. Non-touching loops : Loops that do not have any nodes in common Non-touching loop gain : The product of loop gains from non-touching loops. Example :Find C/R for the attached SFG. Forward Path gain: (Only one path, So, i =1)  P1 = G1.G2.G3.G4.G5 ……………. (1) Loop gains: L1: G2.H1 L2: G4.H2 L3: G7.H4 L4:G2.G3.G4.G5.G6.G6.G7.G8 Non-touching loops taken two at a time: L1&L2 : G2.H1.G4.H2 L1&L3 : G2.H1.G7.H4 L2&L3 : G4.H2.G7.H4 Non-touching loops taken three at a time: L1,L2&L3: G2.H1.G4.H2.G7.H4

50. sum of all individual loop gains According to Mason’s rule: sum of gain products of all possible non-touching loops taken two at a time  = 1 - (G2.H1 + G4.H2 + G7.H4 + G2.G3.G4.G5.G6.G7) + [G2.H1.G4.H2 + G2.H1.G7.H4 + G4.H2.G7.H4] – [G2.H1.G4.H2.G7.H4] ……. ……. ……… (2) Then, we form ibyeliminating from  the loop gains that touch the forward path (Pi).  1=  - loop gains touching the forward path (Pi). sum of gain products of all possible non-touching loops taken three at a time • 1= 1 - G7.H4 …..……. ……… (3) Now Substituting equations (1) , (2) & (3) into the Mason’s Rule as :