buffer sizing for congested internet links amogh dhamdhere, hao jiang and constantinos dovrolis

Buffer Sizing for Congested Internet Links

Amogh Dhamdhere, Hao Jiang and Constantinos Dovrolis(amogh,hjiang,dovrolis)@cc.gatech.edu

Networking and Telecommunications Group,College of Computing,

Georgia Tech.

04/19/23 Amogh DhamdhereIEEE Infocom 2005

Outline

Motivation and related work Objectives and traffic model The utilization constraint alone Utilization and loss rate constraints Parameter estimation and simulation

results


Motivation

Router buffers are important in packet networks Absorb rate variations of incoming traffic Prevent packet losses during traffic bursts

Increasing buffer space increases the utilization of the link and decreases the loss rate

Increasing buffer also increases queuing delays ! So smaller buffers are desirable

Fundamental Question: What is the minimum buffer requirement to satisfy constraints on the utilization, loss rate and queuing delay ?


Rules of Thumb

Some router vendors suggest 500ms of buffering. Why 500ms ?

Bandwidth Delay Product rule: Capacity of link times the “typical” RTT (B = CT) Which RTT should we use ? Many TCP flows with different RTTs ? How do different types of flows (large vs small) affect the

buffer requirement ? Several variants of this rule

e.g. Capacity times link delay


Related Work

Approaches based on queuing models e.g. M/M/1/k TCP is not open-loop. TCP flows are reactive Modeling Internet traffic is difficult

“Stanford” model (Appenzeller et al. Sigcomm 2004) Buffer requirement for full utilization decreases with square

root of N

Did not consider the loss rate at the link Assumed that flows are completely desynchronized Applicable when the number of flows is large

Morris (1997 and 2000) Buffer proportional to the number of flows (B = 6*N) Considered all flows active at the link

CTBN


Outline


results


Our Objectives

Full utilization: The average utilization of the link should be at least

% when the offered load is sufficiently high

Maximum loss rate: The loss rate p should not exceed , typically 1-2% for a

saturated link Minimum queuing delays:

High queuing delay causes higher transfer latencies and jitter

Also increases cost and power consumption Should satisfy utilization and loss rate constraints with

minimum amount of buffering possible All of these objectives may not be feasible !

ˆ 100

p̂


Traffic Classes

Locally Bottlenecked Persistent (LBP) TCP flows Large TCP flows limited by losses at the target link Loss rate p is equal to the loss rate at the target link

Remotely Bottlenecked Persistent (RBP) TCP flows Large TCP flows limited by losses at target link and other links Loss rate is greater than loss rate at target link

Window Limited Persistent TCP flows Large TCP flows, throughput limited by the advertised window

Short TCP flows and non-TCP traffic


Assumption

Key Assumption: LBP flows account for most of the traffic at the target link (80-90 %)

In this case, we can ignore the buffering requirement of non-LBP flows non-LBP flows also contribute to the utilization and loss

rate at the target link Contribution is small if fraction of non-LBP traffic is small

Our model is applicable in links where this assumption holds

Edge links and links in access networks are candidates


Outline


results


TCP Window Dynamics

Saw-tooth behavior of TCP

Padhye (1998) TCP throughput can be

approximated by

Average window size is independent of RTT

Valid when loss rate is small

0.87R

T p


Util. Constraint - Multiple TCP Flows

heterogeneous LBP flows with RTTs Consider initially the worst-case scenario:

Global Loss Synchronization. All flows decrease windows simultaneously in

response to losses. We derive that

As a bandwidth-delay product Where is the harmonic mean of the

RTTs

1

11

Nb

bNi

i i

CB

T

1

1

11

b

b

N

e Ni

i i

TT

eB CT

bN iT


Util. Constraint - Multiple TCP Flows

is called the effective RTT of the flows Influenced more by smaller values

Intuition: Flows with smaller RTTs have larger portion of their

window in the bottleneck buffer Hence have larger influence on the required buffer Flows with large RTTs have larger portion of their

window “on the wire” Practical Implication:

A few connections with very large RTTs cannot significantly influence the buffer requirement, as long as most flows have small RTTs

eT bN


Partial Synchronization Model In practice, flows are not completely synchronized Loss Burst Length: Number of packets lost by

flows during a congestion event Empirical observation: Loss burst length increases

almost linearly with i.e. A simple probabilistic argument gives us,

Partial loss synchronization reduces the buffer requirement.

bN

bN

bN bL N

( ) 2 [1 ( )]

2 ( )b b b

b

q N CT MN q NB

q N


Validation

ns2 simulations. Heterogeneous flows, % Partial synchronization

model accurately predicts the buffer requirement.

Deterministic model overestimates the buffer requirement !

ˆ 98


Outline

Motivation and related work Objectives and traffic model The utilization constraint alone Utilization and loss rate constraint Parameter estimation and simulation

results


Utilization and Loss Rate

End-user perceived service is poor when the loss rate is more than 5-10%

Particularly for short and interactive flows Results by Morris (1997)

High variability in the completion times of short transfers Some “unlucky” flows suffer repeated losses and

timeouts The buffer size controls the loss rate Upper bound the loss rate to . Assume is 1%

p̂p̂


Relation between loss rate and N

homogeneous LBP flows at the target link. Link capacity C, flow RTTs T

Assume that the flows saturate the link and their throughput is given by

p is proportional to the square of

Hence to maintain loss rate at less than

But this requires admission control Such schemes not deployed yet

2 20.87( )bp N

CT

ˆ / 0.87bN pCT

bN

bN

0.87RT p

p̂


Flow Proportional Queueing

First proposed by Morris (2000) Don’t limit

Increase RTTs to decrease loss rate

Increase RTT by increasing buffer, which increases queuing delay

Solving for B gives Where

Practically, packets for , and packets for

9pK

0.87

ˆpK

p

bN

ˆ q p pbB CT K N CT

2 20.87( )bp N

CT

ˆ 1%p 6pK ˆ 2%p


Flow Proportional Queueing (contd.)

Intuition: packets per flow, either in buffer (B term) or “on the

wire” ( term) Differences with Morris’ FPQ scheme

Morris did not take into account the term Set arbitrarily to 6 packets Applied the rule for all flows active at the link

Increasing RTTs may violate delay constraint In that case, choose the minimum buffer that can satisfy

utilization and loss constraints

pCTpK

pCT

pK


Integrated Model

Separate results for utilization and loss rate constraints

Satisfy the most stringent of the two requirements B for utilization decreases with , while B for loss

rate increases with : Crossover point

Called the BSCL formula

bN

bN

( ) 2 [1 ( )]ˆ if 2 ( )

ˆ if

eb b bb b

b

p p eb b b

q N CT MN q NB B N N

q N

B B K N CT N N

bN


Integrated Model - Validation

Simulations using ns2. Heterogeneous flows, varied from 1 to 200.

Utilization % and loss constraint % ˆ 98 ˆ 1p

bN

Utilization constraint Loss rate constraint


Outline


results


Parameter Estimation Flow Classification:

Zhang et al. (2002): Classify TCP flows based on rate limiting factors

Number of LBP flows: LBP flows: all rate reductions due to packet losses at

target link RBP flows: Some rate reductions due to losses elsewhere

Effective RTT: Jiang et al. (2002): Passive algorithm to measure TCP

Round Trip Times from packet traces Loss Synchronization:

Measure loss burst length from trace or use approximation

bN bL N


Evaluation - Setup ns2 simulations. Multi-level tree topology with

wide range of RTTs (20ms to 550ms).

Target link capacity 50Mbps. varied from 1 to 400. 20 RBP flows, 10 window limited

flows. Mice flows with average size 14

packets, exponential inter-arrivals.

Non-LBP traffic (R) is varied between 5% and 20% of C.

bN


Results – Loss Rate


Results – Loss Rate

BSCL can bound loss rate close to the target, if R is less than 10%.

Accuracy decreases as fraction of non-LBP traffic increases.

Stanford model and the rule of thumb cannot bound loss rate.


Results - Utilization

For a large number of flows, all three schemes achieve full utilization.

For smaller number of flows, BSCL sometimes leads to underutilization. Due to the probabilistic nature of loss synchronization.


Summary

Derived a buffer sizing formula (BSCL) for congested links, taking into account both utilization and loss rate of the target link.

Applicable for links in which 80-90% of the traffic comes from large locally bottlenecked TCP flows.

Account for the effects of heterogeneous RTTs and partial loss synchronization.

Validated the results through simulations.


Thank You !


Parameter estimation -

Distinguishing between LBP and RBP flows: Intuition: For a LBP flow, rate reduction should be

preceded by a loss at the target link. For RBP flows, rate reduction will not always be

accompanied by a loss at the target link (due to losses in other links).

bN


Why is Buffer Size Important ?

Router buffer size affects: Utilization of the link. Loss rate of the link. Fairness among TCP connections.

Results by Morris (1997): A very small buffer can lead to underutilization. Loss rate increases as the square of N.


Partial Synchronization Model (contd.)

Consider a congestion event with the average loss-burst length .

A simple probabilistic argument gives us,

Remarks: For global loss synchronization, and the buffer

requirement becomes B = CT. Partial loss synchronization reduces the buffer

requirement. For heterogeneous connections, replace T with the

effective RTT.

( ) 2 [1 ( )]

2 ( )b b b

b

q N CT MN q NB

q N

bNL

( ) 1bq N


Outline


results


Results - Loss Rate

BSCL can bound loss rate close to the target, if R is less than 10%.

Accuracy decreases as fraction of non-LBP traffic increases.

Stanford model and the rule of thumb cannot bound loss rate.

buffer sizing for congested internet links amogh dhamdhere, hao jiang and constantinos dovrolis

Documents

highmaximum loss rate

linksloss rate

loss rateincreasing

lbp flows account

number of flows b

target linkloss rate

average utilization

minimum buffer requirement