Lecture 9 - Egan Family

cursefarmΔίκτυα και Επικοινωνίες

24 Οκτ 2013 (πριν από 4 χρόνια και 17 μέρες)

112 εμφανίσεις

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

2

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.

$

3

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

4

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

5

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

6

M.Ivanovich 9/99

Monash University, Australia

ATM Flexibility

7

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

8

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

9

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

10

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

11

M.Ivanovich 9/99

Monash University, Australia

The Relationship Between Network
Design and Dimensioning

Network Design

Dimensioning

Structuring

“the


engineer”

“the

architect”

12

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.

13

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

14

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”






15

M.Ivanovich 9/99

Monash University, Australia

ATM Network Dimensioning Tradeoffs

(for a given QoS)

Bandwidth

Traffic

Management

Buffering

16

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?

17

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.

18

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)




19

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

20

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


21

M.Ivanovich 9/99

Monash University, Australia

The
Call Scale :

Common Teletraffic
Models

22

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

23

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.

24

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



29

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.

31

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).

34

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 .)

36

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

37

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


38

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

42

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

48

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