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Sizing Router Buffers. Guido Appenzeller Thesis Defense May 24 th , 2004. 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?.

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Sizing router buffers

Sizing Router Buffers

Guido Appenzeller

Thesis DefenseMay 24th, 2004


Routers need packet buffers
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?


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

Source

Destination

Router

C

  • 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

2T


Example
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.


Outline of this work
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


Outline
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


Router

TCP

Only W=2packets may be outstanding

Source

Dest

C’ > C

C

  • 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


Single tcp flow router without buffers

Link not fully utilized

Single TCP FlowRouter without buffers

Only Wpackets may be outstanding

Dest

Source

Router

C’ > C

C

Congestion

Window

  • Rule for adjusting W

    • If an ACK is received: W ← W+1/W

    • If a packet is lost: W ← W/2

W

8

4

t


Single tcp flow router with large enough buffers for full link utilization

For every W ACKs received,

send W+1 packets

RTT

Window size

t

Single TCP FlowRouter with large enough buffers for full link utilization

B

Source

Dest

C’ > C

C




Microscopic tcp behavior when sender pauses buffer drains
Microscopic TCP BehaviorWhen sender pauses, buffer drains

one RTT

Drop




Origin of rule of thumb
Origin of rule-of-thumb

  • Before and after reducing window size, the sending rate of theTCP sender is the same

  • Inserting the rate equation we get

  • The RTT is part transmission delay T and part queuing delay B/C . We know that after reducing the window, the queuing delay is zero.


Rule of thumb
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.


Outline1
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


If flows are synchronized
If flows are synchronized

  • Aggregate window has same dynamics

  • Therefore buffer occupancy has same dynamics

  • Rule-of-thumb still holds.

t


When are flows synchronized
When are Flows Synchronized?

  • Small numbers of flows tend to synchronize

    • In ns2 simulation they are synchronized

    • In at least some cases holds for real networks as well

  • Large aggregates of flows are not synchronized

    • For > 500 flows, synchronization disappears in ns2

    • On a Cisco GSR, 100 flows were not synchronized

    • Measurements in the core give no indication of synchronization

      • C. Fraleigh, “Provisioning Internet Backbone Networks to support Latency Sensisitve Applications”, Ph.D. Thesis, Stanford

      • Hohn, Veitch, Papagiannaki and Diot – “Bridging Router Performance and Queuing Theory”


If flows are not synchronized

Probability

Distribution

Buffer Size

If flows are not synchronized

B

0


Quantitative model
Quantitative Model

model as

where

  • For many de-synchronized flows

    • We assume congestion windows are independent

    • All congestion windows have the same probability distribution

  • Model congestion window of a flow as random variable

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


Buffer vs number of flows for a given bandwidth
Buffer vs. Number of Flowsfor a given Bandwidth

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

  • Standard deviation of sum of windows decreases with n

  • If for a single flow we have

  • Thus as n increases, buffer size should decrease



Summary
Summary

  • Flows in the core are desynchronized

    • Substantial experimental evidence

    • Supported by ns2 simulations

  • For desynchronized flows, routers need only buffers of


Outline2
Outline

  • The Rule of Thumb

  • The buffer requirements for a congested router

  • Buffer requirements for short flows (slow-start)

    • M/G/1 Model

  • Experimental Verification

  • Conclusion


Short flows
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


A single short lived tcp flow flow length 62 packets rtt 140 ms
A single, short-lived TCP flowFlow length 62 packets, RTT ~140 ms

32

Flow Completion Time (FCT)

16

8

4

fin ackreceived

syn

2

RTT


Modelling short flows
Modelling Short Flows

Idea: Find buffer size by modelling queue behaviour

  • Problem: Arrival process is hard to model

    • Simplify by modelling bursts as independent

    • Buffer empties several times during one RTT

Poisson arrivals offlows

Service time is Lflow, the flow length in packets

Poisson arrivals of bursts

Service time is the lengthof the burst: 2,4,8,16…


M g 1 model for short flows
M/G/1 Model for short flows

  • TCP flows generate independent bursts

    • Service times is burst length :

    • Poisson arrivals of rate

  • To verify if this approach works, let’s compare the average queue length in the model and in simulation



Buffer requirements for short flows

Buffer B

Q

Packet Loss

P(Q = x)

Buffer Requirements for Short Flows

  • Buffers absorb fluctuations in queue, reduce packet loss

    • Reduce retransmits, Timeouts and thereby flow completion time

    • Utilization not a good measure of QoS as load << 1

  • We can find a good upper bound for loss, if we have the queue length distribution for an infinite buffer

    • If a packet arrives and queue length is shorter than buffer, packet will not be dropped

  • Problem: For M/G/1 there is no closed form expression for the queue distribution


Queue distribution
Queue Distribution

We derived closed-form estimates of the queue

distribution using Effective Bandwidth

  • Gives very good closed form approximation


Short flow summary
Short Flow Summary

  • Buffer requirements for short flows

    • Can be modeled by M/G/1 model

    • Only depends on load and burst size distribution

    • Example - for bursts of up to size 16 at load 0.8

      • For 1% loss probability B = 115 Packets

      • For 0.01% loss probability B = 230 packets etc.

      • Bursts of size 12 is maximum for Windows XP

    • Independent of line speed and RTT

  • In mixes of flows, long flows dominate buffer requirements


Outline3
Outline

  • The Rule of Thumb

  • The buffer requirements for a congested router

  • Buffer requirements for short flows (slow-start)

  • Experimental Verification

  • Conclusion


Experimental evaluation overview
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


Long flows utilization i small buffers are sufficient oc3 line 100ms rtt
Long Flows - Utilization (I)Small Buffers are sufficient - OC3 Line, ~100ms RTT

99.9%

99.5%

98.0%


Long flows utilization ii model vs ns2 vs physical router gsr 12000 oc3 line card
Long Flows – Utilization (II) Model vs. ns2 vs. Physical RouterGSR 12000, OC3 Line Card


Mixes of flows flow completion time fct of 14 packet flows that share a link with long lived flows
Mixes of FlowsFlow Completion TimeFCT of 14 packet flows that share a link with long-lived flows.


Heavy tailed flow length distribution
Heavy-tailed flow length distribution

  • Experiment

    • Flow arrivals are a Poisson process

    • Flow lengths are Pareto distributed

  • Results

    • Buffers in the order of are still sufficient

    • Number of “long-lived” flows n is now defined as number of flows in congestion avoidance mode


Pareto flow distribution finding the number of flows
Pareto Flow DistributionFinding the number of flows

No. of flows in CA mode

For buffer sizing, pick n = 100

time [seconds]


Pareto flow distribution
Pareto Flow Distribution

Flow arrivalson link 1

Bottleneck

utilization

Buffer

Occupancy


Short flows queue distribution m g 1 model vs gsr 12000 oc3 line card
Short Flows – Queue DistributionM/G/1 Model vs. GSR 12000, OC3 Line Card


Outline4
Outline

  • The Rule of Thumb

  • The buffer requirements for a congested router

  • Buffer requirements for short flows (slow-start)

  • Experimental Verification

  • Conclusion


Related work
Related Work

  • Related Publications

    • Buffer sizing

      • “High Speed TCP in ANS Net” - Villamizar and Song, ACCR 1994

      • “TCP behaviour with many flows” – R. Morris, IEEE ICNP 1997

      • “Scalable TCP congestion control” – R. Morris, INFOCOM 2000

    • Queue Modelling

      • “Modelling, Simulation and Measurement of Queuing Delay” – Garetto and Towsley, SIGMETRICS 2003


Original contributions
Original Contributions

  • Main original contributions of this work

    • Routers only require buffers of instead of

    • Models on TCP buffer interaction for

      • Congestion avoidance mode

      • Slow start

    • Experimental Verification

  • Publication

    • “Sizing Router Buffers – Guido Appenzeller, Isaac Keslassy and Nick McKeown, to appear at SIGCOMM 2004


The commercial internet today
The Commercial Internet Today

  • Today’s internet differs from our assumptions

    • Core is overprovisioned, almost never congested

    • Access links are usually the bottleneck (DSL, Modem)

    • Flows are usually limited by Maximum Window size

      • Maximum Window is from 6-12 (Windows) to 42 (Unix)

    • Are the results still relevant?

  • Answer: Yes, we were intentionally pessimistic

    • Routers still needs to work in case of congestion

      • Even if this “worst case” scenario is rare

    • Slow access links and small TCP windows reduce buffer requirements further

      • Bursts are smoothed out

      • Converges towards constant rate source, poisson packet arrivals

      • We verified reduced buffer requirements experimentally


How much buffer does a router need1
How much buffer does a router need?

The old “Rule-of-Thumb”

Our Contribution


Impact on router design
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




Two tcp flows two flows sharing a bottleneck synchronize
Two TCP FlowsTwo flows sharing a bottleneck synchronize


Impact on protocol design
Impact on Protocol Design

TCP Reno: requires

General: requires

  • The ‘rule-of-thumb’ is due to the nature of TCP

    • We can easily build a TCP that requires less buffers

    • Latency based TCP (Vegas, FAST) suffer from smaller buffers

      • Queuing delay too small to be used as a channel

      • Buffer occupancy similar for different levels of congestion

      • Unclear if these protocols work with aggregated traffic at all

  • For future protocol design, buffer requirements should be considered


Smaller buffers increase loss but this in itself is not a bad thing
Smaller buffers increase lossBut this in itself is not a bad thing

  • Routers drop packets to throttle senders

  • Loss rate is a function of number of flows and sum of TCP windows

  • Rule-of-thumb vs. minimal buffers changes number of outstanding packets by a factor of 2

    • Loss will quadruple with minimal buffers

  • This is just the way how TCP works

    • Quality of service better even with higher loss…


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