Saint-Petersburg State University of
Telecommunications
Analysis of IP-oriented Multiservice Networks
Characteristics with Consideration of Traffic’s
Self-Similarity Properties
Anatoly M. Galkin
galkinam@inbox.ru
Adviser: Dr., Professor Gennady G. Yanovsky
Analysis of IP-oriented Multiservice Networks Characteristics
with Consideration of Traffic’s Self-Similarity Properties
OUTLINE
•Why IP and why self-similarity?
•Self-similarity, what is it?
•Heavy-tailed Distributions
•Self-similarity and Networks
•Conclusions
Analysis of IP-oriented Multiservice Networks Characteristics
with Consideration of Traffic’s Self-Similarity Properties
OUTLINE
•Why IP and why self-similarity?
•Self-similarity,
what is it?
NGN
IP Traffic types
•Heavy-tailed
distributions
•Self-similarity and Networks
•Conclusions
Why IP ?
Growth of data services
Channel switching
Active introduction of IP networks
Packet switching
NGN – next generation network
NGN is united network
 Supports different types of traffic
 Built on the base of the universal technology
 Divides switching, signaling and management
 Provides mentioned QoS (quality of service)
Why IP ?
voice
NGN
FR
...
IP
ATM
-Data networks evolution to NGN: the problem of compatibility of
technologies and standards (providing traffic transmission of
different applications in united transport network)
- Voice networks evolution to NGN: the problem of conversion
from Channel Switching to Packet Switching
Why IP ?
2001 year - Conceptual regulations about multiservice
networks structure in Russian communication networks
NGN architecture
Management system
Management
Application
servers
Applications
Softswitches
Control
Core
Separate networks
Access
Packet network
Mobile network
UTRAN
Business subscribers
PSTN
Broadband
network
DSL
CS
Remote office/SOHO
Media
Gateway
WLL
LE
Home subscribers
Mobile subscribers
Why IP ?
IP oriented networks
Multiservice IP network applications classification of traffic types
Type of
traffic
Applications
IP telephony,
videoconference
Delay sensitivity
Delay jitter sensitivity
Low losses sensitivity
RSVP, RTP,
RTCP,UDP
Control processes,
on-line games
Delay sensitivity
Delay jitter sensitivity
Losses sensitivity
UDP, TCP
Audio on demand
Video on demand
Internet broadcasting
Low delay sensitivity
Delay jitter sensitivity
Losses sensitivity
RSVP,
SCTP,
UDP,TCP
Real time
Stream
Elastic
Requirements
Transport
layer
protocols
Conference of
documentation
Low delay sensitivity
Low delay jitter sensitivity
High losses sensitivity
Animation,
file transfer,
E-mail
Very low delay sensitivity
Low delay jitter sensitivity
High losses sensitivity
TCP
Why self-similarity ?
Problem of NGN is to provide QoS for all types of
traffic
QoS depends on service model
Old Markovian models (memory-less), Poisson laws
and Erlang formulas don’t work in new networks.
1993 year W. Lenard, M. Taqqu, W. Willinger, D.
Wilson. “On the Self-Similar Nature of Ethernet
Traffic”
Analysis of IP-oriented Multiservice Networks Characteristics
with Consideration of Traffic’s Self-Similarity Properties
OUTLINE
•Why IP and why self-similarity?
•Self-similarity, what is it?
Fractals distributions
•Heavy-tailed
Some mathematics
•Self-similarity
and Networks
Hurst parameter
•Conclusions
Self-similarity, what is it?
Fractals
1975 Benua Mandelbrot
fractus (lat.)– consisting of fragments
0D
1D
2D
1.5D
3D
Fern leaf
Fractals property – self-similarity
Fractals are determined by the equations of chaos
Chaos deterministic chaos
Stochastic fractal processes are described by selfsimilarity of statistical characteristics of the second
order
Self-similarity, what is it?
Notations
X  ( X 1 , X 2 ,...)
X ( m )  ( X 1( m ) , X 2( m ) ,...) Aggregated process
Semi-infinite segment of
second-order-stationary
stochastic process
Its discrete argument

X t( m ) 
rm (k )  autocorrel ation function

t  N {1,2,...}
Its parameters
M [ X ]     average
D[ X ]   2   dispersion

r (k )  r (k ) 
( X t  k   )( X t   )
2
Let r(k)  k-L1(k), k
1
 X tmm1  ...  X tm , m,t  N
m
autocorrel ation function
0   1
L1 – is function slowly varying at infinity
Self-similarity, what is it?
Three definitions
Process is
1.Exactly second-order self-similar (es-s) with the parameter H=1  ( / 2), 0<  <1
If rm(k) = r(k), k  Z+, m  {2,3,…}
2.Second-order asymptotical self-similar (as-s) with the parameter H=1  ( / 2), 0<  <1
r k   g k , k  N
If mlim

3.Strictly self-similar (ss-s) with the parameter H=1  ( / 2), 0<  <1
If m1-H X(m) = X, mN
In other words
X is es-s, if the aggregated process X(m) is indistinguishable from the initial process X at
least in term of statistical characteristics in second order.
X is as-s, if it meets es-s process after it is averaged on blocks of length m and m
The relation between ss-s and es-s processes is analogous to relation between secondorder stationary process and strictly stationary process
Self-similarity, what is it?
Hurst parameter
Harold Edwin Hurst detected that foodless and fertile years
are not random
0<H<1 – Hurst parameter (exponent)
H=0.5 – Brownian Motion
0<H<0.5 – antipersistence of the process
0.5<H<1 – persistent behaviour of the process or the process
has long memory
Analysis of IP-oriented Multiservice Networks Characteristics
with Consideration of Traffic’s Self-Similarity Properties
OUTLINE
•Why IP and why self-similarity?
•Self-similarity, what is it?
•Heavy-tailed distributions
Parameters and
of distributions
•Self-similarity
Networks
Heavy tails
•Conclusions
Pareto
Weibull
Log-normal
Heavy-tailed distributions
Probability distributions
X – random value
F(x)=P(X<x) – distribution function
It determines probability of random value X<x, where x is certain value
0≤F(x)≤1
f(x)=dF(x)/dx – probability destiny f(x)≥0
M[x] – mathematical expectation

M [ x]   x  f ( x)dx

D[x] – dispersion, σ – root-mean-square deviation

D[ x]   ( x  M [ x]) 2  f ( x)dx,  ( x)  D( x)

C2 
D[ x]
M [ x]2 - quadratic coefficient of variation
Heavy-tailed distributions
Heavy-tailed distributions
Self-similar processes could be described by so-called
Heavy-tailed distributions
Definition
The random variable is considered to have heavy-tailed
distribution if P[ Z  x] ~ c  x  a , x   with 0<a<2
a – shape parameter , c – a positive constant
Light-tailed distributions (Exponential, Gaussian) have
exponential decrease tails
Heavy-tailed distributions have power law decrease tails
0<a<2 infinite dispersion
0<a≤1 also infinite average
Network interest is the case 1<a<2
Then H=(3-a)/2
Heavy-tailed distributions
Pareto distribution
a
b
F ( x)  P[ Z  x]  1    , b  x
 x
a 1
1
0,9
0,7
,b  x
a is the shape parameter,
b is minimum value of x
0,8
0,6
0,7
0,5
0,6
0,4
0,5
0,4
0,3
0,3
0,2
0,2
0,1
0,1
0
0
0
2
4
6
Prob. density
8
10
12
14
Distribution function
Pareto distribution is most frequently used (VoIP, FTP, HTTP)
Distribution function
a b
 
b  x
0,8
Prob. density
f ( x) 
Pareto Distribution
Heavy-tailed distributions
Weibull distribution
a
Weibull Distribution
, x  x0
a
, x  x0
a is the shape parameter,
β is the averaged weight speed
x0 is the minimum value of x
Prob. density
F ( x)  1  e
 x  x0 
 

 

e
 x  x0 
 

 

0,6
1,2
0,5
1
0,4
0,8
0,3
0,6
0,2
0,4
0,1
0,2
0
0
0
1
2
Prob. density
Weibull distribution is used for FTP
3
4
Distribution function
5
6
Distribution function
a  x  x0 
f x    

   
a 1
Heavy-tailed distributions
Log-normal distribution
 1
 ln x  m 2 
, x  0
exp 

2

f ( x)   x 2
2



0, x  0
Log-normal Distribution
0,1
0,9
0,09
0,8
0,08
Prob. density
0,07
0,6
0,06
0,5
0,05
0,4
0,04
0,3
0,03
Distribution function
0,7
0,2
0,02
0,1
0,01
0
0
0
5
10
Prob. density
15
20
25
Distribution function
It has a finite dispersion but has a subexponential decrease of a tail
It used for call-centers, LANs, etc.
Analysis of IP-oriented Multiservice Networks Characteristics
with Consideration of Traffic’s Self-Similarity Properties
OUTLINE
Kendall classification
Researches
of
networks
•Why IP and why self-similarity?
Limitations for real networks
•Self-similarity,
what
is it?
QoS parameters
calculation
•Heavy-tailed
distributions
Network modeling
•Self-similarity and Networks
•Conclusions
Self-similarity and networks
Kendall classification
A/B/V/K/N
Model of servicing
1
...
1
N
A(x)
S
K=S+V
A – law of incoming traffic
B – law of servicing traffic
S – queue size
V – number of severs
K – number of places in system
N – number of sources
If N=∞ then A/B/V/K
Often S=∞ → K=∞ then
A/B/V
1
...
v
B(x)
Classic teletraffic models
M/M/1, M/M/V/K , M/D/V etc.
M – Poisson law
F ( x)  1  e
 x
D – determinate F(x)=const
Self-similarity and networks
1993 year W. Lenard, M. Taqqu,
W. Willinger, D. Wilson. “On the
Self-Similar Nature of Ethernet
Traffic”
The period is 4 years
From 3 pieces of Bellcore network
It has been shown that
0.7<H<0.98
Poisson
Measured
Further researches
Now – about 10000 works about self-similarity
M. Taqqu, W. Willinger, K. Park, M. Crowell - research on the
network layer.
W. Willinger, M. Taqqu, R. Sherman, D. Wilson, A. Erramili, O.
Narayan - research of the Ethernet traffic on data link layer
N. Sadek, A. Khotanzad, T. Chen - the АТМ traffic
K. Park, G. Kim, M. Crovella,V. Almeida, A. de Oliveira, A. B.
Downey - research of TCP applications
In S. Molnar’s paper VoIP traffic is observed
Researches in Russia
The interest to self-similarity in Russia was initiated by
V.I. Neiman
Rigorous mathematics description of self-similar processes is
given by B. Tsibakov
Applications of self-similar processes in telecommunications
are presented in the book written by O. Sheluhin
Another works by A.J. Zaborovski, V.S. Gorodetski, V.V. Petrov
Self-similarity and networks
Further researches
DISTRIBUTION LAWS FOR DIFFERENT TYPES OF TRAFFIC IN IP NETWORKS
A is law of
incoming traffic
B is law of of size
of protocol data
blocks
Traffic
type
VoIP
FTP/TCP
SMTP/TCP
Distribution
law
M is Poisson law
Authors
А
В
P
Р
Molnar
P
W and
LN
Van
Mieghem
Downey
М
P is Pareto law
М
Molnar
HTTP/TCP
P
LN and P
Crovella
Van
Mieghem
IP
P
P
Paxson
Ethernet
P
P
Taqqu
ATM
D
F-ARIMA
Sadek
LN is lognormal law
F-ARIMA is
Fractal Auto-regressive
Integrated moving
Average
D is determinate
Self-similarity and networks
Even if one source generate self-similar traffic then
aggregated traffic has self-similar properties.
At the network layer aggregated traffic is described with
P/P/m most adequately
Self-similarity and networks
Insertion of limitation for real values of random quantities
If random value is the size of protocol data block then turndown of value is [k; L]. k is minimum size L is maximum.
Restricted distribution
Pareto Distribution
0,8
0,7
Prob. density
0,6
0,5
0,4
L
0,3
0,2
0,1
0
0
2
4
6
8
Prob. density
10
12
14
Self-similarity and networks
Insertion of limitation for real values of random quantities
Restricted distribution has a finite parameters
Mx and Dx
 2 - finite value
Then C 
2
2
Mx
For Pareto law


 Lk   L k
M x 
1    L  k 



  
L  k
2





 2
 L2 k   L k 2
 Lk  L k


2 

 2   


1


L

k

2

1    L  k   L2 k   L k 2
Lk   L k  
2
C 


 2 
1   2 L  k  
Lk  L k   2   
2






Self-similarity and networks
Now we could calculate QoS parameters – delays and losses
Delays
Losses

Ca2  Cs2
  P  , m 

1 
2
2
1 
Ploss 
t m  t  t s
2
2
2
1   Ca Cs
ts
C a2  C s2
t   P  , m 

m1   
2
2
2
 Ca Cs
nb
nb1
nb – buffer size
 - system load
- average time of the packet’s service
t - average time of the packet’s staying
ts

Ca2 and
C s2 are quadratic coefficients of
in the buffer.
variation of incoming flow and service time
- average value of the packets’
number in the queue
distributions, correspondingly
tm - average value of delay
parameter
m
P,m   m1  
1  m
Self-similarity and networks
Graphics
Loss probability in P/G/1 system for
different distributions of service time
The average delay in P/G/1 system for
different distribution laws of service time
Self-similarity boils down to packet losses, delays and
congestions
Self-similarity and networks
Multiservice traffic modeling
Excel, MathCAD, MathLAB – non specialized
OPNET, COMNET ect.
GPSS General Purpose Simulating System
Allows to research discrete models of different types
NS2 network simulator 2
Object-oriented discrete event simulator. Useful for simulating
local and wide area networks
The main advantage – it is free !!!
ns2
Network simulator 2 (ns2) 1996 year
Project VINT (Virtual InterNetwork Testbed), organized by
DARPA (Defense research project agency)
•Specialized for existing modern technologies
•Open source code software
•Core modification availability
•Ns2 is free product
•Result visualization availability
Pareto
TCP
2Mb
TCP1sink
TCP2sink
2Mb
Pareto
TCP
FIFO
RED
2Mb
2Mb
FIFO
RED
2Mb
Pareto
UDP
UDPnull
Results of modeling
•
•
Animation
Trace file
Ploss for P/P/m
Ploss
analysis results
0,3
modeling
0,25
0,2
0,15
0,1
0,05
0
0
0,2
0,4
0,6
0,8

Conclusions
•NGN is based on multiservice IP-oriented network
•Providing QoS is one of the main problem
•Multiservice IP traffic has a self-similarity properties
•Old distributions (Poisson) don’t work
•IP-traffic has Heavy-tailed distributions (the main is Pareto)
•Self-similarity makes worse QoS parameters
THANK YOU !