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All content in this area was uploaded by Khaled Elleithy
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Content uploaded by Khaled Elleithy
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All content in this area was uploaded by Khaled Elleithy
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Content uploaded by Khaled Elleithy
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Network Traffic Characterization for Highspeed Networks Supporting Multimedia
Khaled
M.
Elleithy
Computer Science and Engineering Department
University of Bridgeport
Bridgeport, CT 06601
clleithy
@
bridgcport.cdu
Ali S.
AlSuwaiyan
Computer Engineering Department
King Fahd University
Dhahran 31261, Saudi Arabia
Abstract
Continuously growing needs for distributed
applications that transmit massive amount of data has led
to the emergence of highspeed networks that require
broadband and multimedia capabilities. Such networks
are supposed to have the ability to handle heterogeneous
trajjic and to manage large span of resources and services
effectively.
In
this paper, a single server G/D/l queuing
system with infinite buffer is simulated with the
consideration of three input traffic sources: exponential,
weibull, and normal distrbutions. The upper bounds
on
buffer size are evaluated for the given distributions.
1.
Introduction
Without the knowledge of traffic characteristics, we
would not meet what networks are supposed to achieve.
For example, without accurate traffic characterization, the
network may be forced to use overly conservative resource
schemes leading to underutilized servers. Traffic
characterization
is
an integral part of queuing systems
employed in the study
of
network, protocol, and switch
design performance. It serves the following purposes
[I
21
:
Helps in specifying critical
QoS
parameters such
as
buffer
size
and link capacity.
Predicting bandwidth requirements which allows
for better capacity assignment and congestion
control in communication networks
Estimation of statistical multiplexing gains
of
VBR
transmission over BISDNs
Mathematical analysis and simulation of traffic
signals models in the process of designing
communication networks.
data source (e.g., video, voice, multimedia,
...).
Then the
sample is studied well to see which distribution typifies its
first and second order statistics. When
a
distribution is
found, we must calculate the best fitting curve by choosing
the distribution parameters carefully. After that, the
optimal distribution is an accurate characterization of the
traffic. Usually, secondary steps come after that which are
dependent on the characteristics of the traffic, such as
simulation. In this paper, we have conducted a simulation
study to get the steadystate probabilities.
The process of traffic characterization needs an
empirical study of the source traffic to determine its
distribution
[
16,10,13
141.
We have assumed the
distribution of the traffic source and we have studied the
effects of this assumption by measuring the steadystate
probabilities assuming a
G/D/l
system with infinite buffer.
The result of this study can help in determining the needed
buffer size and several useful metrics (e.g., throughput,
response time,
.
.
.
etc).
This paper is organized as follows. The problem under
study is defined in the next section. Then, we show
simulation results after describing the simulation
mechanism. Finally, the paper offers conclusions.
2.
Problem Definition
We have
a
single server model of type
G/D/l
with
infinite buffer, where
G
(input distribution) can be one of
the following distributions:
1
)Exponential
2)Weibull
3)Normal
These models are used with a single server queue, which
can be considered
as
a router with infinite buffer
as
shown
in Figure
1.
These input models are evaluated one at
a
time independently, not
all
together, and for each input
model, we approximated the steadystate probabilities.
The objective is
to
approximate the steadystate
._
probabilities using simulation, given the above input
distribution, one at a time.
In general, traffic Characterization goes through the
following steps. First,
a
traffic sample is generated from
a
200
0769510922/01
$10.00
0
2001
IEEE
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I
1
1
Exponential],
infinite Queue
I’
I
Figure
1.
System
Model
3.
Simulation
Model
In this section, we develop
a
discrete event simulator
that simulates the behavior
of
the mentioned single server
G/D/l
queuing system
[15].
We first describe the
simulation mechanism used in the simulator, and then we
give some simulation results.
3.1.
Simulation Mechanism
We have used an eventdriven simulator programmed
using the
C
language. The simulator is divided into the
following components:
External definitions:
this part includes the
“#include” directives, the “#define” directives, the
global variable declarations and functions prototypes.
Main function:
this part controls the overall behavior
of the simulator.
Initialization routine:
in this routine, we initialize
some variables including simulation clock, state
variables, the event list
. . .
etc.
Timing routine:
this routine determines the type of
the next event and advances the simulation clock.
New arrival routine:
this is executed whenever we
have an arrival event. It schedules next customer
arrival and current customer departure times.
Departure routine:
this is executed whenever we
have
a
departure event.
If
there is a customer waiting
in the queue, the routine will schedule its departure.
Statistics calculation routine:
This is
a
routine to
calculate some statistics, e.g., the frequency of having
i
customers in the system, maximum number of
customers during the simulation period
.
. .
etc.
Random variate generator:
this could be one of the
following depending on the input distribution:
a)
Expon:
this routine is used to generate
exponentially distributed interarrival times.
b)
c)
Weibull:
this routine is used to generate weibull
distributed interarrival times.
Normal:
this routine is used to generate normally
distributed interarrival times.
Cl
P(i)
=
~
2
Ck
k=O
In order to approximate the steadystate probabilities P(i),
we have used the following formula:
Where
C,
is the number of times in which the system has
i
customers and
m
represents the maximum number of
customers that the system has got during the simulation
period. For the purpose
of
approximation, we can neglect
P(n)
for
n
>
m.
3.2.
Simulation Results
In this section we present some experimental results.
For each input distribution, we have run three experiments
with different parameters, but all the experiments have the
same service time, which is fixed at
0.5
time units. We
have fixed the service time to isolate its effect and see only
the effects of changing the input distribution. Figures 210
Show charts
of
P(N),
which are the steadystate
probabilities, versus
N,
which represents the number of
customers in the system.
These charts give
us
hints about the minimum amount
of buffer needed
to
handle customers in the queue. For
example, Figure2 shows us that we should have at least a
buffer of size seven, because,
as
seen from the figure, the
probability of having above seven customers in the system
can be neglected. Table
1
shows upper bounds on buffer
size associated with each input traffic type.
201
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4.
Conclusion
Interarrival distribution
Traffic modeling or characterization describes the
random flow of traffic associated with network sources in
terms of stochastic models. Network sources might be a
VBR (Variable BitRate) video
or
LANWAN data. In this
paper, it was shown how traffic characterization helped in
determining critical
QoS
parameters, such
as
buffer size.
In addition, we have seen how the upper bound on buffer
changes as the
input
distribution changes. These results
on the importance of traffic characterization as a necessary
step
on
evaluating the performance of a network system
that supports multimedia applications.
Upper Bound on Buffer Size
5.
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Analysis,
2”d
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7
Exponential(0.8)
9
Exponential(0.6)
Weibul( 1,l)
17
7
Weibul( 1,1.2)
I I
Weibu1(0.2,8.2)
8
3
I
14
I
Normal(
1,
1.69)
Normal(0.8, 1.69)
Normal(0.6, 6.25)
30
308
202
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45
40
35
0
30
2
*
25
E
20
15
10
5
0
0
1
2
3 4 5
6
7N
Figure
2.
Expon(1
.O)
Interarrivals
35
30
25
za
x

r
15
10
5
0
0
1
2
3
4
5
6
7
8
9
N
Figure
3.
Expon
(0.8)
lnterarrivals
203
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0
2
P

18
16
14
12
10
8
6
A
0
12 3 4
5
6 7 8
9
1011 121314151617
N
Figure
4.
Expon(O.6)
Interarrivals
0
1
2
3 4 5
6
7
N
Figure
5.
Weibul(1
,I)
Interarrivals
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60
50
0
1
2
N
3
Figure
6.
Weibull(2, 1.2) Interarrivals
.o
1
2
3
4
5
6
7
a
N
Figure
7.
Weibull (0.2, 8.2) lnterarrivals
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35
30
25
20
8

z
15
10
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18
19
20
21
22
23 24
N
Figure
8.
Normal(1, 1.69) Interarrivals
25
20
15
10
5
Figure
9.
Normal(0.8,1.69) lnterarrivals
206
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4.5
4
3.5
3
Figure
10.
Normal
(0.6,6.25)
Interarrivals
207
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