Transcript Document

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.
Outline
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Motivation and related work
Objectives and traffic model
The utilization constraint alone
Utilization and loss rate constraints
Parameter estimation and simulation results
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Amogh Dhamdhere
IEEE Infocom 2005
Motivation
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Router buffers are important in packet networks
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Increasing buffer space increases the utilization of
the link and decreases the loss rate
Increasing buffer also increases queuing delays !
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Absorb rate variations of incoming traffic
Prevent packet losses during traffic bursts
So smaller buffers are desirable
Fundamental Question: What is the minimum buffer
requirement to satisfy constraints on the utilization,
loss rate and queuing delay ?
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IEEE Infocom 2005
Rules of Thumb
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Some router vendors suggest 500ms of buffering.
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Bandwidth Delay Product rule: Capacity of link times
the “typical” RTT (B = CT)
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Why 500ms ?
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
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e.g. Capacity times link delay
Amogh Dhamdhere
IEEE Infocom 2005
Related Work
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Approaches based on queuing models e.g. M/M/1/k
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TCP is not open-loop. TCP flows are reactive
Modeling Internet traffic is difficult
“Stanford” model (Appenzeller et al. Sigcomm 2004)
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Buffer requirement for full utilization decreases with square
root of N
CT
B 
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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)
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Buffer proportional to the number of flows (B = 6*N)
Considered all flows active at the link
Amogh Dhamdhere
IEEE Infocom 2005
Outline
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Motivation and related work
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Objectives and traffic model
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The utilization constraint alone
Utilization and loss rate constraints
Parameter estimation and simulation results
7/22/2015
Amogh Dhamdhere
IEEE Infocom 2005
Our Objectives
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Full utilization:
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Maximum loss rate:
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ˆ, typically 1-2% for a
The loss rate p should not exceed p
saturated link
Minimum queuing delays:
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The average utilization of the link should be at least
% when the offered load is sufficiently high
ˆ  100
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 !
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IEEE Infocom 2005
Traffic Classes
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Locally Bottlenecked Persistent (LBP) TCP flows
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Remotely Bottlenecked Persistent (RBP) TCP flows
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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
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Large TCP flows limited by losses at the target link
Loss rate p is equal to the loss rate at the target link
Large TCP flows, throughput limited by the advertised
window
Short TCP flows and non-TCP traffic
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Assumption
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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
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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
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IEEE Infocom 2005
Outline
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Motivation and related work
Objectives and traffic model
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The utilization constraint alone
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Utilization and loss rate constraints
Parameter estimation and simulation results
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IEEE Infocom 2005
TCP Window Dynamics
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Saw-tooth behavior of
TCP
Padhye (1998)
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TCP throughput can be
approximated by
R 
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0 .8 7
T
p
Average window size is
independent of RTT
Valid when loss rate is
small
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IEEE Infocom 2005
Util. Constraint - Multiple TCP
Flows
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N b heterogeneous LBP flows with RTTs T i
Consider initially the worst-case scenario: Global
Loss Synchronization.
All flows decrease windows simultaneously in
response to losses.
C
We derive that B  
1
Nb
i 1
Nb
i
1
Ti
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As a bandwidth-delay product
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Where
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Te 
1
Nb
i
1
Nb
i
1
1
Ti
B  CT e
is the harmonic mean of the RTTs
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IEEE Infocom 2005
Util. Constraint - Multiple TCP
Flows
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T e is called the effective RTT of the N b flows
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Intuition:
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Influenced more by smaller values
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:
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A few connections with very large RTTs cannot
significantly influence the buffer requirement, as long
as most flows have small RTTs
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IEEE Infocom 2005
Partial Synchronization Model
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In practice, flows are not completely synchronized
Loss Burst Length: Number of packets lost by N b
flows during a congestion event
Empirical observation: Loss burst length increases
almost linearly with N i.e. L   N
A simple probabilistic argument gives us,
b
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B 
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Nb
b
q ( N b )C T  2 M N b [1  q ( N b )]
2  q (N b )
Partial loss synchronization reduces the buffer
requirement.
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Amogh Dhamdhere
IEEE Infocom 2005
Validation
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ns2 simulations.
Heterogeneous flows,
ˆ  98 %
Partial synchronization
model accurately
predicts the buffer
requirement.
Deterministic model
overestimates the
buffer requirement !
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IEEE Infocom 2005
Outline

Motivation and related work
Objectives and traffic model
The utilization constraint alone
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Utilization and loss rate constraint
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Parameter estimation and simulation results
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IEEE Infocom 2005
Utilization and Loss Rate
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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)
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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 pˆ . Assume
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pˆ
is 1%
Relation between loss rate and N
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N b 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
R  0.87
T
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p is proportional to the square of N b
2
p  Nb (
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0 .8 7
CT
)
2
Hence to maintain loss rate at less than pˆ
Nb 
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p
pˆC T / 0 .8 7
But this requires admission control
 Such schemes not deployed yet
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IEEE Infocom 2005
Flow Proportional Queueing
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First proposed by Morris (2000)
Don’t limit N b
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Increase RTTs to decrease loss rate
2
p  Nb (
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0 .8 7
CT
)
2
Increase RTT by increasing buffer, which increases
queuing delay
Solving for B gives B  C Tˆq  K p N b  C T p
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Where
Kp 
0 .8 7
Practically, K p
pˆ  1%
pˆ
 6
packets for
pˆ  2 % ,
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IEEE Infocom 2005
and
Kp  9
packets for
Flow Proportional Queueing (contd.)
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Intuition:
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Differences with Morris’ FPQ scheme
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K p packets per flow, either in buffer (B term) or “on the
wire” ( CT p term)
Morris did not take into account the term C T p
Set K p arbitrarily to 6 packets
Applied the rule for all flows active at the link
Increasing RTTs may violate delay constraint
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In that case, choose the minimum buffer that can satisfy
utilization and loss constraints
Amogh Dhamdhere
IEEE Infocom 2005
Integrated Model
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Separate results for utilization and loss rate
constraints
Satisfy the most stringent of the two requirements
B for utilization decreases with N b , while B for loss
rate increases with N b
N b : Crossover point
Bˆ  B  
q ( N b )C T e  2 M N b [1  q ( N b )]
2  q (N b )
Bˆ  B p  K p N b  C T e
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Called the BSCL formula
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IEEE Infocom 2005
if N b  N b
if N b  N b
Integrated Model - Validation
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Simulations using ns2.
Heterogeneous flows, N b varied from 1 to 200.
Utilization ˆ  9 8 % and loss constraint pˆ  1 %
Utilization constraint
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Loss rate constraint
Amogh Dhamdhere
IEEE 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
7/22/2015
Amogh Dhamdhere
IEEE Infocom 2005
Parameter Estimation
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Flow Classification:
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Number of LBP flows:
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LBP flows: all rate reductions due to packet losses at target
link
RBP flows: Some rate reductions due to losses elsewhere
Effective RTT:
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Zhang et al. (2002): Classify TCP flows based on rate limiting
factors
Jiang et al. (2002): Passive algorithm to measure TCP Round
Trip Times from packet traces
Loss Synchronization:
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Measure loss burst length from trace or use approximation
LN b   N b
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IEEE Infocom 2005
Evaluation - Setup
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ns2 simulations.
Multi-level tree topology with
wide range of RTTs (20ms to
550ms).
Target link capacity 50Mbps.
N b varied from 1 to 400.
20 RBP flows, 10 window limited
flows.
Mice flows with average size 14
packets, exponential interarrivals.
Non-LBP traffic (R) is varied
between 5% and 20% of C.
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IEEE Infocom 2005
Results – Loss Rate
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Results – Loss Rate
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IEEE Infocom 2005
Results – Loss Rate
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IEEE Infocom 2005
Results – Loss Rate
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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.
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Amogh Dhamdhere
IEEE Infocom 2005
Results - Utilization
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For a large number of flows, all three schemes
achieve full utilization.
For smaller number of flows, BSCL sometimes leads
to underutilization.
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Due to the probabilistic nature of loss synchronization.
Amogh Dhamdhere
IEEE Infocom 2005
Summary
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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.
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IEEE Infocom 2005
Thank You !
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Amogh Dhamdhere
IEEE Infocom 2005
Parameter estimation - N b
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Distinguishing between LBP and RBP flows:
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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).
Amogh Dhamdhere
IEEE Infocom 2005
Why is Buffer Size Important ?
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Router buffer size affects:
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Utilization of the link.
Loss rate of the link.
Fairness among TCP connections.
Results by Morris (1997):
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A very small buffer can lead to underutilization.
Loss rate increases as the square of N.
Amogh Dhamdhere
IEEE Infocom 2005
Partial Synchronization Model
(contd.)
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Consider a congestion event with the average lossburst length LN .
A simple probabilistic argument gives us,
b
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B 
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q ( N b )C T  2 M N b [1  q ( N b )]
2  q (N b )
Remarks:
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For global loss synchronization, q ( N b )  1 and the buffer
requirement becomes B = CT.
Partial loss synchronization reduces the buffer requirement.
For heterogeneous connections, replace T with the effective
RTT.
Amogh Dhamdhere
IEEE 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
7/22/2015
Amogh Dhamdhere
IEEE Infocom 2005
Results - Loss Rate
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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.
Amogh Dhamdhere
IEEE Infocom 2005