1. SNRC Meeting June 7 th, 2001 1 Crossbar Switch Scheduling Nick McKeown Professor of Electrical Engineering and Computer Science, Stanford University nickm@stanford.edu http://www.stanford.edu/~nickm

2. SNRC Meeting June 7 th, 2001 2 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.

3. SNRC Meeting June 7 th, 2001 3 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.

4. SNRC Meeting June 7 th, 2001 4 History of the theory 3.[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(N 3 ). 5.[Mekkittikul and M 1998] A carefully picked maximum size match can give 100% throughput. Matching O(N 2.5 )

5. SNRC Meeting June 7 th, 2001 5 Maximum Size Matching Q 11 11 = a 12 = b 22 = 0 21 = b b a With random tie breaks: Unstable a+b=1 With “clever” tie breaks: Stable [Mekkittikul, 1998]

6. SNRC Meeting June 7 th, 2001 6 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.

7. SNRC Meeting June 7 th, 2001 7 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).

8. SNRC Meeting June 7 th, 2001 8 Implementation State 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.

9. SNRC Meeting June 7 th, 2001 9 Recap of Observations 1.Randomization + memory seems promising and simple (Balaji’s talk), 2.Maximum size matching needs to be revisited.

10. SNRC Meeting June 7 th, 2001 10 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.

11. SNRC Meeting June 7 th, 2001 11 With benign uniform traffic

12. SNRC Meeting June 7 th, 2001 12 With “tricky” non-uniform traffic input output

13. SNRC Meeting June 7 th, 2001 13 What we’re doing (2) Motivated by “revisiting MSM”: –What tie-breaking policies in MSM will lead to 100% throughput?