Sizing Router BuffersSizing Router Buffers

Nick McKeown

Guido Appenzeller & Isaac Keslassy

SNRC ReviewMay 27th, 2004

2

Routers need Packet BuffersRouters 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

How much Buffer does a Router How much Buffer does a Router need?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

CTB 2

CRouterSource Destination

2T

4

ExampleExample

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

Outline of this WorkOutline of this Work

Main Results The rule of thumb is wrong for a core routers today

Required buffer is instead of CT 2n

CT 2

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

OutlineOutline

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

TCPTCP

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

RouterSource

RTT

WR

Dest

8

Single TCP FlowSingle TCP FlowRouter with large enough buffers for full link utilizationRouter with large enough buffers for full link utilization

B

DestCC’ > C

Source

maxW

2maxW

t

Window size RTT

For every W ACKs received, send W+1 packets

RTT

WR

9

Required buffer is height of Required buffer is height of sawtoothsawtooth

t

B

0

10

Buffer = rule of thumbBuffer = rule of thumb

11

Over-buffered LinkOver-buffered Link

12

Under-buffered LinkUnder-buffered Link

13

Origin of rule-of-thumbOrigin 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.

newold RR

new

new

old

old

RTT

W

RTT

W

T

W

CBT

W oldold

2

2/

/2

CTB 2

)1( 1

noldnew WW CTBn

2)(1

1

14

Rule-of-thumbRule-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.

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OutlineOutline

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

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If flows are synchronizedIf flows are synchronized

Aggregate window has same dynamics Therefore buffer occupancy has same dynamics Rule-of-thumb still holds.

2maxW

t

max

2

W

maxW

maxW

17

When are Flows When are Flows Synchronized?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

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If flows are not If flows are not synchronizedsynchronized

ProbabilityDistribution

B

0

Buffer Size

W

19

Quantitative ModelQuantitative Model Model congestion window of a flow as random variable

)(tWi model as )(][ xfxWP i iW where

For many de-synchronized flows We assume congestion windows are independent All congestion windows have the same probability distribution

2]var[][ WiWi WWE

Now central limit theorem gives us the distribution of the sum of the window sizes

)1,0()( NnntW WWn

i

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Buffer vs. Number of FlowsBuffer vs. Number of Flowsfor a given Bandwidthfor a given Bandwidth

If for a single flow we have

Standard deviation of sum of windows decreases with n

)1,0(1

)( 11 Nn

tW nnn

i

Thus as n increases, buffer size should decrease

n

BB n 1

211 ]var[][ nn WWE

For a given C, the window W scales with 1/n and thus2

11 ]var[][

nW

nWE nn

21

Required buffer sizeRequired buffer size

2T C

n

Simulation

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SummarySummary Flows in the core are desynchronized

For desynchronized flows, routers need only buffers of

n

CTB

2

23

OutlineOutline

The Rule of Thumb The buffer requirements for a congested router Buffer requirements for short flows (slow-start)

Experimental Verification Conclusion

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Short FlowsShort 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

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A single, short-lived TCP flowA single, short-lived TCP flowFlow length 62 packets, RTT ~140 msFlow length 62 packets, RTT ~140 ms

2

4

8

16

32

RTTsynfin ack

received

Flow Completion Time (FCT)

26

Average Queue lengthAverage Queue length

capacity :C 40Mbit sload : 0.8

ρ)E[S]-2(1]E[Sρ 22

27

Queue DistributionQueue 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

]E[S

E[S]

ρ

ρ)(κeb)P(Q bκ

2

12

28

OutlineOutline

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

29

Experimental Evaluation Experimental Evaluation OverviewOverview

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

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Long Flows - Utilization (I)Long Flows - Utilization (I)Small Buffers are sufficient - OC3 Line, ~100ms RTTSmall Buffers are sufficient - OC3 Line, ~100ms RTT

2T C

n

99.9%

98.0%

99.5%2T C

n

2×

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Long Flows – Utilization (II)Long Flows – Utilization (II) Model vs. ns2 vs. Physical Model vs. ns2 vs. Physical

RouterRouterGSR 12000, OC3 Line CardGSR 12000, OC3 Line Card

TCP

Flows

Router Buffer Link Utilization

Pkts RAM Model Sim Exp

100 0.5 x

1 x

2 x

3 x

64

129

258

387

1Mb

2Mb

4Mb

8Mb

96.9%

99.9%

100%

100%

94.7%

99.3%

99.9%

99.8%

94.9%

98.1%

99.8%

99.7%

400 0.5 x

1 x

2 x

3 x

32

64

128

192

512kb

1Mb

2Mb

4Mb

99.7%

100%

100%

100%

99.2%

99.8%

100%

100%

99.5%

100%

100%

99.9%

2T C

n

32

OutlineOutline

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

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Impact on Router DesignImpact 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