Newly designed analyzer with self-similar traffic for optical
Ethernet network 1
Abstract
A creative suit of hardware scheme that generates physical self-similar traffic is proposed for the first
time. A novel optical Ethernet network analyzer is developed by using this scheme. The analyzer
transmits self-similar traffic for networks with different Hurst parameter. The packet loss probability,
delay and jitter performance can be measured by the analyzer. With two well-known and effective
techniques to determine the presence and degree of self-similarity - Aggregated Variance method and
R/S method, the statistical analysis of realistic streams generated by the analyzer is presented to verify
the usability and reliability of the designed network analyzer.
Keywords：Self-similarity，Hurst parameter，optical Ethernet networks，analyzer.
1. Introduction
Many studies have demonstrated the presence of self-similarity in local-area and wide-area networks
[1, 2]. And many optical Ethernet systems are being or have been built. Thus the system performance
parameters such as packet loss probability, delay, and delay jitter, must be measured.
The self-similar nature of Internet traffic has a significant impact on network performance. For the
nature of congestion [3] and critical parameters above by self-similar traffic models differ drastically
form that predicted by traditional models (, Poisson) and displays a far more complicated picture
than has been typically assumed in the past. So a universal analyzing equipment, that can simulate the
actual Ethernet traffic the most closely, is demanded to evaluate the performance parameters of the
networks.
The newly designed analyzer transmits self-similar traffic with different self-similarity degree and
standard Ethernet frame format into the optical Ethernet networks, simulates the different type of
network services and obtains the factual network performance parameters.
2. System Architecture
As Figure1 shows, the system consists of four modules: The parameter producing module, system
administration module, traffic producing module, and traffic process module.
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The parameter producing module continuously generates the parameter values and traffic property
information (including source address, destination address, frame length, frame interval and frame
content, etc) for ON/OFF streams according to user’s configuration. The administration module
analyses and displays the traffic from traffic process module and administers the system running. The
two modules are implemented by computer software.
The physical standard Ethernet streams with different self-similarity degree are generated by traffic
producing module according to above parameters and property information. When running in optical
Ethernet networks, data frame is transmitted from analyzer to the networks and feed back to the
analyzer. The traffic process module achieves the receiving and statistic of the feedback data frame,
calculation of the network performance parameters, and reports the results to administration module to
display. These are achieved by a FPGA (Field Programmable Gate Array) chip.
The communication module is an embedded CPU chip, taking action of a bridge, transmitting data
among above four modules.
3. The Algorithm and Design Scheme with Hardware Equipment for
Producing Self-similar Traffic.
3. 1 Heavy-tailed distribution and ON/OFF source model
The heavy-tailed distribution [3-5] is distinguished by its large variability. This variability is
controlled by the tail behavior of the distribution. Formally, a random variable X is said to be
heavy-tailed if the distribution probability satisfies:
{ } 1 ( ) ~P X x F x x α−> = − , ,0 2x α→∞ < < （1）
Where ( ) ( ),f x g x x →∞: means that lim ( ) / ( ) 1
x
f x g x→∞ = ,
α is called the tail parameter.
The simplest heavy-tailed distribution is the Pareto distribution [8]. Its probability density function f(x)
is: 1( ) , , 0,f x k x k x kα αα α− −= > ≥ （2）
And its cumulative distribution function is given by
When x k≤ ： ( ) 0F x = ;
When x k> : ( )( ) 1F x k x α= − （3）
It can be inferred from the definition that:
Figure. 1. System architecture
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When 2α ≤ , the distribution has infinite variance; when 1α ≤ , it has infinite mean, and the mean
value of X is: [ ] 1E X kα α= − （4）
Parameter k represents the smallest possible value of the random variable; Parameter α determines
equalizing value and variance of random variable.
In this paper, we will concern with a finite mean and infinite variance. Thus parameter α will fall
between 1 and 2.
Murad Taqqu [6] proposed ON/OFF source model for the self-similarity Ethernet traffic. This model
assumed: when Ethernet flow is in the data transmission period, it is viewed as on the ON state and the
speed rate of data flow is constant; when not, the flow is viewed as on the OFF state. Flow state
generally switches between the two ON/OFF states. If the distribution of ON duration and OFF duration
is independent and Heavy-tailed, the new data flow, aggregated by N paths of such ON/OFF sources, is
self-similar. The precision of this model is dependent on the number of aggregated ON/OFF sources,
that is, parameter N. On how to confirm N will be introduced in part C. Figure 2 shows the ON/OFF
flow model and designed data frame format.
In the following design, we adopt this ON/OFF flow model.
3. 2 Generation Algorithm and aggregation mechanism of physical ON/OFF flow
in FPGA chip
According to above model, the aim is to obtain the ON and OFF duration, namely that produce a
series of samples to simulate the random variable X , whose distribution function is: ( )( ) 1F x k x α= − .
The inverse function method can solve it. If the cumulative distribution function of random variable X
is ( )F x , and u is a random number that obeys () interval of being evenly distributed, then 1 ( )F u−
can be considered a new random variable, and it has the same distribution with X . Thus we get the
sample of variable X through calculating 1 ( )F u− . The algorithm to obtain OFF duration is the same as
the ON duration. However, the most critical issue is ON duration and OFF duration must be calculated
independently.
Applied in physical implementation, we designed the frame format as follows: equal-length Ethernet
frame is transmitted when ON duration. Frame length plus frame gap is 1T and every ON duration must
be integer multiple of 1T . The Ethernet IDLE control code [7] is transmitted when OFF duration, the
code length is 2T and every OFF duration must be integer multiple of 2T too. Figure 2 gives the
Figure. 2. N-ON/OFF flows aggregating model and the designed data format
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detailed frame format. Calculating random and dependent 1T and 2T , then FPGA can produce every
path ON/OFF source, and aggregate them to self-similar traffic.
On the aggregation process of N paths ON/OFF sources, we creatively put forward the polling
mechanism. As showed in Figure 3. N paths of ON/OFF sources aggregate separately in each
memorizer at the speed of 0f , once there is a complete frame in a memorizer, an corresponding
indicating bit is set to wait for inquiring transmission. A system frequency of 010 f is used to poll and
transmit data in the aggregation end to insure the system has no contention.
Furthermore, parameter N (the number of aggregated ON/OFF sources) indicates the precision of
generated self-similar traffic. It is crucial to the analyzer design results. However, in a physical FPGA
chip, N can’t be infinite for the hardware resource is finite. We carried out the simulation for a group of
self-similar sequence. The results show that the variance of parameter H is no more than under
the condition of N>12. Thus, the N adopted in the system is 12
3. 3 Arithmetic simulation and traffic statistic results Tables
To validate the algorithm that we designed to generating self-similar traffic to be valid and the
analyzer’s performance to be reliable, we record the actual packet traffic from analyzer, present the
statistical analysis and give the parameter H of the collected traces. For different H, we take =, ,
and for example.
Figure 4 and Figure 5 show the aggregated variance plots and R/S plots for actual traces of =. In
the Aggregated Variance plots, the X-axis represents the logarithm of the aggregation level and the
Y-axis represents the logarithm of the variance of an aggregated process. In the R/S plots, the X-axis
represents the logarithm of the aggregation level and the Y-axis represents the logarithm of R/S. In the
plots a linear fitness of the original curve is used to estimate the Hurst (H) parameter and the slope of
the fitness line is .
The H estimated in the Aggregated Variance plots is , according to in Figure 4, and that in R/S
plots is , that is in Figure 5. Both is accordance with the theoretical H and indicate the existence
of self-similarity.
Figure. 3. Aggregation procedure of self-similarity flow
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Aggregated Variance and R/S plots for =, , are also obtained. Due to the space limitation,
those plots are omitted from the paper. And all the analysis results are summarized in Table1 and
Table2. The results indicate that the design satisfies the request of the analyzer and transmits
self-similar traffic with different H parameters according to user’s configuration.
Table 1 Hurst Parameter of Aggregated Variance Method
Table 2 Hurst Parameter of R/S Method
4. Conclusion
A novel optical Ethernet network analyzer is designed. The analyzer can provide self-similar traffic
for networks with different self-similarity degree. According to the experimental results, the traffic
from the analyzer has good self-similarity and can effectively simulate the different Ethernet services.
Since the presence of self-similarity in network traffic has significant impact on the network
performance, results of this design is critical for the analysis, control, and design of experimental
optical Ethernet networks.
Figure. 5. R/S analysis for actual traces from the
designed analyzer
Figure. 4. Aggregated Variance analysis for actual
traces from the designed analyzer
Alpha(ON) Alpha(OFF) H
(theoretical)
H
(measured)
Alpha(ON) Alpha(OFF) H
(theoretical)
H
(measured)
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References
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[7] IEEE Std , 2000 Edition.
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