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

2. CIOQ Switches

3. Cell-Mode Scheduling

6. 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

7. Packet-Mode Scheduling

8. 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]

9. 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?

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. 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 Possible with speedup S  2: CCF algorithm Lower bound: S≥2-1/N is required [Chuang et al.,1999] Cell-Mode Emulation is Possible What is the speedup required for packet-mode emulation?

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

13. Packet-Mode Emulation is Impossible

18. 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?

19. 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 First algorithm: S  4 with RQD=O(NL max )

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

21. Underlying CCF Algorithm Observation: Packet-Mode OQ switch is a Cell-Mode OQ switch with different queuing discipline (called PIFO) 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 =

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

23. 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

24. 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

25. 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.

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

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

28. 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. Iteration t-1 Iteration t Cells left from 1 to 1  Speedup: RQD: 2T+L max -2

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

30. Packet-Mode Emulation w/ S  2 Separate demand matrix for every possible packet size Concatenate packets of the same size into mega-packets of size k =LCM(1,…,L max ) Leftover matrix for each size m Packet Mode CIOQ Packet Mode OQ Cell Mode CIOQ w/ S=2 Two sub-steps: 1.Framing 2.Contiguous Decomposition

31. Packet-Mode Emulation w/ S  2 Optimally decompose (w/ Birkhoff von-Neumann)  the mega-packets matrix  then the leftover matrices Packet Mode CIOQ Packet Mode OQ Cell Mode CIOQ w/ S=2 Two sub-steps: 1.Framing 2.Contiguous Decomposition

32. 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 ??

33. Thank You!