snrc meeting june 7 th, 2001 1 crossbar switch scheduling nick mckeown professor of electrical...
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SNRC Meeting June 7 th, 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.TRANSCRIPT
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SNRC Meeting 1June 7th, 2001
Hi gh Pe rf orm a nceSwi tc hi ng and Routi ngTe lec om Ce nter W orks ho p: Sep t 4 , 19 97.
Crossbar Switch Scheduling
Nick McKeownProfessor of Electrical Engineering and Computer Science, Stanford [email protected]://www.stanford.edu/~nickm
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SNRC Meeting 2June 7th, 2001
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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SNRC Meeting 3June 7th, 2001
History of the theory1. [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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SNRC Meeting 4June 7th, 2001
History of the theory3. [Anderson et al. 1993] Observed analogy to maximum
size matching in a bipartite graph.
4. [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).
5. [Mekkittikul and M 1998] A carefully picked maximum size match can give 100% throughput.
Matching
O(N2.5)
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SNRC Meeting 5June 7th, 2001
Maximum Size MatchingQ11
11 = a12 = b
22 = 021 = b
bb
b
112
1 2
11 Q of rate service Maximum
b
a
With random tie breaks: Unstable a+b=1
With “clever” tie breaks: Stable
[Mekkittikul, 1998]
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SNRC Meeting 6June 7th, 2001
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.
6. [P and Dai 2000] 100% throughput possible for maximal matching with a speedup of two.
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SNRC Meeting 7June 7th, 2001
History of the theory (3)Randomized Algorithms
7. [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.
8. [Giaccone, Shah & P 2001] “Laura” and “Apsara” algorithms (more on these in Balaji’s talk).
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SNRC Meeting 8June 7th, 2001
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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SNRC Meeting 9June 7th, 2001
Recap of Observations
1. Randomization + memory seems promising and simple (Balaji’s talk),
2. Maximum size matching needs to be revisited.
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SNRC Meeting 10June 7th, 2001
What we’re 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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SNRC Meeting 11June 7th, 2001
With benign uniform traffic
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SNRC Meeting 12June 7th, 2001
With “tricky” non-uniform traffic
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20000002000000
020000000200000002000000020000000200000002
inpu
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output
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SNRC Meeting 13June 7th, 2001
What we’re doing (2)
• Motivated by “revisiting MSM”:– What tie-breaking policies in MSM will
lead to 100% throughput?