SNRC Meeting 1June 7th, 2001

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Crossbar Switch Scheduling

Nick McKeownProfessor of Electrical Engineering and Computer Science, Stanford Universitynickm@stanford.eduhttp://www.stanford.edu/~nickm

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.

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)

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]

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.

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).

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.

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.

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.

SNRC Meeting 11June 7th, 2001

With benign uniform traffic

SNRC Meeting 12June 7th, 2001

With “tricky” non-uniform traffic

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output

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?