1. Packet-Mode Emulation of Output-Queued Switches David Hay, CS, Technion Joint work with Hagit Attiya (CS) and Isaac Keslassy (EE)

2. Outline Cell-Mode Scheduling vs. Packet-Mode Scheduling Impossibility of an Exact Emulation Speedup-RQD Tradeoff  Emulation with S  4  Emulation with S  2 Emulation of OQ switch w/ bounded buffer Simulation Results

3. CIOQ Switches

4. Cell-Mode Scheduling

7. Trend towards Packet-Mode Cell-mode scheduling is getting too hard  Fragmentation and reassembly should work very fast, at the external rate  Extra header for each cell  loss of bandwidth For optical switches such fragmentation and reassembly are prohibitive Cell-mode schedulers are packet-oblivious  Degradation of the overall performance

8. Packet-Mode Scheduling

9. No need for fragmentation and reassembly Must ensure contiguous packet delivery over the fabric  While input i delivers a packet to output j, neither input i nor output j can handle other packets. Can packet-mode schedulers provide similar performance guarantees as cell-mode schedulers? [Marsan et al., 2002][Ganjali et al., 2003][Turner, 2006]

10. Output Queuing Emulation OQ switches are considered optimal with respect to queuing delay and throughput  But too hard to implement in practice… Emulation: Same input traffic  same output traffic How hard is it for cell-mode / packet-mode CIOQ switch to emulate OQ switch?

11. Output Queuing Emulation OQ switches are considered optimal with respect to queuing delay and throughput  But too hard to implement in practice… Emulation: Same input traffic  same output traffic How hard is it for cell-mode / packet-mode CIOQ switch to emulate OQ switch?

12. Easy with speedup S=N  N scheduling decisions every time-slot:  In the 1 st decision forward the cell of input 1  In the 2 nd decision forward the cell of input 2 ⋮  In the N th decision forward the cell of input N Cell-Mode Emulation is Possible

13. Easy with speedup S=N  N scheduling decisions every time-slot:  In the 1 st decision forward the cell of input 1  In the 2 nd decision forward the cell of input 2 ⋮  In the N th decision forward the cell of input N Cell-Mode Emulation is Possible

14. 1 st Key Concept: Slackness of a cell (in the input side) L(C) = OC(C) - IT(C) Slackness may decrease by at most 2 in every time-slot  A cell leaves the destination of C  OC--  A cell arrives at the input and is queued before C  IT++ Initial slackness can be made non-negative  When C arrive, Insert it in the OC(C) th place of its input buffer. Plan: Ensure that slackness always increases by 2  Slackness is never negative  All cells are delivered on time Cell-Mode Emulation w/ S=2 [Chuang et al.,1999] Input Thread: (“bad guys”) How many cells proceed C in its input-port buffer? Output Cushion: (“good guys”) How many cells are queued in the output-buffer of C’s destination, and should leave the OQ switch before C

15. Stable Marriage (stable matching): Given two equal-size sets M,W and preference lists from every m  M, w  W. Find a matching in which there are no two pairs (m,w),(m’,w’) s.t.  m prefer w’ over w  w’ prefer m over m Classical problem in CS  Stable marriage always exists  Many algorithms.. Cell-Mode Emulation w/ S=2 [Chuang et al.,1999]

16. Critical Cell First (CCF) algorithm performs stable marriage at each decision:  M is the set of inputs, W is the set of outputs  i prefers o 1 over o 2 if there is a cell for o 1 that is queued before all cells for o 2  o prefers i 1 over i 2 if there is a cell from i 1 that should leave before all cells from i 2 Cell-Mode Emulation w/ S=2 [Chuang et al.,1999]

17. For each cell C from input-port i to output port j, and each scheduling decision:  C is forwarded (and we don’t care about it)  C’ was forwarded from i, and i preferred to forward it  IT--  C’ was forwarded to j, and j preferred to receive it  OC++ Two scheduling decisions every time-slots  Slackness always increases by 2 Cell-Mode Emulation w/ S=2 [Chuang et al.,1999]

18. Easy with speedup S=N Possible with speedup S=2 (w/ CCF)  Lower bound: S≥2-1/N is required [Chuang et al.,1999] Cell-Mode Emulation What is the speedup required for packet-mode emulation?

19. Outline Cell-Mode Scheduling vs. Packet-Mode Scheduling Impossibility of an Exact Emulation Speedup-RQD Tradeoff  Emulation with S  4  Emulation with S  2 Emulation of OQ switch w/ bounded buffer Simulation Results

20. Packet-Mode Emulation is Impossible Regardless of speedup  Even with speedup S=N

21. Packet-Mode Emulation is Impossible

26. Outline Cell-Mode Scheduling vs. Packet-Mode Scheduling Impossibility of an Exact Emulation Speedup-RQD Tradeoff  Emulation with S  4  Emulation with S  2 Emulation of OQ switch w/ bounded buffer Simulation Results

27. Emulation w/ Relative Queuing Delay The CIOQ switch is allowed a bounded lag behind the shadow OQ switch  Exact same behavior as the optimal OQ switch, but with some extra delay  Called relative queuing delay Can we provide packet-mode OQ emulation with bounded RQD and small speedup?

28. Our Results: Speedup-RQD tradeoff Speedup RQD 2 4 2L max Lower bound on RQD (even with infinite speedup) Lower bound on the speedup (from cell-mode scheduling) Generalization of cell-mode scheduling with S=2: Taking each packet of size ≤ L max as one huge cell L max = maximum packet size (known value)

29. Intuition for Emulation Algorithms Packet Mode CIOQ Packet Mode OQ Cell Mode CIOQ w/ S=2

30. PIFO Cell-Mode OQ Switch FIFO = First-In First-Out

31. PIFO Cell-Mode OQ Switch FIFO = First-In First-Out PIFO = Push-In First-Out

32. PIFO Cell-Mode OQ Switch FIFO = First-In First-Out PIFO = Push-In First-Out  FIFO Packet-Mode OQ Switch is a PIFO Cell-Mode Switch

33. Underlying CCF Algorithm Cell-Mode CIOQ w/ CCF (and speedup S=2) emulates any PIFO cell- mode OQ switch [Chuang et al.,1999]  But, CCF does not maintain contiguous packet forwarding over the fabric! Packet Mode CIOQ Packet Mode OQ Cell Mode CIOQ w/ S=2 PIFO Cell-Mode OQ =

34. Intuition for Emulation Algorithms Packet Mode CIOQ Packet Mode OQ Cell Mode CIOQ w/ S=2 Two sub-steps: 1.Framing 2.Contiguous Decomposition

35. Frame-Based Schedulers Works in pipelined frame-based manner Within each frame: Build a demand matrix for this frame Schedule the demand matrix of the previous frame time

36. At each frame of size T, CCF forwards at most 2T cells from each input and to each output. Building the Demand Matrix Number of cells CCF sent from input 1 to output 1 in the last frame +++ + + + + + ++ + + ≤ 2T +++ + ++++ ++++ ≤ ≤ ≤ ≤ Problem: A packet may span several frames. 2T

37. Building the Demand Matrix Count only packets whose last cell is forwarded by the CCF in the frame Each row/column in the matrix is bounded by 2T+N(L max -1)  For each input-output pair only cells of one additional packet can be added. Translates into RQD of 2T+(L max -2).

38. Intuition for Emulation Algorithms Packet Mode CIOQ Packet Mode OQ Cell Mode CIOQ w/ S=2 Two sub-steps: 1.Framing 2.Contiguous Decomposition

39. Decomposing the Demand Matrix Challenge: Decompose the matrix into permutations while maintaining contiguous packet delivery.  Each permutation dictates a scheduling decision. First try: optimal Birkhoff von-Neumann decomposition results in 2T+N(L max -1) permutations.

40. Contiguous Greedy Decomposition To maintain contiguous packet delivery:  If (i,j) was matched in iteration t-1 and there are more (i,j) cells to schedule  keep for iteration t. Find a greedy matching for the rest of the matrix.  Speedup: RQD: 2T+L max -1

41. Our Results: Speedup-RQD tradeoff Speedup RQD 2 4 2L max S=4+ (N(L max -1))/T RQD = 2T+L max -1 Next…

42. Intuition for Emulation Algorithms Packet Mode CIOQ Packet Mode OQ Cell Mode CIOQ w/ S=2 Two sub-steps: 1.Framing 2.Contiguous Decomposition

43. Emulation w/ S  2 - Framing Keep a separate demand matrix for every possible packet size Example: Possible packets sizes are 3,4,6 # of size 3 packets # of size 4 packets # of size 6 packets

44. Emulation w/ S  2 - Framing Concatenate packets of the same size into mega-packets of size k =LCM(1,…,L max ) Leftover matrix for each size m size 6 size 4size 3Mega Packets (of size 12)

45. Emulation w/ S  2 - Framing Concatenate packets of the same size into mega-packets of size k =LCM(1,…,L max ) Leftover matrix for each size m size 6 size 4size 3Mega Packets (of size k=12)

46. Emulation w/ S  2 - Framing Concatenate packets of the same size into mega-packets of size k =LCM(1,…,L max ) Leftover matrix for each size m size 6 size 4size 3 (leftovers) Mega Packets (of size 12)

47. Emulation w/ S  2 - Framing Concatenate packets of the same size into mega-packets of size k =LCM(1,…,L max ) Leftover matrix for each size m size 6 size 4 (leftovers) size 3 (leftovers) Mega Packets (of size 12)

48. Emulation w/ S  2 - Framing Concatenate packets of the same size into mega-packets of size k =LCM(1,…,L max ) Leftover matrix for each size m size 6 (leftovers) size 4 (leftovers) size 3 (leftovers) Mega Packets (of size 12)

49. Emulation w/ S  2 - Framing Sum of each row/column is bounded  For mega packets matrix: ≤ (2T+N(L max -1))/ k  For each leftover matrix of size m: ≤ N( k -1)/m size 6 (leftovers) size 4 (leftovers) size 3 (leftovers) Mega Packets (of size 12) < 12/3 < 12/4 < 12/6

50. Emulation w/ S  2 - Decomposition Optimally decompose (w/ Birkhoff von- Neumann) the mega-packets matrix and then the leftover matrices Bound on the mega- packets matrix Hold each permutation k times for contiguous (mega)-packet delivery

51. Our Results: Speedup-RQD tradeoff Speedup RQD 2 4 2L max S=4+ (N(L max -1))/T RQD = 2T+L max -1 S=2+(NkL max -1)/T RQD = 2T+Lmax-1

52. Wrap-up Packet-mode scheduling can be done with the same speedup as cell-mode scheduling  With the price of bounded RQD  Future work: lower bounds ??

53. Thank You!