1. CSC 778 Presentation Waveband Switching Neil D’souza Jonathan Grice

2. What is Waveband Switching? Grouping wavelengths into bands –Switch as groups rather than individual wavelengths –Using a single port Only demultiplex to add/drop traffic –75% of traffic is bypass Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Wavelength

3. Why Waveband Switching? $$$ Reduced Port Count Size Power Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004

4. So how does this reduce port count??? Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 No waveband switching: Node A: 1 incoming fiber port 8 incoming wavelength ports 8 outgoing wavelength ports 2 outgoing fiber ports Total: 19 ports

5. So how does this reduce port count??? Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 No waveband switching: Node A: 1 incoming fiber port 2 incoming waveband ports 2 outgoing waveband ports 2 outgoing fiber ports Total: 7 ports – over 50% reduction!

6. A 3-Layer MG-OXC w/ WLC Switch a wavelength Switch a waveband Switch a fiber Wavelength conversion Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004

7. Wavelength Conversion Input/Output on different wavelength –Expensive, signal degradation In waveband switched networks: –Even if ports & converters available, conversion requires demultiplexing to wavelength level. Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004

8. Waveband Assignment with Path Graph An algorithm to satisfy a new request –Minimize use of wavelength conversion –Maximize benefit of wavebanding Assumes: –Fixed routing –Intraband wavelength conversion Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004

9. Our example: Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Waveband Assignment with Path Graph Wavelength conversion New Path Existing Path Fibers have 4 wavelengths in 2 bands

10. Step 1: Split nodes by wavelength Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Waveband Assignment with Path Graph

11. Step 2: Add converters Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Waveband Assignment with Path Graph

12. Step 3: Draw available wavelengths Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Waveband Assignment with Path Graph

13. Step 4: Assign weights Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Waveband Assignment with Path Graph Wavelengths = λ Converters = # wavelengths x # hops 11 22 33 444 3 2 16

14. Step 5: Create logical source & destination Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Waveband Assignment with Path Graph 11 22 33 444 3 2 16 0 0 0 0 0 0 0 0

15. Dijkstra’s Algorithm: With the weighted links will: 1. Try to find a wavelength continuous path 2. Try to find a path using the minimum number of wavelength converters. Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004

16. Step 6: Find path Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Waveband Assignment with Path Graph 11 22 33 444 3 2 16 0 0 0 0 0 0 0 0

17. Another Example: Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Waveband Assignment with Path Graph 11 2 3 44 3 16 0 0 0 0 0 0 0 0

18. Another Example: Random Fit Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Waveband Assignment with Path Graph 11 2 3 44 3 16 0 0 0 0 0 0 0 0

19. Another Example: First Fit Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Waveband Assignment with Path Graph 11 2 3 44 3 16 0 0 0 0 0 0 0 0

20. Another Example: Path Graph Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Waveband Assignment with Path Graph 11 2 3 44 3 16 0 0 0 0 0 0 0 0

21. Performance Results: With no conversion same as First Fit –Fixed routing – path already set Less blocking than First Fit or Random Fit Intraband conversion – nearly as good as full –High cost to demux two bands Large reduction in wavelength conversion Even better when not all fibers can be demuxed Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004

22. Waveband Aggregation techniques Source to End Switching Intermediate Waveband Switching –Intermediate to Destination (ITD-WBS) –Source to Intermediate (STI-WBS)* –Both-end-to-Intermediate (BETI-WBS)

23. Terms used Waveband granularity is defined as the number of wavelengths that can be grouped or aggregated into a waveband. Uniform waveband switching if the granularity of all the wavebands is an arbitrary constant g.

24. Wavelength Grooming Problem is to groom wavelengths into wavebands such that the number of ports saved is maximized. Depends on Uniform or Non-uniform waveband switching. Depends on the location of aggregation.

25. Intermediate-to-destination uniform waveband switching: (ITD-UWBS) Inputs : –Graph G=(V,E) –Routed Demands P d ={p 1,p 2,……..,p k } –Lightpaths for each demand C={c 1,c 2 ……..c k } –Destination : d –Waveband granularity : g

26. Limitations Connections that have the same destination. Complete set of paths can be partitioned into sub-sets based on their destination nodes. Waveband grooming only occurs among paths within a partition and not across partitions

27. Notations Waveband B of granularity g is denoted by (Q, s, d, g) Q = {(p1, b1), (p2, b2),... (pm, bm)} Set of tuples (pi, bi) –p i is a routed-demand –b i is the number if units (lightpaths) of the routed-demand.

28. Notations number of wavelength ports used by a waveband of length L and granularity g is 4g + 2(L + 1). number of ports required for routing g wavelength level connections of length L is 2g(L + 1) number of ports saved by a waveband route of length L and granularity g is 2(L + 1)(g − 1) − 4g.

29. Algorithm (ITD-WBS) Algorithm 1 1: Input: (G, Pd, C) –Pd = {p1, p2,..., pm} –C = {c1, c2,..., cm} 2: Output: Destination-rooted capacitated tree T 3: compute graph T using paths in the set Pd 4: transform T into a tree by deleting cycles in T and modifying paths accordingly 5: compute the height hi for each node i in the tree T 6: initialize the residual capacity Rj of the leaf node j to ni where j the source node of the path pi 7: compute the residual capacity Ri of each intermediate node i as the sum of the residual capacities of its child nodes

30. A B Dest Source 2 Source 1 4 9 9 9 4 4 Paths p1 : dabs1; c1 = 4 p2 : dbas2; c2 = 9 Subset of Graph with Cycles

31. A B Dest Source 2 Source 1 9 9 5 4 4 Paths p1 : dbs1; c1 = 4 p21 : das2; c21 = 4 p22 : dbas2; c22 = 5 With No Cycles

32. Dest Source 2 1 9 4 5 4 Assign Heights Source 1 Source2 B A 4 5 A G = 3 0 1 1 2 2 3 2

33. Dest Source 2 1 Calculate Residual Capacities Source 1 Source2 A A G = 3 0,13 1,4 1,9 2,5 2,4 3,5 2,4 B

34. Algorithm 2 1: Input:(G, Pd, C, g) 2: Output: Waveband set B 3: run Algorithm 1 on input (G, Pd, C) 4: for i = h; i ≤ 2; i−− do 5: for each u where hu = i, and Ru ≥ g do 6: if ((Su = 2(i + 1)(g − 1) − 4g) > 0) then 7: form waveband B = (Q, u, d, g) from node u to root node d and add to B 8: update the residual capacities Ru of all the nodes along the paths included in the waveband 9: end if 10: end for 11: end for

35. Dest Source 2 1 Iteration 1 Source 1 Source2 A A G = 3 0,13 1,4 1,9 2,5 2,4 3,5 2,4 B

36. Source 2 1 Iteration 2 Source 1 Source2 A A G = 3 0,10 1,4 1,6 2,2 2,4 3,2 2,4 B Dest Waveband: B1=s 2 -a-b-d

37. Source 2 1 Iteration 3 Source 1 Source2 A G = 3 0,7 1,4 1,3 2,2 2,1 3,1 2,4 B Waveband: B1=s 2 --a--b---d B2= s1—b---d A Dest

38. Source 2 1 Iteration 4 Source 1 Source2 A G = 3 0,4 1,1 1,3 2,2 2,1 3,2 2,1 B Waveband: B1=s 2 --a--b---d B2= s1—b---d B3= s2---a---d A Dest

39. Source 2 1 Iteration 5 Source 1 Source2 A G = 3 0,1 1,1 1,0 2,2 2,1 3,2 2,1 B Waveband: B1=s 2 --a--b---d B4= b-d B2= s1—b---d B3= s2---a---d A Dest

40. Algorithm for BETI waveband switching Create a Destination-rooted capacitated tree and Source rooted capacitated tree.

41. Algorithm 3 The Initialization Algorithm for the BETI problem. 1: Input: (G, P,C) 2: compute graphs Tt and Ts using paths in the set P 3: add super destination node d and super source node s to trees Tt and Ts respectively 4: add edges from node d to all the destination nodes in tree Tt 5: add edges from node s to all the source nodes in tree Ts 6: transform Tt and Ts into a trees by deleting cycles in Tt and ts and modifying paths accordingly 7: compute the height hi for each node i in the tree T 8: initialize the residual capacity Rj of the leaf node sj of the tree Tt to ni where sj the source node of the path pi 9: initialize the residual capacity Rj of the leaf node tj of the tree Ts to ni where tj the source node of the path pi 10: compute the residual capacity Ri of each intermediate node of the trees Tt and Ts as the sum of the residual capacities of its child nodes

42. Algorithm 4 The BETI Algorithm for computing the wavebands. 1: Input:(G, P,C) 2: Output: Waveband set B 3: run Algorithm 3 on input (G, P,C) to compute trees Tt and Ts 4: let ht and hs be the heights of the trees 5: let h be the maximum of the heights hd and ht 6: for i = h; i ≤ 2; i−− do 7: for each u in Tt and Ts where hu = i in the corresponding tree, and Ru ≥ g do 8: if ((Su = 2(i + 1)(g − 1) − 4g) > 0) then 9: form waveband B = (Q, u, d, g) from node u to root node d/s corresponding to tree Tt/Ts and add to B 10: update the residual capacities Ru of all the nodes along the paths in included in the waveband in both the trees Tt and Ts 11: end if 12: end for 13: end for

43. ?

44. HAPPY HALOWEEN

45. BACKUP

46. Wavelength Assignment Methods: Always start with lowest wavelength If there is a continuous path – TAKE IT! Else: –Random fit: Randomly choose next wavelength –First fit: Choose the first available wavelength –Path Graph: Use dijkstra’s algorithm to find path Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004

47. So how does this reduce port count??? An simple example: –1 fiber – 64 wavelengths – 8 bands –Need to drop 1 wavelength Wavelength Assignment in Waveband Switching Networks with Wavelength Conversion; Cao, Qiao, Anand & Li ©2004 Traditional OXCWaveband Switching BXC Ports:08 in – 8 out OXC Ports:64 in – 64 out8 in – 8 out Total:12832