Upload
fiona-rios
View
24
Download
0
Tags:
Embed Size (px)
DESCRIPTION
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. Motivation and related work Objectives and traffic model - PowerPoint PPT Presentation
Citation preview
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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 ?
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
Validation
ns2 simulations. Heterogeneous flows, % Partial synchronization
model accurately predicts the buffer requirement.
Deterministic model overestimates the buffer requirement !
ˆ 98
04/19/23 Amogh DhamdhereIEEE Infocom 2005
Outline
Motivation and related work Objectives and traffic model The utilization constraint alone Utilization and loss rate constraint Parameter estimation and simulation
results
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
Results – Loss Rate
04/19/23 Amogh DhamdhereIEEE Infocom 2005
Results – Loss Rate
04/19/23 Amogh DhamdhereIEEE Infocom 2005
Results – Loss Rate
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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.
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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.
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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.
04/19/23 Amogh DhamdhereIEEE Infocom 2005
Thank You !
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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.
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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
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
04/19/23 Amogh DhamdhereIEEE Infocom 2005
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.