Crossbar Switch Scheduling

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Crossbar Switch Scheduling
Nick McKeown Professor of Electrical Engineering
and Computer Science, Stanford
University nickm_at_stanford.edu http//www.stanford.
edu/nickm
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Goal

• Design crossbar scheduling algorithms for
  switches with 100s of Tb/s of capacity.
• Problems
• Existing algorithms are
• Heuristic (and therefore unpredictable), and
• Reaching their scaling limits.
• Ideal algorithms are too complex.

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History of the theory

1. Karol et al. 1987 Throughput limited by
   head-of-line blocking to for
   Bernoulli IID uniform traffic.
2. Tamir 1989 Observed that with Virtual Output
   Queues (VOQs) Head-of-Line blocking is reduced
   and throughput goes up.

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History of the theory

• Anderson et al. 1993 Observed analogy to
  maximum size matching in a bipartite graph.
• M et al. 1995 (a) Maximum size match can not
  guarantee 100 throughput if ties are broken
  randomly.(b) But maximum weight match does
  O(N3).
• Mekkittikul and M 1998 A carefully picked
  maximum size match can give 100 throughput.

Matching O(N2.5)
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Maximum Size Matching
?11 a
Q11
?12 b
?21 b
?22 0
With random tie breaks Unstable
ab1
a
With clever tie breaks Stable Mekkittikul,
1998
b
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History of the theory (2)Speedup

• 5. P, M et al. 1997 Precise emulation of a
  central shared memory switch is possible with a
  speedup of two and a stable marriage scheduling
  algorithm.
• P and Dai 2000 100 throughput possible for
  maximal matching with a speedup of two.

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History of the theory (3)Randomized Algorithms

• Tassiulas 1998 100 throughput possible for
  simple randomized algorithm with memory.Step 1
  Pick any permutation at random.Step 2 Compare
  weight with match from previous time slot.Step
  3 Pick the match with the largest weight.
• Giaccone, Shah P 2001 Laura and Apsara
  algorithms (more on these in Balajis talk).

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ImplementationState of the art

• Implementation is a long way behind the theory
• Packet switches today use maximal, or sub-maximal
  size algorithms and a speedup of 1-1.5 (e.g. Tiny
  Tera 1996, many commercial systems and
  chipsets).
• Most are iterative Request-Grant-Accept
  algorithms such as iSLIP.
• Even these simple algorithms are reaching their
  scaling limits.

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Recap of Observations

1. Randomization memory seems promising and simple
   (Balajis talk),
2. Maximum size matching needs to be revisited.

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What were doing (1)

• Motivated by simple to implement
• Intuition use arrivals as estimate of state.
• RADAR Randomized algorithm memory arrivals.
• Step 1 Calculate weight of arrival matrix
• Step 2 Compare with previous match.
• Step 3 Pick largest.

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With benign uniform traffic
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With tricky non-uniform traffic
output
input
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What were doing (2)

• Motivated by revisiting MSM
• What tie-breaking policies in MSM will lead to
  100 throughput?