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What do Packet Dispersion Techniques Measure?
Constantinos Dovrolis, Univ-Delaware
Parmesh Ramanathan, Univ-Wisconsin
David Moore, CAIDA
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 1 of 28
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Overview
� Background: capacity and available bandwidth
� Dispersion of packet-pairs
� Dispersion of packet-trains
� A capacity estimation methodology: pathrate
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 2 of 28
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Part I
Background
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 3 of 28
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Definition of capacity� Maximum IP-layer throughput that a flow can get, without any cross traffic
AC
Source Sink
Link-1 Link-2 Link-3
� Ci: capacity of link i (i � �� � � � �H)
� Path capacity C is limited by narrow link n:
C � min
i�����HfCig � Cn
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 4 of 28
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Definition of available bandwidth� Maximum IP-layer throughput that a flow can get, given (stationary) cross traffic
AC
Source Sink
Link-1 Link-2 Link-3
� ui: utilization of link i
� Available bandwidth A limited by tight link t:
A � min
i�����HCi ��� ui� � Ct ��� ut�
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 5 of 28
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Part II
Packet-pair dispersion
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 6 of 28
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Packet-pair: basic idea� Packet transmission time: � � LC
� Send two packets back-to-back
� Measure dispersion � at receiver
� Estimate C as L�
C3C
=L/C∆L/CL/3C
� But.. cross traffic ‘noise’ can affect the packet dispersion �Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 7 of 28
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Previous works on packet-pair dispersion
� Largely considered cross traffic effects as ‘random noise’
� Carter and Crovella (Infocom 1997), Lai and Baker (Infocom 1999): Statistical
techniques to extract most common measurement range (mode)
� Paxson (Sigcomm 1997): observed multimodalities but did not relate them with
cross traffic
� They suggest use of maximum-size packet-pair packets
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 8 of 28
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Multimodality of packet-pair estimates� Cross-traffic causes local modes below (SCDR) and above (PNCM) capacity
mode (CM)
0 10 20 30 40 50 60 70 80Bandwidth (Mbps)
0
40
80
120
160
200
240
280
320
360
400
# of
mea
sure
men
ts
P={100,75,55,40,60,80}, L=Lc=1500B
u=20%
Capacity Mode (CM)
Post−NarrowCapacity Mode
Sub−CapacityDispersion Range (SCDR)
(PNCM)
0 10 20 30 40 50 60 70 80Bandwidth (Mbps)
0
20
40
60
80
100
120
140
160
# of
mea
sure
men
ts
P={100,75,55,40,60,80}, L=Lc=1500B
SCDR
PNCM
CMu=80%
� Heavier cross traffic load makes CM weaker
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 9 of 28
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Creation of SCDR and PNCM modes
� SCDR is caused by cross traffic interfering with packet-pair
i
L/40L/40
t
L/60 L/60 L/60
CT 21C =60Mbpsi-1
C =40Mbps t1 2
L/40 + (2 L/60 - L/40) = L/30
� PNCMs are caused by back-to-back packet-pairs after narrow link (first packet
is adequately delayed)
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 10 of 28
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Effect of cross traffic packet size� Distinct cross traffic packet sizes cause SCDR local modes
� Common Internet traffic packet sizes: 40B, 550B, 1500B
0 10 20 30 40 50 60 70 80Bandwidth (Mbps)
0
20
40
60
80
100
120
140
160
# of
mea
sure
men
ts
P={100,75,55,40,60,80}, u=50%, L=1500B
Fixed CT packet size: Lc=1500B
SCDR CM
PNCMs
0 10 20 30 40 50 60 70 80Bandwidth (Mbps)
0
10
20
30
40
50
60
70
80
90
100
110
120
# of
mea
sure
men
ts
P={100,75,55,40,60,80}, u=50%, L=770B
SCDR
Lc uniform in [40,1500]BVariable CT packet size:
CM
PNCM
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 11 of 28
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Effect of packet-pair size� Previous work suggests use of maximum-sized packets
� But.. this is not optimal for uncovering capacity mode
0 10 20 30 40 50 60 70 80Bandwidth (Mbps)
0
20
40
60
80
100
120
140
160
180
200
220
# of
mea
sure
men
ts
P={100,75,55,40,60,80}, u=50%
L=100B
SCDR
Lc : uniform in [40,1500]B
CMPNCM
0 10 20 30 40 50 60 70 80Bandwidth (Mbps)
0
10
20
30
40
50
60
70
80
90
100
110
120
# of
mea
sure
men
ts
P={100,75,55,40,60,80}, u=50%
L=1500B
SCDR Lc : uniform in [40,1500]B
CM
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 12 of 28
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Packet-pair dispersion: summary� Packet-pair technique: simple in unloaded paths
� Multimodal bandwidth distribution in loaded paths
� Most common measurement range (mode) is not always the capacity
� Capacity is normally a local mode (CM)
� Interfering cross traffic packets cause local modes or SCDR
� Loaded post-narrow links also cause local modes (PNCMs)
� Maximum packet size is not optimal for uncovering CM
� How can we tell which local mode is related to the capacity?
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 13 of 28
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Part III
Packet-train dispersion
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 14 of 28
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Packet-train dispersion
� What do we measure with the dispersion of packet trains?
3N 2 1 N 23 1123N
∆(N) (N)(N)∆
CT CT
∆
CT
R
RS C C C1 2 3
0 2
� Bandwidth estimate:
�N���L
��N�
� What is the effect of length N on bandwidth estimate?
� Carter & Crovella: packet-train dispersion estimates A
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 15 of 28
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Packet-train experiments� What happens as we increase the packet-train length N?
0 10 20 30 40 50 60 70 80Bandwidth (Mbps)
0
20
40
60
80
100
120
140
# of
mea
sure
men
ts
P={100,75,55,40,60,80}, u=80%, L=Lc=1500B
N=2
CM
0 10 20 30 40 50 60 70 80Bandwidth (Mbps)
0
20
40
60
80
100
120
140
160
180
200
# of
mea
sure
men
ts
P={100,75,55,40,60,80}, u=80%, L=Lc=1500B
CM
N=3
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 16 of 28
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Packet-train experiments (cont’)� Range of measurements decreases and becomes unimodal
� Measurements tend to Asymptotic Dispersion Rate (ADR) (less than C)
0 10 20 30 40 50 60 70 80Bandwidth (Mbps)
0
40
80
120
160
200
240
# of
mea
sure
men
ts
P={100,75,55,40,60,80}, u=80%, L=Lc=1500B
N=5
0 10 20 30 40 50 60 70 80Bandwidth (Mbps)
0
40
80
120
160
200
240
280
320
360
400
# of
mea
sure
men
ts
P={100,75,55,40,60,80}, u=80%, L=Lc=1500B
N=10Asymptotic DispersionRate R=15Mbps
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 17 of 28
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ADR in single-hop paths� For sufficiently large N :
R ��N � ��L
���
�
C�
� � u�C�
C�
� C�
� ADR is not the capacity C
� ADR is not the available bandwidth A
� For single-hop paths, we can estimate A from R
A � C��
C�R
� ��
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 18 of 28
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Effect of cross traffic routing
� Path-persistent and one-hop persistent cross traffic
1 CCCC
Source
2 3 HC
Path
0
Path
. . .
Sink
Sources SinkCross Traffic Cross Traffic
H321
H30 CCCCC
PathSource
2
Path
1. . .
3 H21Sink
Cross Traffic Sources
Cross TrafficSinks
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 19 of 28
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Packet-train dispersion in multi-hop paths� Can we derive the ADR for general cross traffic routing and paths?
� Cross traffic packets cause ‘bubbles’ between packet-train packets
� For one-hop path persistent cross traffic with Ci � C :C
� �PH
i�� ui� R �
C
� �maxi�����H ui
� Lower bound: bubbles are never filled in
� Upper bound: bubbles are determined by tight link
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 20 of 28
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Packet-train dispersion: summary
� Packet-trains: do not lead to more robust capacity estimation
� Packet-trains: do not lead to available bandwidth estimation
� As N increases, measurement range decreases and becomes unimodal
� As N increases, measurements tend to ADR
� ADR is always less than capacity
� Available bandwidth can be computed from ADR in single-hop paths
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 21 of 28
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Part IV
A capacity estimation methodology
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 22 of 28
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Pathrate: a capacity estimation methodology
Phase I:
� Perform many (2000) packet-pair experiments to form distribution B
� Use packet size of about 800 bytes (maximum size: 1500 bytes)
� Determine local modes of distribution B
� Sequence of local modes in increasing order: M� fm��m�� � � � mMg
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 23 of 28
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Pathrate: a capacity estimation methodology (cont’)
Phase II:
� Perform several packet-train experiments with certain N to get B�N�
� If bandwidth distribution not unimodal, increase N and repeat previous step
� Let �N be the minimum value of N such that B�N� is unimodal
� Let ���� ��� be range of the unique mode in B�N�
� Estimate capacity as:
C � mk � minfmi �M mi � ��gConstantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 24 of 28
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Example: Path f100,70,60,40,55,80,65,90,40,75,90g
� Packet-pair modesM=f9,14,17,23,26,29,33,40,44,56,75,90g
0 10 20 30 40 50 60 70 80 90Bandwidth (Mbps)
0
10
20
30
40
50
60
70
# of
mea
sure
men
ts
P={100,70,60,40,55,80,65,90,40,75,90}, u=30%
L=770B
N=2
CM=40Mbps
Lc: uniform in [40,1500]B
0 10 20 30 40 50 60 70 80 90Bandwidth (Mbps)
0102030405060708090
100110120130140
# of
mea
sure
men
ts
P={100,70,60,40,55,80,65,90,40,75,90}, u=30%
L=770B
N=8
ζ
Lc: uniform in [40,1500]B
=37Mbps+
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 25 of 28
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From CAIDA (San Diego) to ETH (Zurich)� Packet-pair modesM=f9,11,13,15.5, 19.5, 27, 32, 43g
0 10 20 30 40 50 60Bandwidth (Mbps)
0
10
20
30
40
50
60
# of
mea
sure
men
ts
jhana (CAIDA) to drwho (Zurich), L=1500B
N=2
CM=27Mbps
0 10 20 30 40 50 60Bandwidth (Mbps)
0
10
20
30
40
50
# of
mea
sure
men
ts
jhana (CAIDA) to drwho (Zurich), L=1500B
N=12
ζ+=24Mbps
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 26 of 28
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Pathrate verification
0 10 20 30 40 50 60 70 80Actual capacity (Mbps)
0
10
20
30
40
50
60
70
80
Cap
acity
est
imat
e (M
bps)
ϖ=1Mbps
0 10 20 30 40 50 60 70 80Actual capacity (Mbps)
0
10
20
30
40
50
60
70
80
Cap
acity
est
imat
e (M
bps)
w=1Mbps if C<40Mbps, w=2Mbps otherwise
ϖ ϖ=1Mbps =2Mbps
� Higher capacity values require larger bandwidth resolution �
� Adaptive selection of bandwidth resolution?
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 27 of 28
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Summary and contributions
� Capacity estimation in heavily-loaded paths is hard!
� Statistical filtering of packet-pair measurements does not work
� Use of maximum-sized packets is not optimal
� Packet-train dispersion does not estimate available bandwidth
� Available bandwidth can be computed from ADR in single-hop paths
� Pathrate takes into account effect of cross traffic on packet-trains
Constantinos Dovrolis - IEEE Infocom 2001 - April 24-26, 2001 28 of 28