1. Sizing Router Buffers Nick McKeown Guido Appenzeller & Isaac Keslassy SNRC Review May 27 th, 2004

2. 2 Routers need Packet Buffers  It’s well known that routers need packet buffers  It’s less clear why and how much  Goal of this work is to answer the question: How much buffering do routers need? Given that queueing delay is the only variable part of packet delay in the Internet, you’d think we’d know the answer already!

3. 3 How much Buffer does a Router need?  Universally applied rule-of-thumb:  A router needs a buffer size:  2T is the two-way propagation delay (or just 250ms)  C is capacity of bottleneck link  Context  Mandated in backbone and edge routers.  Appears in RFPs and IETF architectural guidelines..  Usually referenced to Villamizar and Song: “High Performance TCP in ANSNET”, CCR, 1994.  Already known by inventors of TCP [Van Jacobson, 1988]  Has major consequences for router design C Router Source Destination 2T

4. 4 Example  10Gb/s linecard  Requires 300Mbytes of buffering.  Read and write 40 byte packet every 32ns.  Memory technologies  DRAM: require 4 devices, but too slow.  SRAM: require 80 devices, 1kW, $2000.  Problem gets harder at 40Gb/s  Hence RLDRAM, FCRAM, etc.

5. 5 Outline of this Work  Main Results  The rule of thumb is wrong for a core routers today  Required buffer is instead of  Outline of this talk  Where the rule of thumb comes from  Why it is incorrect for a core router in the internet today  Correct buffer requirements for a congested router  Buffer requirements for short flows (slow-start)  Experimental Verification  Conclusion

6. 6 Outline  The Rule of Thumb  Where does the rule of thumb comes from? (Answer: TCP)  Interaction of TCP flows and a router buffers  The buffer requirements for a congested router  Buffer requirements for short flows (slow-start)  Experimental Verification  Conclusion

7. 7 TCP CC’ > C Only W=2 packets may be outstanding  TCP Congestion Window controls the sending rate  Sender sends packets, receiver sends ACKs  Sending rate is controlled by Window W,  At any time, only W unacknowledged packets may be outstanding  The sending rate of TCP is Router Source Dest

8. 8 Single TCP Flow Router with large enough buffers for full link utilization B Dest CC’ > C Source t Window size RTT For every W ACKs received, send W+1 packets

9. 9 Required buffer is height of sawtooth t B 0

10. 10 Buffer = rule of thumb

11. 11 Over-buffered Link

12. 12 Under-buffered Link

13. 13 Origin of rule-of-thumb  Before and after reducing window size, the sending rate of the TCP sender is the same  Inserting the rate equation we get  The RTT is part transmission delay T and part queueing delay B/C. We know that after reducing the window, the queueing delay is zero. 

14. 14 Rule-of-thumb  Rule-of-thumb makes sense for one flow  Typical backbone link has > 20,000 flows  Does the rule-of-thumb still hold?  Answer:  If flows are perfectly synchronized, then Yes.  If flows are desynchronized then No.

15. 15 Outline  The Rule of Thumb  The buffer requirements for a congested router  Synchronized flows  Desynchronized flows  The 2T×C/sqrt(n) rule  Buffer requirements for short flows (slow-start)  Experimental Verification  Conclusion

16. 16 If flows are synchronized  Aggregate window has same dynamics  Therefore buffer occupancy has same dynamics  Rule-of-thumb still holds. t

17. 17 When are Flows Synchronized?  Small numbers of flows tend to synchronize  Large aggregates of flows are not synchronized  For > 200 flows, synchronization disappears  Measurements in the core give no indication of synchronization

18. 18 If flows are not synchronized Probability Distribution B 0 Buffer Size

19. 19 Quantitative Model  Model congestion window of a flow as random variable model aswhere  For many de-synchronized flows  We assume congestion windows are independent  All congestion windows have the same probability distribution  Now central limit theorem gives us the distribution of the sum of the window sizes

20. 20 Buffer vs. Number of Flows for a given Bandwidth  If for a single flow we have  Standard deviation of sum of windows decreases with n  Thus as n increases, buffer size should decrease  For a given C, the window W scales with 1/n and thus

21. 21 Required buffer size Simulation

22. 22 Summary  Flows in the core are desynchronized  For desynchronized flows, routers need only buffers of

23. 23 Outline  The Rule of Thumb  The buffer requirements for a congested router  Buffer requirements for short flows (slow-start)  Experimental Verification  Conclusion

24. 24 Short Flows  So far we were assuming a congested router with long flows in congestion avoidance mode.  What about flows in slow start?  Do buffer requirements differ?  Answer: Yes, however:  Required buffer in such cases is independent of line speed and RTT (same for 1Mbit/s or 40 Gbit/s)  In mixes of flows, long flows drive buffer requirements  Short flow result relevant for uncongested routers

25. 25 A single, short-lived TCP flow Flow length 62 packets, RTT ~140 ms 2 4 8 16 32 RTT syn fin ack received Flow Completion Time (FCT)

26. 26 Average Queue length

27. 27 Queue Distribution  We derived closed-form estimates of the queue distribution using Effective Bandwidth  Gives very good closed form approximation  Buffer requirements for short flows  Small & independent of line speed and RTT  In mixes of flows, long flows dominate buffer requirements

28. 28 Outline  The Rule of Thumb  The buffer requirements for a congested router  Buffer requirements for short flows (slow-start)  Experimental Verification  Conclusion

29. 29 Experimental Evaluation Overview  Simulation with ns2  Over 10,000 simulations that cover range of settings  Simulation time 30s to 5 minutes  Bandwidth 10 Mb/s - 1 Gb/s  Latency 20ms -250 ms,  Physical router  Cisco GSR with OC3 line card  In collaboration with University of Wisconsin  Experimental results presented here  Long Flows - Utilization  Mixes of flows - Flow Completion Time (FCT)  Mixes of flows - Heavy Tailed Flow Distribution  Short Flows – Queue Distribution

30. 30 Long Flows - Utilization (I) Small Buffers are sufficient - OC3 Line, ~100ms RTT 99.9% 98.0% 99.5% 2×2×

31. 31 Long Flows – Utilization (II) Model vs. ns2 vs. Physical Router GSR 12000, OC3 Line Card TCP Flows Router BufferLink Utilization PktsRAMModelSimExp 1000.5 x 1 x 2 x 3 x 64 129 258 387 1Mb 2Mb 4Mb 8Mb 96.9% 99.9% 100% 94.7% 99.3% 99.9% 99.8% 94.9% 98.1% 99.8% 99.7% 4000.5 x 1 x 2 x 3 x 32 64 128 192 512kb 1Mb 2Mb 4Mb 99.7% 100% 99.2% 99.8% 100% 99.5% 100% 99.9%

32. 32 Outline  The Rule of Thumb  The buffer requirements for a congested router  Buffer requirements for short flows (slow-start)  Experimental Verification  Conclusion

33. 33 Impact on Router Design  10Gb/s linecard with 200,000 x 56kb/s flows  Rule-of-thumb: Buffer = 2.5Gbits  Requires external, slow DRAM  Becomes: Buffer = 6Mbits  Can use on-chip, fast SRAM  Completion time halved for short-flows  40Gb/s linecard with 40,000 x 1Mb/s flows  Rule-of-thumb: Buffer = 10Gbits  Becomes: Buffer = 50Mbits  For more details…  “Sizing Router Buffers – Guido Appenzeller, Isaac Keslassy and Nick McKeown, to appear at SIGCOMM 2004