CapProbe: An Efficient and
Accurate Capacity Estimation
Technique
Rohit Kapoor**, Ling-Jyh Chen*, Li Lao*,
M.Y. Sanadidi*, Mario Gerla*
** Qualcomm Corp R&D
*UCLA Computer Science Department
The Capacity Estimation Problem

Estimate minimum link capacity on an Internet
path, as seen at the IP level
100 Mbps
50 Mbps
100 Mbps
10 Mbps
(Link Capacity)

Design Goals



End-to-end: assume no help from routers
Inexpensive: Minimal additional traffic and processing
Fast: converges to capacity fast enough for the
application
Applications





Adaptive multimedia streaming
Congestion control
Capacity planning by ISPs
Overlay network structuring
Wireless link monitoring and mobility detection
Packet Pair Dispersion
T1
T3
Narrowest Link
T2
20Mbps
10Mbps
T3
5MbpsT3
10Mbps
T3
20Mbps
8Mbps
Ideal Packet Dispersion

No cross-traffic
Capacity = (Packet Size) / (Dispersion)
Expansion of Dispersion



Cross-traffic (CT) serviced between PP packets
Second packet queues due to Cross Traffic (CT )=>
expansion of dispersion =>Under-estimation
More pronounced when CT pkt size < probe pkt size
Compression of Dispersion

First packet queueing => compressed dispersion =>
Over-estimation
 More pronounced when CT pkt size > probe pkt size
Previous Work

Jacobson’s Pathchar




Estimates capacity for every link
Sends varying size packets
Relies on round trip delays
Packet Pairs (PP)

Crovella
• Capacity is reflected by the packet pair dispersion that
occurs with highest frequency

Lai
• Filters samples whose dispersion reflects a capacity
greater than their “potential bandwidth”


Both these techniques assume unimodal
distribution
Paxson showed distribution can be multimodal
Previous Work

Dovrolis’ Work


Analyzed under/over estimation of capacity
Designed Pathrate
• First send packet pairs
• If multimodal, send packet trains
• Identifies modes to distinguish ADR (Asymptotic
Dispersion Rate), PNCM (Post Narrow Capacity Mode)
and Capacity Modes

Previously proposed techniques have relied
either on dispersion or delay
Key Observation

First packet queues more than the second
Compression
Over-estimation

Second packet queues more than the first
• Expansion
• Under-estimation

Both expansion and compression are the
result of probe packets experiencing queuing
• Sum of PP delay includes queuing delay
CapProbe Approach

Filter PP samples that do not have minimum
queuing time

Dispersion of PP sample with minimum delay
sum reflects capacity

CapProbe combines both dispersion and e2e
transit delay information
Techniques for Convergence Detection

Consider set of packet pair probes 1…n

If min(d1) + min(d2) ≠ min(d1+d2), dispersion obtained
from min delay sum may be distorted
• Above condition increases correct detection probability to that of
a single packet (as opposed to packet pair)

If above minimum delay sum condition is not
satisfied in a run

New run, with packet size of probes
• Increased if bandwidth estimated varied a lot across probes

Errors in dispersion measured by OS
• Decreased if bandwidth estimated varied little across probes

Packet sizes too large to go through without queuing
Experiments

Simulations
 TCP (responsive), CBR (non-responsive), LRD
(Pareto) cross-traffic
 Path-persistent, non-persistent cross-traffic
Simulations

6-hop path: capacities {10, 7.5, 5.5, 4, 6, 8} Mbps
 PP pkt size = 200 bytes, CT pkt size = 1000 bytes
 Path-Persistent TCP Cross-Traffic
Bandwidth Estimate
Frequency
Minimum Delay Sums
0.01
0.009
1Mbps
2Mbps
4Mbps
0.008
0.007
1Mbps
2Mbps
4Mbps
0.7
0.005
0.004
0.6
0.5
0.4
0.003
0.3
0.002
0.2
0.001
0.1
0
0
1.6
3.2
4.8
6.4
Bandw idth Estim ate (Mbps)
Cross Traffic Rate
0.8
0.006
0
Over-Estimation
0.9
Frequency
Min Delay Sums (sec)
1
Cross Traffic Rate
8
0
1.6
3.2
4.8
6.4
Bandw idth Estim ate (Mbps)
8
Simulations

PP pkt size = CT pkt size = 500 bytes
 Non-Persistent TCP Cross-Traffic
Bandwidth Estimate
Frequency
Minimum Delay Sums
0.0063
1
1Mbps
0.9
1Mbps
0.8
3Mbps
0.7
0.0042
Frequency
Min Delay Sum (sec)
3Mbps
0.0021
0.6
Under-Estimation
0.5
0.4
0.3
0.2
0.1
0
0
0
1.6
3.2
4.8
6.4
Bandw idth Estim ate (Mbps)
8
0
1.6
3.2
4.8
6.4
Bandw idth Estim ate (Mbps)
8
Simulations

Non-Persistent UDP CBR Cross-Traffic
Bandwidth Estimate
Frequency
Minimum Delay Sums
1
0.014
0.01
1Mbps
2Mbps
3Mbps
4Mbps
0.8
0.7
Frequency
Min Delay Sums (sec)
0.9
1Mbps
2Mbps
3Mbps
4Mbps
0.012
0.008
0.006
0.6
0.5
0.4
0.3
0.004
0.2
0.002
0.1
0
0
0

1.6
3.2
4.8
6.4
Bandw idth Estim ate (Mbps)
8
0
1.6
3.2
4.8
6.4
Bandw idth Estim ate (Mbps)
Case where CapProbe may not work


UDP (non-responsive), extremely intensive
No correct samples are obtained
8
CapProbe Accuracy

Sufficient requirement


At least one PP sample where both packets
experience no CT induced queuing delay.
How realistic is this requirement?


Internet is reactive (mostly TCP): high chance of
some probing samples not being queued
To validate, we performed extensive
experiments
• Only cases where such undistorted samples are
not obtained is when cross-traffic is UDP and
very intensive (typically >75% load)
Probability of Obtaining Sample
Second Packet
First Packet
Link
No Queue
No Cross
Traffic Packets


Assuming PP samples arrive in a Poisson manner
Poisson cross-traffic: product of probabilities


No queue in front of first packet: p(0) = 1 – λ/μ
No CT packets enter between the two packets
(conservative estimate)
• Only dependent on arrival process
p = p(0) * e- λL/μ = (1 – λ/μ) * e- λL/μ
Analysis also for Deterministic and Pareto cross-traffic


Probability of Obtaining Sample (cont)
Avg number of samples required to
obtain an unqueued PP for a single
link; Poisson cross-traffic
Avg number of samples required to
obtain an unqueued PP for a single
link; LRD cross-traffic
Effect of Packet Size on Accuracy

For CapProbe to estimate accurately


Second packet of PP


Neither packet of the PP should queue due to cross traffic
Smaller  less chances of queuing due to cross-traffic
First packet of PP

Probability of queuing independent of size (queuing theory)
Thus, smaller PP packets  higher probability of sample
not subject to queuing
 Previous authors (Dovrolis) have shown that


Smaller packets reduce chances of under-estimation but increase
chances of over-estimation
Effect of Packet Size on Accuracy

Our observations are entirely consistent with earlier ones

For the second packet, smaller packet size  Smaller
probability of being queued  Relative probability of
queuing of first packet is increased  Chances of overestimation are increased
0.12
0.3
(b)
(a)
0.25
0 .1
0.08
Fre que nc y
Frequency
0.2
0.15
0.1
0.06
0.04
0.02
0.05
0
0
0
1
2
3
4
5
Bandw idth ( Mbps )
6
7
8
0
1
2
3
4
5
6
7
8
Bandwidt h (M bps )
Frequency of occurrence of bandwidth samples when packet size of probes
is (a) 100 and (b) 1500 bytes
Measurements- Internet, Internet2 (Abilene),
Wireless (802.11, Bluetooth)
• CapProbe implemented using PING packets, sent in pairs
UCLA-2
To
Cap
Probe
Pathrate
Pathchar
UCLA-3
UA
NTNU
Time
Capacity
Time
Capacity
Time
Capacity
Time
Capacity
0’03
5.5
0’01
96
0’02
98
0’07
97
0’03
5.6
0’01
97
0’04
79
0’07
97
0’03
5.5
0’02
97
0’17
83
0’22
97
6’10
5.6
0’16
98
5’19
86
0’29
97
6’14
5.4
0’16
98
5’20
88
0’25
97
6’5
5.7
0’16
98
5’18
133
0’25
97
21’12
4.0
22’49
18
3 hr
34
3 hr
34
20’43
3.9
27’41
18
3 hr
34
3 hr
35
21.18
4.0
29’47
18
3 hr
30
3 hr
35
Issues

CapProbe may be implemented either in the
kernel or user mode


Kernel mode more accurate, particularly over highspeed links
One-way or round-trip estimation

One-way
• Requires cooperation from receiver
• Can be used to estimate forward/reverse link

Active vs passive


Probing packets or data packets used as probes
Heavy cross-traffic/extremely fast links

Difficulty in correct estimation
Summary
 CapProbe
is accurate, fast, and
inexpensive, across a wide range of
scenarios
 Potential applications in overlay structuring,
and in case of fast changing wireless link
speeds
 High-speed dispersion measurements
needs more investigation
 CapProbe website:
http://nrl.cs.ucla.edu/CapProbe