Character of USER Port Traffic in AX.25 Network
Remigiusz Olejnik
West Pomeranian University of Technology, Szczecin Faculty of Computer Science and Information Technology
ul. ˙ Zołnierska 49, 71-210 Szczecin, Poland e-mail: r.olejnik@ieee.org
Abstract—The paper presents the study of the traffic nature collected from USER port in AX.25 network. Conditions that must be met to consider the traffic for self-similar are presented.
Then collected traffic samples are examined for the presence of self-similarity — research was carried out using: IDC index of dispersion and CV coefficient of variation, R/S method and variance analysis method. The article ends with conclusions based on found correlations.
Index Terms—self-similarity, computer networks.
I. I NTRODUCTION
Many years of research have shown that traffic in computer networks is characterized by long-term dependencies, i.e. in a larger time-scale the traffic generated by the sources has the characteristics of self-similarity. These dependences were observed at several layers, as well as for a variety of network topologies and technologies [1]–[7].
Character of the traffic has a significant impact on the perfor- mance of computer networks such as the length of queues in the switches, which results in a higher probability of delay or packet loss due to buffers overflow. Knowledge of the traffic nature allows to design algorithms ensuring adequate quality of service.
The vast majority of previous work concerned wired net- works. This paper presents study of nature of the traffic found in amateur radio AX.25 network, specifically at the USER port.
The further part of this paper is divided into following parts: second section contains the theoretical foundations of stochastic self-similar processes, while third section presents the results of AX.25 network traffic analysis. The fourth section summarizes the work.
II. M ETHODS OF S ELF -S IMILARITY E VALUATION
The definition of self stochastic process is assumed as follows [1], [8]:
A stochastic process X t is self-similar with the self-similarity parameter H, if for a positive g rescaled process g −H X gt has the same distribution as the original process X t .
The H parameter is called a Hurst exponent. A stochastic process for which H = 0.5 is a process in which there are long-term dependencies and value of H indicates “memory length”.
There are many well known methods for verification and evaluation of self-similarity; the most popular are based on ex- periments and analysis of Hurst, originally on the fluctuations in the water level of the Nile River [10]. Four most popular methods of the network traffic evaluation are presented below.
A. R/S Method
Normalized dimensionless measure characterizing the vari- ability is rescaled range R/S [9]. For a set of observations X = {X m , m ∈ Z + }, with a mean X(m), a variance S 2 (m) and a range R(m), the R/S is defined as [10]:
R(m)
S(m) = max(0, Δ 1 , Δ 2 , . . . , Δ m ) − min(0, Δ 1 , Δ 2 , . . . , Δ m )
S(m) ,
(1) where Δ k =
k i=1
X i − kX for k = 1, 2, . . . , m.
Hurst also observed that for many natural phenomena, for m → ∞ and for constant c independent from m following formula is valid:
E
R(n) S(n)
∼ cm H . (2)
After logarithmisation, for m → ∞ we obtain:
log 10
E
R(m) S(m)
∼ H log 10 (m) + log 10 (c). (3) Hurst exponent value can be estimated using that formula — to do so, we must take into account the characteristics of log 10
E
R(m) S(m)
as a function of log 10 (m), then approx- imate it with a straight line, which slope coefficient gives an estimated value of H. Value of Hin range 0, 5 ≤ H ≤ 0, 75 is a premise of the presence of self-similarity, so the graph should be placed between the auxiliary straight lines given by the formulas: y 1 = x and y 2 = 1 2 x.
B. Aggregated Process Time Variance Analysis Method The variance of aggregated process X k (m) is defined as [1]:
V ar(X k (m) ) = σ 2 m −β , (4) where 0 < β < 1, and σ 2 is variance of X k (m) process for m = 1. Value of β is related with Hurst exponent H value:
H = 1 − β
2 , (5)
where value of β corresponds to the slope of the graph log 10 V ar(X σ
2k(m)) to log 10 (m).
50 XVII Poznańskie Warsztaty Telekomunikacyjne
C. Method of IDC (Index of Dispersion) and CV (Coefficient of Variation) Estimation
Method of estimation of index of dispersion IDC and coefficient of variation CV for a process mX k (m) during m is based on the analysis of IDC and CV analysis [1]:
IDC index of dispersion is given by the formula:
IDC(m) = V ar(mX k (m) )
E(mX k (m) ) , (6) where:
• V ar(mX k (m) ) is the variance of the number of packets arriving in a time window of length m,
• E(mX k (m) ) is the average number of packets during m.
For self-similar processes the value of IDC increases mono- tonically [1].
CV coefficient of variation is given by the formula:
CV (m) =
V ar(mX k (m) )
E(mX k (m) ) , (7) where:
•
V ar(mX k (m) ) is standard deviation of the number of packets arriving in a time window of length m,
• E(mX k (m) ) is the average number of packets during m.
For self-similar processes the value of CV is much greater than 1 for small time intervals [1].
D. Graphical Method
In graphical method graph’s temporal variability is evaluated (here: the number of packets in a time window of length m) when changing the time scale a correlation between the properties of the graph for different time scales is sought.
This method is not covered by further part of this work.
III. S TUDY OF AX.25 T RAFFIC N ETWORK N ATURE
As mentioned before, evaluation issues of computer net- works traffic nature are not new. Summary of work carried out on the wired networks can be found in [1].
A. Research Methodology
The traffic was collected from USER port of AX.25 net- work, i.e. all data transmitted and received at that port. The configuration of collecting node was:
• computer: Asus Eee PC 1005HA (M) — Intel Atom N270, 1,6 GHz, 1 MB RAM,
• operating system: Linux Ubuntu 10.10,
• AX.25 network connection: IP-tunnel to SR1BSZ (http://www.sr1bsz.ampr.org) node,
• radio USER port: 144.800 MHz.
Collected traffic was saved to the file, then time of arrival for each packet was exported to another file. Finally CSV file has been created that contained number of collected bytes for each minute. That file was the source of analysis in MATLAB R2012a environment. MATLAB script outputs were plots and values of H for three Hurst exponent evaluation methods that were presented before.
B. Experimental Results
Table I contains collected results of measurements: number of bytes, collecting time (in minutes) and values of Hurst ex- ponent H: H 1 , H 2 i H 3 obtained with methods: R/S, aggvar and IDC/CV . The Figures 1–4 present plots generated by the methods for sample 6 (which is a sum of samples 1–5).
TABLE I M
EASUREMENTS RESULTSsample number time H
1H
2H
3H
number of bytes [mins] IDC/CV R/S aggvar variance
1 39217 840 0.6158 0.6034 0.4790 0.0057
2 68455 1440 0.6487 0.5672 0.4888 0.0064
3 76655 1440 0.6399 0.4648 0.4503 0.0111
4 110403 1440 0.6447 0.4656 0,4742 0.0102
5 55512 788 0.6546 0.4785 0,5144 0.0087
6 350242 5948 0.6721 0.5069 0,5824 0.0068
Table I clearly shows that the Hurst exponent H values obtained using various methods vary considerably. IDC/CV method indicates the presence of self-similarity (0, 5 < H <
1; see Fig. 1 and Fig. 2) for all of the samples. Results given by other two methods are not clear. Aggregated process time variance analysis method ( aggvar) indicates self-similarity in samples 5 and 6 (see Fig. 3), while R/S method shows self- similar nature of traffic in samples 1, 2 and 6 (see Fig. 4). The value of H variance is very low, not exceeding 0.0111.
All of the methods show self-similar nature of traffic for sample 6, which is a sum of samples 1–5, so final conclusion is that AX.25 network’s USER port traffic nature is self-similar, despite different results given by aggvar and R/S for most of the samples.
Further research should prove if self-similar nature is still existent for much higher m value and resolve the differences between results given by different methods.
10−0.5 10−0.4 10−0.3 10−0.2 10−0.1 100 100.1 100.41
100.42 100.43 100.44 100.45
Index of Dispersion (IDC)
Window Width (m)
Fig. 1. IDC(m) =
V ar(mXk(m))E(mXk(m))
as a function of m for sample 6
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 0.7
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Coefficient of Variation (CV)
Window Width (m)
Fig. 2. CV (m) =
V ar(mXk(m))
E(mXk(m))
as a function of m for sample 6
0 0.5 1 1.5 2 2.5 3 3.5
1 1.5 2 2.5 3 3.5 4
log10(Window Width (m))
log10(Variance)
Variance−Time Method
Fig. 3. log
10V ar(Xσ2k(m))as a function of log
10(m) for sample 6
IV. S UMMARY
The paper presented results of experiments which covered analysis of traffic character collected from USER port in AX.25 radio network. Four methods of such analysis has been shown and three of them used in the study. Obtained results vary between the methods although for larger traffic sample all three methods indicate self-similar nature of the traffic.
Further research is necessary to confirm if that nature is existent for much higher traffic sample size and to resolve the differences between results given by different methods.
Another problem is possible incompleteness of measurement data due to “hidden node problem” encountered in every wireless network. That issue can be prevented using more than one node for data collecting, but such approach needs also additional effort to compare and select unique packets.
0 0.5 1 1.5 2 2.5 3 3.5 4
0 0.5 1 1.5 2 2.5 3
log10(Window Width m)
log10(R/S)
R/S Method
H=0.5 H=1
Fig. 4. log
10E
R(m)S(m)
