Available Bandwidth
Estimation
Manish Jain
Networking and Telecom Group
CoC, Georgia Tech
Outline
Introduction and definitions
 Estimation methodologies

 Train
of Packet Pairs(TOPP)
 Self Loading Periodic Streams (SLoPS)
 Packet Train Gap Model

Open Issues
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Definition





Available Bandwidth: unutilized capacity
Varies with time
ui : utilization of link i in time interval t ( 0 <= ui <= 1 )
Available bandwidth in link i:
Ai  Ci(1 - ui)
Available bandwidth in path (Avail-bw):
A  min Ai  min Ci (1 - ui)
i 0..H

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i 0..H
Tight link: minimum avail-bw link
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Available Bandwidth:time varying
metric
t
A(t)
T
t


t defines sampling/averaging timescale
Average avail-bw in t
 Does
not tell how avail-bw varies
 Variation range gives more information
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Why do we care ?
ssthresh in TCP
 Streaming applications
 SLA verification
 Overlay routing
 End-to-end admission control

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Measuring per-hop available
bandwidth




Can be measured at each link from interface
utilization data using SNMP
MRTG graphs: 5-minute averages
But users do not normally have access to SNMP data
And MRTG graphs give only per-hop avail-bandwidth
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Measuring path Available
Bandwidth

Blast path with UDP packets


Intrusive
Carter & Crovella: cprobe (Infocom 1996)


Measure throughput of large TCP transfer


Packet train dispersion does not measure available bandwidth
(Dovrolis et.al. Infocom’01)
TCP throughput depends on network buffer
Ribeiro et.al. : Delphi (ITC’00)


Correct estimation when queuing occurs only at single link
Assumes that cross traffic can be modelled by MWM model
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A New End-to-end probing and
analysis method for
estimating bandwidth
bottlenecks
B. Melander et al, In Global Internet
Symposium, 2000
8
Introduction

In FCFS queue, output rate is function of
input rate and cross-traffic rate
Oj-1
Mj-1


In one hop:
In two hop:
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Oj
Cj
Cj+1
Cj+1-Mj > Cj-Mj-1
Mj

o
o j   j 1o j 1
*C j

 o j 1m j 1
Oj+1
if o j 1C j m j
if o j 1C j -m j
 o j 1
if o j C j 1 m j 1&o j 1C j m j
 o
j 1
*C j
if o j C j 1 m j 1&o j 1 C j m j

 o j 1  m j 1

o j 1  
o j 1

o j 1m j 1
*C j *C j 1 if o j C j 1-m j 1 &o j 1 C j m j
 o
j 1
m j 1

 o j 1  m j 1
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Key Idea:TOPP


o :sending rate
f: receiving rate
Break points
o
 a i  bi o
f


where i is number links
with different available
bandwidth
For i=1


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b1=1/Ctight
a1=1-Atight/Ctight
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Algorithm

Algorithm:





Avail-bw and capacity of other links can be
measured
 if

Send n probe pairs with a minimum rate
Record receive rate at receiver
Increment rate by fixed d and repeat
Measure available bandwidth from the relation of o/f vs o
links in ascending order of avail-bw
In practice, break points may be hard to
identify
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End-to-end Available Bandwidth:
Measurement Methodology,
Dynamics and Relation with TCP
Throughput
M. Jain and C. Dovrolis, In IEEE/ACM
TON, August 2003
12
Key idea: SLoPS

Examine One-Way Delay (OWD) variations of a fixed rate
stream




Relate rate to avail-bw
R
S
OWD: Di = Tarrive-Tsend
= Tarrive - Tsend + Clock_Offset(S,R)
SLoPS uses relative OWDs, DDi = Di+1 – Di-1 (independent of
clock offset)
With a stationary & fluid model for the cross traffic, and FIFO
queues:
R


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R
If R > min Ai, then DDi > 0 for I = 1…N
Else DDi = 0 for for I = 1…N
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Illustration of SLoPS

Periodic Stream: K packets, size L bytes, rate R = L/T

If R>A, OWDs gradually increase due to self-loading of stream
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Trend in real data

For some rate R


Increasing trend in OWDs  R > Avail-bw
No trend in OWDs  R < Avail-bw
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Iterative algorithm in SLoPS




At sender: Send periodic stream n with rate Rn
At receiver: Measure OWDs Di for i=1…K
At receiver: Notify sender of trend in OWDs
At sender: If trend is :

increasing (i.e. Rn >A )  repeat with Rn+1 < Rn
non-increasing (i.e. Rn <A )  repeat with Rn+1>Rn



Selection of Rn+1 : Rate adjustment algorithm
Terminate if Rn+1 – Rn < 
 : resolution of final estimate
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If things were black and white…

Grey region: Rate R not clearly greater or smaller
than Avail-bw during the duration of stream

Rate R is within variation range of avail-bw
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Big Picture



Increasing trend  R > variation range of
Avail-bw
No trend  R < variation range of Avail-bw
Grey trend  R inside variation range
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Variation Range
Rate adjustment algorithm
Rmax
Grey region
>A
Gmax
Gmin
Rmin < A
Terminate if:
(Rmax – Gmax) && (Rmin– Gmin) < 
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Increasing trend :
Rmax = R(n)
R(n+1) = (Gmax + Rmax)/2
Non-increasing trend:
Rmin = R(n)
R(n+1) = (Gmax +Rmin)/2
Grey region & R(n) > Gmax:
Gmax = R(n)
R(n+1) = (Gmax + Rmax )/2
Grey region & R(n) < Gmin:
Gmin = R(n)
R(n+1) = (Gmin + Rmin )/2
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How do we detect an increasing trend?
(D  D )

I
(
D

D
)

R 
R 
K 1
 |D D |
K
K
j 2
j
j 2
j  1
pdt
pct
j  1
j
K
j 2
j
j  1
Infer increasing trend when PCT or PDT trend  1.0
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Verification approach

Simulation




Multi-hop topology
Cross traffic: Exponential and Pareto interarrivals
Varying load conditions
Experiment




Paths from U-Delaware to Greek universities and U-Oregon
MRTG graphs for most heavily used links in path
Compare pathload measurements with avail-bw from MRTG
graph of tight link
In 5-min interval, pathload runs W times, each for qi secs 5min average avail-bw R reported by pathload:
W
qi Rimax  Rimin
R
2
i 1 300
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Verification: Simulation

Effect of tight link load
Pathload range versus avail-bw during simulation (average of 50 runs)
 5 Hop, Ctight=10Mbps, utilnon-tight=.6 %


Center of pathload range: good estimate of average of avail-bw
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Verification: Experiment

Tight link: U-Ioannina to AUTH (C=8.2Mbps), =1Mbps
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Avail-bw Variability versus
stream length

Relative variation index:

Longer probing stream observe lower variability

However, longer streams can be more intrusive
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Avail-bw variability versus
traffic load

Heavier link utilization leads to higher avail-bw variability
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Evaluation and
Characterization of
Available Bandwidth
Techniques
N. Hu et al, JSAC, August 2003
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Packet Pair Model: Single Hop

In single hop path


Competing traffic may be inserted between packet pair
Packet pair gap at receiver is function of cross traffic
Gi
Input
Go
q
t
Case1: Go = Gi – q/C < Gi
Case2: Go=m/C+Gb


Go
m/C
Assumption: Fluid cross traffic
In practice, CT is bursty

t
t
Packet train will capture average
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Packet Train Model: Single Hop
Gi
Gb
M
Gi+
t
C *  (g  gB )

i
i 1
M
K
N
i 1
i 1
i 1



g

g

g
 i  i  i

Assumption:


t
Where Total numer of probing packets = M+K+N
Only increased gap sees CT
Packet dispersion not affected by CT at post-tight link
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IGI and PTR Algorithm
Start by sending out packet train with
minimum gap ( gB)
 If gap@receiver != gap@sender

 Send

another train with increased gap
Else calculate available bandwidth
 IGI:
Use equation
 PTR: Available Bandwidth = Rate of last
train measured at receiver
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Summary: Single Hop Model

IGI:
 Need
to know the capacity of tight link
 Assume that tight link is same as narrow link

PTR:
 Same

as TOPP
Relation of amount of cross-traffic and
dispersion
 May
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not hold in multi-hop path
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Open Issues

Integrate avail-bw estimation methodology with
application


Implement avail-bw estimation algorithm in network
interface card



Use data packets in place of probe packets
Allow routers to do avail-bw estimation
Can we make some short-term predictions of availbw?
High bandwidth paths

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Time stamping packets
MTU limitations
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Pathchirp


Uses exponentially spaced packet train
Main idea:


Avail-bw > Rk , if qk >= qk+1
Avail-bw < Rk , otherwise




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Can be used when probe packets are close enough
Identify excursions: consecutive packets show increased
queuing delays
Per-packet avail-bw Ek
Final estimate: Expected value of Rk
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