PacketMode Emulation of OutputQueued Switches David Hay CS

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

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

CIOQ Switches

Cell-Mode Scheduling

Cell-Mode Scheduling

Cell-Mode Scheduling

Trend towards Packet-Mode n 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 n n For optical switches such fragmentation and reassembly are prohibitive Cell-mode schedulers are packet-oblivious ¨ Degradation of the overall performance

Packet-Mode Scheduling

Packet-Mode Scheduling [Marsan et al. , 2002][Ganjali et al. , 2003][Turner, 2006] n n 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?

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

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

Cell-Mode Emulation is Possible Easy with speedup S=N è N scheduling decisions every time-slot: n In the 1 st decision forward the cell of input 1 ¨ In the 2 nd decision forward the cell of input 2 ¨ ⋮ ¨ In the Nth decision forward the cell of input N

Cell-Mode Emulation is Possible Easy with speedup S=N è N scheduling decisions every time-slot: n In the 1 st decision forward the cell of input 1 ¨ In the 2 nd decision forward the cell of input 2 ¨ ⋮ ¨ In the Nth decision forward the cell of input N

Cell-Mode Emulation w/ S=2 [Chuang et al. , 1999] n 1 st Key Concept: Slackness of a cell (in the input side) L(C) = OC(C) - IT(C) Output Cushion: (“good guys”) n Slackness may decrease by at most. Input 2 in. Thread: every(“bad time-slot guys”) How many cells are queued in How many cells proceed C in ¨ A cell leaves the output-buffer of C’s the destination of C OC-input-port ¨ A cell at the input and is queuedits before C buffer? IT++ destination, and arrives should leave then. OQ switchslackness before C Initial 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 è Slackness is never negative è All cells are delivered on time

Cell-Mode Emulation w/ S=2 [Chuang et al. , 1999] n 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 n Classical problem in CS ¨ Stable marriage always exists ¨ Many algorithms. .

Cell-Mode Emulation w/ S=2 [Chuang et al. , 1999] n 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] n 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++ n Two scheduling decisions every time-slots Slackness always increases by 2

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

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

Packet-Mode Emulation is Impossible n Regardless of speedup ¨ Even with speedup S=N

Packet-Mode Emulation is Impossible

Packet-Mode Emulation is Impossible

Packet-Mode Emulation is Impossible

Packet-Mode Emulation is Impossible

Packet-Mode Emulation is Impossible

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

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

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

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

PIFO Cell-Mode OQ Switch n FIFO = First-In First-Out

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

PIFO Cell-Mode OQ Switch FIFO = First-In First-Out n PIFO = Push-In First-Out n F FIFO Packet-Mode OQ Switch is a PIFO Cell-Mode Switch

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

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

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

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

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

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

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

Contiguous Greedy Decomposition n 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. n Find a greedy matching for the rest of the matrix. è Speedup: RQD: 2 T+Lmax-1

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

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

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

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

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

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

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

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

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

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

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

Wrap-up Packet-mode scheduling can be done with the same speedup as cell-mode scheduling G With the price of bounded RQD FFuture work: lower bounds ? ?

Thank You!