1
M.Ivanovich 9/99
Monash University, Australia
Dimensioning
ATM
Networks
Dr. Milosh V. Ivanovich
e

mail:
ivanovic@sub.net.au
ISDN
Networks and
Applications
Week 9
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M.Ivanovich 9/99
Monash University, Australia
The Question
The FUNDAMENTAL DILEMMA of Carriers and
Service Providers :
??? How ???
to provide telecommunications
services
at minimal cost
Subject to

meeting Quality Of Service (QoS) requirements.
$
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M.Ivanovich 9/99
Monash University, Australia
The Answer lies in ...
By applying sound NETWORK DESIGN principles
... but Network Design
has conflicting
objectives !!
economic
robustness
QoS
fairness
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M.Ivanovich 9/99
Monash University, Australia
... Cleverly Exploiting ATM Network
Features
ATM network
=
a collection of
partially separated
logical networks.
Physical
Virtual Path
Virtual Channel
* Cell Priority Mgmt.
* VC Switching
* VP Switching
* Layered Network Architecture
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M.Ivanovich 9/99
Monash University, Australia
... First a Brief ATM Refresher
What is ATM ?
•
A
synchronous
T
ransfer
M
ode
•
Cell switching (relay)
•
Fixed cell size of 53 octets
•
Connection

oriented technology
48 Bytes
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M.Ivanovich 9/99
Monash University, Australia
ATM Flexibility
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M.Ivanovich 9/99
Monash University, Australia
Why is it called “ASYNCHRONOUS” ?
•
Cells are transmitted continuously (idle cells are
inserted)
•
Supports bursty services, easily and efficiently
•
Header identifies information stream
Cell Travel (full link rate)
Headers
Idle
Idle
Idle
Idle
Idle
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M.Ivanovich 9/99
Monash University, Australia
The Roles of ATM Traffic Management
•
Call Level
–
Connection Admission Control
•
point to point
•
broadcast
–
Call Set

up
–
Call Management (VC, VP)
–
Routing
•
Cell / Stream Level
–
Usage Parameter Control (Policing)
–
Congestion Control; Selective Discard
•
General
–
QoS Class
–
Transfer Capability
–
Traffic Shaping
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M.Ivanovich 9/99
Monash University, Australia
ATM Transfer Capabilities
ITU

T
vs.
ATM Forum
ITU

T ATM
Transfer Capability
ATM Forum
Service Category
DBR

Deterministic Bit Rate
SBR

Statistical Bit Rate
CBR

Constant Bit Rate
VBR

RT

Real Time Variable Bit Rate
VBR

NRT

Non Real Time
Variable Bit Rate
ABT

ATM Block Transfer
ABR

Available Bit Rate
N/A
ABR

Available Bit Rate
UBR

Unspecified Bit Rate
N/A
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M.Ivanovich 9/99
Monash University, Australia
ATM Traffic Categories and
Associated Applications
–
Interactive
Audio and Video (e.g. voice call,
videoconference), Circuit Emulation:
»
CBR, QoS Class 1
»
VBR

rt, QoS Class 1
–
Transfer for
immediate
use (e.g. image transfer, n.r.t.
guaranteed constant bit rate applications, maybe
some TCP applications

TELNET, HTTP).
»
CBR, QoS Class 2/3
»
VBR

nrt / ABR, QoS Class 2/3
–
Transfer for
later
use (e.g most TCP applications

FTP, SMTP).
»
ABR / UBR, QoS Class 2
Most Stringent
QoS Requirement
Least Stringent
QoS Requirement
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M.Ivanovich 9/99
Monash University, Australia
The Relationship Between Network
Design and Dimensioning
Network Design
Dimensioning
Structuring
“the
engineer”
“the
architect”
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M.Ivanovich 9/99
Monash University, Australia
ATM Network Structuring
Key factors to consider :
•
Distribution of user population.
•
Traffic:
expected volume, type, and time
+ geographical distributions.
•
Flexibility and scalability
•
Reliability
•
Low overall
{switching, transmission}
cost.
Guiding principles :
•
Choose a
flat
or
layered
switching architecture
based on the above factors.
•
Pre

emptive traffic segmentation

maintain QoS.
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M.Ivanovich 9/99
Monash University, Australia
ATM Network Structuring :
Traffic Segregation
S
ws
ws
ws
ws
ws
ws
ws
ws
S
S
S
ws
ws
ws
ws
ws
ws
ws
ws
S
S
VBR
only
VBR
CBR
Architecture A:
Segregation
Architecture B:
Symmetry
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M.Ivanovich 9/99
Monash University, Australia
ATM Network Structuring :
an “ATM
LAN” example
ws
ws
ws
ws
ws
S
VBR
CBR
mesh
Mixing traffic types, while guaranteeing QoS may be achieved by:
–
Architectural Traffic Segregation
–
Traffic Shaping (Buffering!) and Policing VBR conns.
–
“Throwing raw bandwidth at the problem”
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M.Ivanovich 9/99
Monash University, Australia
ATM Network Dimensioning Tradeoffs
(for a given QoS)
Bandwidth
Traffic
Management
Buffering
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M.Ivanovich 9/99
Monash University, Australia
The Subject In a Nutshell : ... at the Burst
Scale
What is the smallest bandwidth
(service rate) we can use to serve
an SSQ fed by
real traffic
such that
required CLR is met ? (for a given
buffer size).
ATM Network Dimensioning most commonly boils down to:
Link Dimensioning
CLR Prediction
OR
What is the predicted Cell
Loss Ratio (CLR) of a
single server queue fed
by the modeled process?
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M.Ivanovich 9/99
Monash University, Australia
Hierarchy of Time Scales
Calls
Bursts
Cells

Randomness from
phase independence.

Fluid flow models.

REM and RS.

Effective BW concept.

Multi

rate C.S. network.
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M.Ivanovich 9/99
Monash University, Australia
The
Call Scale : Effective Bandwidth
EB

Necessary to enable associating a “fixed” amount of
bandwidth with each inherently variable bit

rate call. Can
then model ATM network as a circuit switched network.
No single formula

EB depends on model used.
Example [GAN91], [KWC93] :
We wish to determine the minimal required service rate
C
B
(
e
)
such that the
probability
P
B
=Pr{X > B}
that the buffer occupancy (
X
) exceeds some level
B
is
below
e
. The buffer is part of a Single Server Queue (SSQ) system fed by a
Markov Modulated Rate Process (MMRP). Its complementary content
distribution is approximately given by the exponential,
–
Q(x) = Pr{X > x}
~
h
e

z
x
Making the assumptions from [GAN91] (i.e. that
h
~ 1) we get the Effective
Bandwidth to be:
–
C
B
(
e
) =
z

1
(

log
e
/ B)
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M.Ivanovich 9/99
Monash University, Australia
The
Call Scale :
Review of some
“Classical” Dimensioning Methods
Some Definitions:
Traffic Volume = Total of Service Times
Traffic Volume = Number of Calls x Average Service Time
Total of Service Times
Number of Calls
Average Service Time =
Traffic Volume___
Period of Observation
Average Traffic =
The unit of traffic is the “erlang”, symbolised by “E”
Erlangs
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M.Ivanovich 9/99
Monash University, Australia
Fundamental Relationship of
Teletraffic Engineering
Number of Calls__
Period of Observation
Average Traffic =
x Average Service Time
Average Arrival
Rate,
l
(Avg. Departure Rate)

1
m

1
A
... and what about “congestion” ??
A call encounters
congestion
or
blocking
if it can not proceed
immediately due to lack of resources.
*
Call Congestion
* Time Congestion
*
Traffic Congestion
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M.Ivanovich 9/99
Monash University, Australia
The
Call Scale :
Common Teletraffic
Models
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M.Ivanovich 9/99
Monash University, Australia
The
Call Scale :
A Model of Repeat
Call Attempts
Often a blocked call’s initiator will try again ...
S
Total
Attempts
First
Attempts
Repeat
Attempts
R
1

R
Abandoned
Calls
Ineffective
Attempts
Successful
Calls
All possible causes of
Ineffective Attempts
B
1

B
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M.Ivanovich 9/99
Monash University, Australia
The
Call Scale :
Modelling a Loss
System (Erlang

B)
The first step is to construct a State Transition
Diagram.
0
1
2
n
l
l
l
l
m
2m
3m
n
m
l
P
(0) = m
P
(1)
l
P
(1) = 2m
P
(2)
... up to
n
Define A =
l / m
...
(Offered Traffic, or
alternatively, Utilisation).
Use the “Cut”
Method to obtain
Balance Eqns.
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M.Ivanovich 9/99
Monash University, Australia
Comparison of Poisson & Erlang

B PDFs
25
M.Ivanovich 9/99
Monash University, Australia
Can we Really Use the Erlang

B Formula
for ATM Network Dimensioning ?
YES, but ...
–
Only in
one
very special, and
not very useful
case:
when all connections sharing the ATM bearer are of
the same rate (“?!But the whole point of ATM is ...”)
–
For example, we could have 10 combined CBR
and VBR VC connections, with EB = 2Mbit/s,
sharing a 34Mbit/s ATM VP.
–
Blocking Probability would be = E (10, 34 / 2)
»
where E(*, *) is the Erlang

B Loss Function.
Conclusion :
–
WE NEED MORE SOPHISTICATED MODELS !
26
M.Ivanovich 9/99
Monash University, Australia
The Answer: Multi

rate Models
Basic Link Model for the
Complete Sharing Policy
•
N
different traffic classes accessing an ATM Tx link with cap.
c
Mbps
•
Arrival process for class
i
calls is Poisson, rate
l
i
.
•
Holding time follows a general distribution function, mean
1/
m
i
.
•
During the lifetime of a class
i
call, a constant rate denoted by
c
i
, is
allocated to it, and released immediately after its departure.
27
M.Ivanovich 9/99
Monash University, Australia
Kaufman and Roberts Recursive Solution
Exact algorithm

not an approximation.
Based on a mapping of the multi

dimensional state
space into a one dimensional state space.
Uses “proper bandwidth discretisation”.
Prevents “State Explosion” by compressing many
different states into one.
•
Basic Bandwidth Unit,
BBU
:
•
gcd
is the “greatest common divisor”.
•
In broadband networks, typical
BBUs
may be 64kbps or 2.048Mbps.
•
Max. No. of available
BBUs
:
•
No. of
BBUs
required for class
i
:
•
System states defined by one quantity

the no. of occupied
BBUs
:
m
28
M.Ivanovich 9/99
Monash University, Australia
An Example : A Four Class System
Call Blocking Probabilities

note the
UNFAIRNESS
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M.Ivanovich 9/99
Monash University, Australia
An Example : A Four Class System (cont.)
Link utilisation sharing

related to UNFAIRNESS,
note the
under

utilisation
for greater BW classes.
30
M.Ivanovich 9/99
Monash University, Australia
Equalisation and Fairness Issues
Basic link model for Trunk Reservation (
TR
).
•
Many different Connection Admission Control (CAC) strategies for
achieving some form of fairness exist :
complete sharing, partial
sharing, class limitation, trunk reservation (TR).
•
For a comparson of such strategies, see [KW88].
•
Briefly consider
TR

one of the
simplest and most effective
methods
to adjust/equalise call blocking.
•
Aim is to influence performance parameters such as call blocking pr.
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M.Ivanovich 9/99
Monash University, Australia
Enhancements :
Combined Call and Burst Scale Model
Similar to complete sharing model outlined on p25.
Tx link capacity
c
,
N
traffic classes (CBR & VBR).
CBR calls modelled at call level only.
VBR calls modelled at both burst and call levels.
Connection admission control and blocking
behaviour is different for CBR and VBR calls:
–
CBR calls of class
i
»
Must be accepted at CALL level.
»
And at BURST level.
–
VBR calls of class
j
»
Must be accepted at CALL level only.
Call Blocking
Burst Blocking
32
M.Ivanovich 9/99
Monash University, Australia
The
Burst (Stream) Scale

What is it?
A time scale typical of an:
–
ON/OFF source’s activity period,
–
Video Frame duration,
–
IP packet (carrying say a UDP datagram),
–
Or any other “interval” aggregating some cells, but
not being as long as a call duration.
The discrete nature of cell arrivals can be ignored.
Instead, we focus on the incoming
“stream”
of cells.
–
Denoted by the continuous random variable
A
n
or
A(t)
representing the “amount of work” entering
the system,
–
A
n
used for discrete time modelling,
–
A(t)
used for continuous time modelling .
33
M.Ivanovich 9/99
Monash University, Australia
The
Burst Scale (cont.)
Time can either be modelled as :
–
Continuous:
generally used for fluid flow
based models.
–
Discrete:
time divided into fixed

length
sampling intervals
.
Burst scale congestion

modelled by :
–
Burst scale
loss
, in the form of Rate
Envelope Multiplexing (REM), and /or
–
Burst scale
delay
, in the guise of Rate
Sharing (RS).
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M.Ivanovich 9/99
Monash University, Australia
Three approaches for Link Dimensioning
(and CAC) at the Burst Scale
•
Peak Allocation
•
Rate Envelope Multiplexing
(REM)
•
Rate Sharing (RS)
35
M.Ivanovich 9/99
Monash University, Australia
Three approaches for Link Dimensioning
(and CAC) at the Burst Scale (cont .)
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M.Ivanovich 9/99
Monash University, Australia
Burst Scale Link Dimensioning Example
•
Want to dimension an ATM bearer,
•
Given 70 variable bit

rate 2 Mb/s connections,
•
How much capacity is needed?
70 x 2 = 140 Mb/s
A Simple Solution:
Peak Rate Allocation
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M.Ivanovich 9/99
Monash University, Australia
Example Continued: Let’s Try REM
•
More information required for each connection:
Peak
(
p
) = 2 Mb/s,
Mean
(
m
) = 0.2 Mb/s
•
Assume
On/Off Model
for each connection so:
Variance
= (p

m) m = 1.8 x 0.2 = 0.36
•
For 70 connections (linear superposition):
Aggregate Mean = 70 x 0.2 = 14
Aggregate Variance = 70 x 0.36 = 25.2
•
By the Central Limit Theorem, the Aggregate Traffic
Rate (Mb/s) can be modelled by a Gaussian R.V.
X
:
m
=
14
and
s
2
= 25.2
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M.Ivanovich 9/99
Monash University, Australia
REM Example

Continued
•
Minimize
Required Link Bandwidth
,
B
(Mb/s)
•
Subject to Bit Loss Ratio (BLR) < 10

5
•
Where BLR is given by:
BLR =
E [( X

B )
+
] / E [X]
Solution:
(1)
(
X

B)
+
= X

B
if
X >B
and =
0
if X < B.
(2)
If
X
has density
f(x)
then:
39
M.Ivanovich 9/99
Monash University, Australia
REM Example

Continued
Solution (cont.):
(3)
The Bit Loss Ratio
is thus given by
(4)
Using the
bisection algorithm
, this equation is then
numerically solved (e.g. use C++ program, or tool
such as
Mathematica
):
B
min
= 32.485376
Mb/s.
40
M.Ivanovich 9/99
Monash University, Australia
Rate Sharing
•
More complex to model because :
–
Large buffers as well as bandwidth is
considered,
–
Now correlation is important.
•
Traffic Modelling
•
Queueing Theory & Simulation
•
Real traffic traces
•
Two approaches: Classical and Direct.
41
M.Ivanovich 9/99
Monash University, Australia
Gamma Loss Prediction Tool
:
SSQ Dimensioning by the Classical Method
Compute Cell
Loss Rate (CLR)
Find new
service rate
Input:
* Queue information
(service, buffer)
* Traffic model or trace
CLR
service rate
Aim:
Find
Minimum service rate
Subject to CLR
Method:
Bisection
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M.Ivanovich 9/99
Monash University, Australia
Autocorrelation of a Traffic Stream
•
Low autocorrelation
–
Low dependence between traffic arriving in intervals
separated in time.
High autocorrelation
–
High dependence between traffic arriving in intervals
separated in time.
43
M.Ivanovich 9/99
Monash University, Australia
Real Life Example of RS versus REM (1)
Link Utilisation vs. Buffer Size
Measured Ethernet TRAFFIC

Loss Probability = 1/10,000
Buffer Size (cells)
100,000
10,000
1,000
Utilisation %
0
100
80
60
40
20
100
REM
Rate Sharing
44
M.Ivanovich 9/99
Monash University, Australia
Real Life Example of RS versus REM (2)
Link Utilisation vs. Buffer Size
VBR Video TRAFFIC (MPEG)
Loss Probability=1/10,000
Utilisa tion %
Buffer Size (cells)
0
10
20
30
40
50
60
70
100
1,000
10,000
100,000
REM
RS
45
M.Ivanovich 9/99
Monash University, Australia
Critical Statistical Characteristics of a
Traffic Process
•
Mean,
•
Variance,
•
Autocovariance Sum or Autocovariance
Integral (equal to the Asymptotic
Variance Rate).
46
M.Ivanovich 9/99
Monash University, Australia
Arrival Process Autocovariance Sum / Integral

5.0

4.0

3.0

2.0

1.0
0.0
1.0
2.0
3.0
4.0
5.0
The Variance
v=Autocovariance Integral
Lag
47
M.Ivanovich 9/99
Monash University, Australia
Common SRD Traffic Models ...
•
Bernoulli Process
•
Geometric (or Binomial) Batch
Process
•
On

Off
•
n

state Markov Modulated Processes
•
Gaussian
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M.Ivanovich 9/99
Monash University, Australia
But what if the Autocovariance sum is
infinite?
LONG RANGE DEPENDENCE (LRD)
otherwise known as
SELF

SIMILAR (FRACTAL) TRAFFIC
lag
autocorrelation
LRD
SRD
49
M.Ivanovich 9/99
Monash University, Australia
SRD Process :
Poisson
Traffic at Different
Timescales
50
M.Ivanovich 9/99
Monash University, Australia
LRD Process :
Ethernet
Traffic (Self Similar)
51
M.Ivanovich 9/99
Monash University, Australia
Measuring Self

Similarity : the Hurst Parameter
Slope = 1: Non

fractal (SRD)
Slope > 1: Fractal (LRD)
Log
V(A(t))
Log
(t)
52
M.Ivanovich 9/99
Monash University, Australia
Hurst Parameter Values for VBR Video Traffic
53
M.Ivanovich 9/99
Monash University, Australia
Why is Real Traffic Bursty and Correlated on
a Wide Range of Timescales (FRACTAL) ?
•
Very diverse IP packet lengths
–
FTP, SMTP, IP Phone ... etc. packets have very
different size distributions.
•
Large differences exist in WWW document
sizes
•
VBR Video streams found to be self similar
•
People and business timing characteristics
(meeting, holidays, etc.)
54
M.Ivanovich 9/99
Monash University, Australia
A Wide Difference of Document Sizes
Available Through the WWW
Data Entity
Bytes
ASCII Page
10
3
X

Ray
10
7
Star War (JPEG coded)
5
10
9
Word document (10 pages)
5
10
4
55
M.Ivanovich 9/99
Monash University, Australia
References 1/2
[AZN98]
R.G. Addie, M. Zukerman, and T. D. Neame, “Broadband Traffic Modelling: Simple
Solutions to Hard Problems”,
IEEE Communications Magazine
, p88

95, August, 1998.
[EGHS96]
V. Elek, Z. Gal, P. L. Huong and C. Szabo, “ATM LAN Network Design”,
Journal on
Telecommunications,
vol. XLVII, January

February, 1996.
[EM73]
O. Enomoto and H. Miyamoto, “An analysis of mixtures of multiple bandwidth traffic on
time division in switching networks”, In
7th Int. Teletraffic Congress Proceedings
, pages
635.1

8, North Holland

Elsevier Science Publishers , 1973.
[HR93]
F. Huebner and M. Ritter, “Blocking in multi

service broadband systems with CBR and
VBR input traffic.”,
In 7th ITG/GI Conference,
pages 212

225, Aachen, September 1993.
[Hui88]
J. Y. Hui, “Resource Allocation for Broadband Networks”,
IEEE J. Sel. Areas in
Comm.,
vol. 6 no. 9: p.1598

1608, 1988.
[Kau81]
J. S. Kaufman, “Blocking in a shared resource environment”,
IEEE Trans. Comm.,
vol.
29, no. 10 : 1474

1481, 1981.
[KW88]
R. Kleinewillinghoefer

Kopp and E. Wollner, “Comparison of access control strategies
for ISDN

traffic on common trunk groups”, In 12th Int. Teletraffic Congress Proceedings,
pages 5.4A.2.1

7, North Holland

Elsevier Science Publishers, 1988.
[KWC93]
G. Kesidis, J. Walrand, and C

S. Chang, “Effective bandwidth for multiclass Markov
fluids and other ATM sources”, IEEE/ACM Trans. Networking, vol.1 no. 4: p424

428,
August, 1993.
56
M.Ivanovich 9/99
Monash University, Australia
References 2/2
[LPTB93]
J. Lubacz, M. Pioro, A. Tomaszewski and D. Bursztynowski, “A framework for network
design and management”,
Internal Report, Institute of Telecommunications, Warsaw
University of Technology,
1993.
[RMV96]
J. Roberts, U. Mocci and J. Virtamo (Eds.), “Broadband Network Teletraffic”,
Final
Report of Action COST 242
, Springer, Berlin, 1996.
[Rob81]
J. W. Roberts, “Teletraffic models for the telecom 1 integrated services network”, In
10th Int. Teletraffic Congress Proceedings
, page 1.1.2, North Holland

Elsevier Science
Publishers, 1983.
[TGH93]
P. Tran

Gia and F. Huebner, “An analysis of trunk reservation and grade of service
balancing mechanisms in multiservice broadband networks.”,
In IFIP Workshop TC6,
Modeling and Performance Evaluation of ATM Technology,
page 2.1, La Martinique, 1993.
57
M.Ivanovich 9/99
Monash University, Australia
Acknowledgments
Thanks to the following people for ideas / illustrations /
and selected references:
A. Prof. Moshe Zukerman, University of Melbourne
Dr. Robert Warfield, Telstra
Peter Black,
Telstra Research Laboratories
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