The Arbitration Problem

Transcription

1 HighPerform Switchingand TelecomCenterWorkshop:Sep outing ance t4, 97. EE84Y: Packet Switch Architectures Part II Load-balanced Switches ick McKeown Professor of Electrical Engineering and Computer Science, Stanford University The Arbitration Problem A packet switch fabric is reconfigured for every packet transfer. For example, at 60Gb/s, a new IP packet can arrive every ns. The configuration is picked to maximize throughput and not waste capacity. Known algorithms are probably too slow.

2 Approach We know that a crossbar with VOQs, and uniform Bernoulli i.i.d. arrivals, gives 00% throughput for the following scheduling algorithms: Pick a permutation uar from all permutations. Pick a permutation uar from the set of size in which each inputoutput pair (i,j) are connected exactly once in the set. From the same set as above, repeatedly cycle through a fixed sequence of different permutations. Can we make non-uniform, bursty traffic uniform enough for the above to hold? Design Example Stanford Optics in outers project Some challenging numbers: 00Tb/s 60Gb/s linecards 640 linecards Goals Scale to High Linecard Speeds (60Gb/s) o Centralized Scheduler Optical Switch Fabric Low Packet-Processing Complexity Scale to High umber of Linecards (640) Provide Performance Guarantees 00% Throughput Guarantee o Packet eordering 4

3 line Basic idea of load-balancing Packet mis-sequencing An optical switch fabric Scaling number of linecards 5 00% Throughput in a Mesh Fabric????????? Switch capacity = outer capacity = 6

4 If Traffic Is Uniform λ / µ = / / / / 7 / / / eal Traffic is ot Uniform / / /? / / / 8 4

5 Load-Balanced Switch Load-balancing stage Forwarding stage 00% throughput for weakly mixing traffic (Valiant, C.-S. Chang) 9 Load-Balanced Switch 0 5

6 Load-Balanced Switch tuition: 00% Throughput a b C Arrivals to second mesh: b = U a, where U = Capacity of second mesh: C = U Second mesh: arrival rate < service rate b -C = ( U a U ) < 0 [C.-S. Chang] 6

7 Another way of thinking about it External puts ternal puts External puts Load Balancing Load-balancing cyclic shift Switching cyclic shift First stage load-balances incoming packets Second stage is a cyclic shift Load-Balanced Switch External puts ternal puts External puts Load-balancing cyclic shift Switching cyclic shift 4 7

8 Main esult [Chang et al.]:. Consider a periodic sequence of permutation matrices: tˆ P( t) = P, where P is a one-cycle permutation matrix (for example, a TDM sequence), and tˆ = t mod.. If st stage is scheduled by a sequence of permutation matrices: P( t) = P( t + φ ), where φ is a random starting phase, and. The nd stage is scheduled by a sequence of permutation matrices: P ( t) = P( t + φ ), 4. Then the switch gives 00% throughput for a very broad range of traffic types. Observation: and breaks up burstiness. st stage makes non-uniform traffic uniform, 5 line of Chang s Proof. Let a( t) be the matrix of arrivals at time t, where a ( t) indicates an arrival at i for j. ij b( t) = P ( t) a( t). Let be the input traffic to the second stage.. Let q( t) be the queue length matrix: q( t ) = max q( t) + b( t + ) P ( t + ), 0, expands to + [ ] t 0 s t τ = s+ ( τ ) ( τ ) q( t) = max b P. Theorem: If no output is oversubscribed, q( t) converges to steady state q( ). Proof: E [ b( t) ] = E[ P ( t) a( t) ] = E [ P ( t) ] E[ a( t) ] = eλ. t lim b( s) P ( s) = eλ e 0. t t s= Holds under some mild conditions on a( t) (weakly mixing arrival processes). 6 8

9 line Basic idea of load-balancing Packet mis-sequencing An optical switch fabric Scaling number of linecards 7 Packet eordering 8 9

10 Bounding Delay Difference Between Middle Ports cells 9 UFS (Uniform Frame Spreading) = 0 0 0

11 FOFF (Full Ordered Frames First) FOFF (Full Ordered Frames First) 4 put Algorithm FIFO queues corresponding to the output flows Spread each flow uniformly: if last packet was sent to middle port k, send next to k+. Every time-slots, pick a flow: - If full frame exists, pick it and spread like UFS - Else if all frames are partial, pick one in round-robin order and send it

12 Bounding eordering FOFF put 4 put properties FIFO queues corresponding to the middle ports Buffer size less than packets If there are packets, one of the head-of-line packets is in order 4

13 FOFF Properties Property : FOFF maintains packet order. Property : FOFF has O() complexity. Property : Congestion buffers operate independently. Property 4: FOFF maintains an average packet delay within constant from ideal output-queued router. Corollary: FOFF has 00% throughput for any adversarial traffic. 5 put-queued outer????????? 6

14 line Basic idea of load-balancing Packet mis-sequencing An optical switch fabric Scaling number of linecards 7 From Two Meshes to One Mesh One linecard 8 4

15 From Two Meshes to One Mesh One linecard First mesh Second mesh 9 From Two Meshes to One Mesh Combined mesh 0 5

16 Many Fabric Options One linecard channels each at rate C, C,, C C C Options C Any spreading device Space: Full uniform mesh Time: ound-robin crossbar Wavelength: Static WDM C AWG (Arrayed Waveguide Grating outer) A Passive Optical Component Linecard λ, λ λ λ Linecard Linecard x AWG λ Linecard Linecard λ Linecard Wavelength i on input port j goes to output port (i+j-) mod Can shuffle information from different inputs 6

17 Static WDM Switching: Packaging A A, A, A, A A, B, C, D B B, B, B, B A, B, C, D AWG C D C, C, C, C A, B, C, D D, D, D, D A, B, C, D Passive and Almost Zero Power WDM channels, each at rate line Basic idea of load-balancing Packet mis-sequencing An optical switch fabric Scaling number of linecards 4 7

18 Scaling Problem For < 64, an AWG is a good solution. We want = 640. eed to decompose. 5 A Different epresentation of the Mesh Mesh 6 8

19 A Different epresentation of the Mesh 7 Example: =8 /

20 When is Too Large Decompose into groups (or racks) 4 4/ When is Too Large Decompose into groups (or racks) Group/ack Group/ack L L L/G L/G L L Group/ack G L L L/G L/G Group/ack G L L 40 0

21 line Basic idea of load-balancing Packet mis-sequencing An optical switch fabric Scaling number of linecards 4