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Very Small Buffers - Theory
• Assumptions:
– Minimum distance between consecutive packets of the same flow; – desynchronized flows – random and independent start times for flows
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Many TCP Flows
W
B 0
Buffer Size
Probability Distribution
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What you said
"I found it quite shocking that before 2004, nobody had bothered putting effort into researching something that was clearly causing huge engineering (and thus financial) hurdles in scaling up the internet infrastructure." David Schneider
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Announcements
Critiques: We will post some selected comments publicly. If you don't want your name listed, mark as “anon” and we won't use your name.
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Required Buffer Size Simulations
2T C n
Simulation
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What you said
"Since this paper is almost ten years old I kept wondering whether these recommendations where ever tested in the backbone routers and confirmed.” Jack Dubie "This paper's title is "Sizing Router Buffers," but it might be more accurately titled "Sizing Core Internet Router Buffers.” Carl Case
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Time Evolution of a Single TCP Flow
Time evolution of a single TCP flow through a router. Buffer is 2T*C Time evolution of a single TCP flow through a router. Buffer is < 2T*C

Assumption: link over-provisioned by 1/, and packets from each flow launched smoothly Theorem: We need
2 Wmax B log1/ 21 O (log W )
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The Story
# packets at 10Gb/s
1,000,000
(1)
10,000
20
2T C ( 2) 2T C O(log W ) n
Intuition & Proof
Sawtooth Peak-to-trough
Smoothing of many sawtooths
Simulations, Experiments
Non-bursty arrivals
Simulations, Experiments
Simulation, Evidence Single TCP Flow
(1) Assume: Large number of desynchronized flows; 100% utilization (2) Assume: Large number of desynchronized flows; <100% utilization
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Smooth Traffic
• Theory: For smooth traffic very small buffers are enough. • Poisson Traffic
Poisson
M/D/1 D
loss B
i.e. 80%, B 20pkts loss 1%
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The Story
# packets at 10Gb/s
1,000,000
(1)
10,000
20
2T C ( 2) 2T C O(log W ) n
Intuition & Proof
Sawtooth Peak-to-trough
Smoothing of many sawtooths
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Drop vs. Load, Buffer = 190ms, 10ms 0.2
Packet Drop Rate (%)
0.16 0.12 0.08 0.04 0 0 20 40 60 80 100
Load (%)
Buffer Sizing in Internet Routers
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Drop vs. Load, Buffer = 1ms
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Internet Backbone Experiment
• High link utilization • Long duration (about two weeks) • Buffer sizes 190ms (250K packets), 10ms (10K packets), 1ms (1000 packets)
Simulations, Experiments
Non-bursty arrivals
Simulations, Experiments
Simulation, Evidence Single TCP Flow
(1) Assume: Large number of desynchronized flows; 100% utilization (2) Assume: Large number of desynchronized flows; <100% utilization
0.2
Packet Drop Rate (%)
0.16 0.12 0.08 0.04 0 0 20 40 60 80 100
Load (%)
Buffer Sizing in Internet Routers
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The Story
# packets at 10Gb/s
1,000,000
(1)
10,000
pdf转word http://www.skycn.com/soft/appid/16287.html
CS244 Spring 2012 Lecture 4 Buffer Sizing
1. “Sizing router buffers”, Appenzeller et al, Sigcomm 2004 2. “Safe and effective fine-grained TCP…”, Vasudevan et al, Sigcomm 2009
"You have to wonder how the buffer sizing rule of thumb lasted a decade, and further, whether the answer to this question might be that large buffers don't pose as grave a threat as the authors would have us believe.” Justin Costa-Roberts
• Theorem: Buffer size of O(log W) guarantees very low packet drop probability. • Note: Distance between packets
– Slow access links With a buffer size of 10-20 packets we can gain – TCP Pacing high throughput.
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The Story
# packets at 10Gb/s
1,000,000
(1)
10,000
20
2T C ( 2) 2T C O(log W ) n
Intuition & Proof
Sawtooth Peak-to-trough
Smoothing of many sawtooths
Simulations, Measurements
Non-bursty arrivals
Simulations, Measurements
Simulation, Evidence Single TCP Flow
(1) Assume: Large number of desynchronized flows; 100% utilization (2) Assume: Large number of desynchronized flows; <100% utilization
Simulations, Experiments
Non-bursty arrivals
Simulations, Experiments
Simulation, Evidence Single TCP Flow
(1) Assume: Large number of desynchronized flows; 100% utilization (2) Assume: Large number of desynchronized flows; <100% utilization
Nick McKeown
The Story
# packets at 10Gb/s
1,000,000
(1)
10,000
20
2T C ( 2) 2T C O(log W ) n
Intuition & Proof
Sawtooth Peak-to-trough
Smoothing of many sawtooths
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O(log W) Buffers
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Experiment Results
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Summary
100%
About 90%
Throughput
About 50 pkts
RTT ´ C N
RTT ´ C
Buffer Size
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Consequences
10-50 packets on a chip
Simulations, Experiments
Simulation, Evidence Single TCP Flow
(1) Assume: Large number of desynchronized flows; 100% utilization (2) Assume: Large number of desynchronized flows; <100% utilization
20
2T C ( 2) 2T C O(log W ) n
Intuition & Proof
Sawtooth Peak-to-trough
Smoothing of many sawtooths
Simulations, Experiments
Leabharlann Baidu
Non-bursty arrivals
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Synchronized Flows
W
max
Wmax 2
Wmax
Wmax 2
t
• Aggregate window has same dynamics • Therefore buffer occupancy has same dynamics • Rule-of-thumb still holds.
B
– Loss independent of link rate, – RTT, number of flows, etc.
Can we make traffic look “Poisson-enough” when it arrives to the routers…?
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Very Small Buffers - Theory