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Категория: Компьютерные технологии

Автор: Sumtsov D.

Запропоновано метод експериментального ощ-нювання швидкостi мультимедшного потоку даних на основi методiв математичног статистики. Метод дозволяв отримати значення математично-го очшування та середньоквадратичного видхилен-ня швидкостi потоку даних. Метод також дозволяв оцтити узгоджетсть гтотези про нормальний характер закону розподЫу швидкостi мультимедшного потоку даних. Наведет експериментальш оцтки величини швидкостi мультимедшного потоку даних при рiзних параметрах видео

Ключовi слова: аналiз мережевого трафша, статистична обробка результатiв експерименту,

швидтсть потоку даних

Предложен метод экспериментального оценивания скорости мультимедийного потока данных на основе методов математическош статистики. С помощью метода могут быть получены значения математического ожидания и среднеквадратичного отклонения скорости потока данных. Метод позволяет оценить согласованность гипотезы о нормальном характере закона распределения скорости мультимедишного потока данных. Приведены экспериментальные оценки величины скорости мульти-медишного потока данных при различных параметрах видео

UDC 004.77:519.254

[DPI: 10.15587/1729-4061.2018.128045|

DEVELOPMENT OF A METHOD FOR THE EXPERIMENTAL ESTIMATION OF MULTIMEDIA DATA FLOW RATE IN A COMPUTER NETWORK

D. S u m tsov

PhD, Associate Professor* E-mail: dmytro.sumtsov@nure.ua S. Osiievskyi PhD, Associate Professor Department of Mathematical and Software of Automated Control Systems Ivan Kozhedub Kharkiv University of Air Force Sumska str, 77/79, Kharkiv, Ukraine, 61023 E-mail: sergeyo@meta.ua V. Le bed i ev* E-mail: lebedevvalen@gmail.com *Department of Electronic Computers Kharkiv National University of Radio Electronics Nauky ave., 14, Kharkiv, Ukraine, 61166

1. Introduction

Multimedia information is widespread in the modern world. The multimedia information is understood as digital video information, graphics, and audio information.

Compared with other types of information, multimedia information is generally characterized by large amounts of data. Therefore, when multimedia is transmitted, a computer network often experiences delays, distortions, and other difficulties. Internet users are often not satisfied with the quality of online video playback, video conferences, or IP telephony. One possible problem is the insufficient throughput of a computer network or its individual segments. In addition, there are a number of other applications that require a substantial amount of transmitted data, which are appropriately named Big Data [1].

When designing a new, or analyzing existing, computer network, there emerges a task to evaluate data flow rate, and, in this case, the volume of multimedia traffic often turns out to be the largest and even decisive. When designing computer networks, in order to estimate the characteristics of data flow, a variety of mathematical models of traffic are typically applied [2 5]. However, such an approach is justified only if the constraints in the mathematical models themselves are

met, such as, for example, stationarity, ordinarity, and the absence of aftereffect for the Poisson stream of packets, etc. A real pattern of the performance of a network traffic can only be obtained by experimental observations with compulsory subsequent statistical processing. This will not only make it possible to obtain the desired characteristics, but also to assess the reliability of the results derived. Accordingly, the development of a method for experimental estimation of the multimedia data flow rate in a computer network seems to be a very relevant task.

2. Literature review and problem statement

The model of PTFK control protocol over TCP transmission, proposed in paper [2], enables the estimation of the effect of TCP parameters on the rate of data transfer among nodes in a computer network. A given model was further developed in papers [3, 4] where it is shown that the data transfer rate depends on the frequency of errors in a data transmission channel, applied algorithms for retransmissions, and timeouts. The model, described in [5], makes it possible to estimate parameters of the improved version of the mechanism TCP NewReno. However, the above models

do not take into account features of the inner nature of traffic, transported by a flow of TCP segments.

Study [6] illustrates a contribution from each of the levels of a TCP/IP protocol stack to the redundancy, introduced to transmitted data, and defines an effective data transmission rate as the percentage of useful information in the overall flow of data.

The issue of efficiency of data transmission is addressed in paper [7] where it is proposed an integrated indicator of multi-factor efficiency, taking into consideration both technical and economic characteristics of several existing technologies of computer networks. However, the proposed indicator does not account for the requirements to parameters of quality of service (QoS) in the traffic of various nature.

This shortcoming was eliminated in paper [8], which also considered a comprehensive indicator of multifactor data transfer efficiency, taking into account the QoS settings. In an earlier work [9], a similar performance indicator was used to generate requirements put forward to modern computer networks. However, this indicator includes data transmission rate as only one of the constraints, while in most cases the transmission rate must be the main component of the performance indicator in data transmission.

Article [10] described a comprehensive indicator of the effectiveness of data transmission, which reflects a rate of data transmission as a function of BER bit error frequency and a method, applied in a network, for retransmissions ARQ. However, the proposed indicator is more applicable to describe processes that occur at the channel level of the model of interaction between open systems OSI; it does not account for patterns in the nature of transmitted data.

It should be noted that the forms of a data transfer efficiency indicator, described in [7-10], are continuation of the indicator proposed in an earlier work [11].

A slightly different approach was proposed in paper [12]. The authors suggested a performance indicator for data transmission, the basis of which is the duration of processing a packet by the network; while a data transfer rate, similar to [7-9], is included in the system of constraints. A mathematical model, described in [13], takes into consideration a delivery time of data package and the likelihood of its errors, the rate of data transmission is not addressed in this case.

Authors of study [14] proposed a conceptual approach to the synthesis of an information-telecommunication network structure. This approach takes into consideration the principles of synthesis and is based on mathematical models of the information and technical structure of the network. One of the input parameters in the proposed model is, in particular, the amount of data transmitted. The proposed method for the experimental estimation of multimedia data flow rate in a computer network makes it possible to obtain a value for the volume of transferred data for subsequent application of the conceptual approach, suggested in [14].

Network traffic analysis methods are described in detail in several papers. Thus, [15] describes a prototype of the infrastructure for measurement, storage, and comparison of network data of different type and character in the commercial IP network of the firm ATT, which employs the principle of a network traffic analysis. Article [16] shows a circuit and reports results of traffic analysis in the Fast Ethernet network using the network analyzer Wireshark. Comparison of different network traffic analysis tools is described in paper [17]. Summing up the results of studies [15-17] makes it possible to draw a conclusion on the feasibility of the approach to assessing rate of a multimedia data stream based on the use of experimental statistical data, which in this case should be properly processed and interpreted. Article [18] reports results of research into traffic at the Internet TV and IPTV access level; authors obtained distribution of packet durations and intervals between the moments the packets arrive.

The generalization of results given in the above studies allows us to suggest that existing approaches to solving the task on estimation of multimedia data flow rate in a computer network rely on mathematical models based on the provisions from the theory of information and the probability theory. It is clear that the processes taking place in a computer network are stochastic in nature, and the use of methods of mathematical statistics to analyze network traffic seems to be sufficiently justified.

Thus, the task on estimating the rate of multimedia data flow in a computer network has remained unresolved in full up to now. We propose using an approach to the estimation of a multimedia data flow rate based on the application of experimental statistical data; the method for acquisition, processing, and interpreting them is described in this paper.

3. The aim and objectives of the study

The aim of present study is the acquisition, processing, and interpretation of reliable experimental estimates of the magnitude of a multimedia data flow rate in a computer network. This would make it possible to correctly identify the required throughput for the segments of the designed computer network, and to ensure a proper level of service quality.

To accomplish the aim, the following tasks have been set:

- to capture a traffic of multimedia data flow between the client and the media server and to obtain a set of observed values for a random variable of the multimedia data flow rate in a computer network at various parameters of video;

- to develop a method for the experimental estimation of a multimedia data flow rate in a computer network based on the methods of mathematical statistics;

- to run an analysis of the results obtained using the developed method for the experimental estimation of a multimedia data flow rate in a computer network.

4. Materials and methods to study the multimedia data flow rate in a computer network

The multimedia data flow rate can be estimated both theoretically and experimentally. Theoretically, the amount of transmitted data of online video is composed of two parts: a video stream and an audio stream.

The volume of a video stream depends on the resolution of the video, color depth, frame frequency rate, and a degree of data compression enabled by the chosen codec.

The audio stream volume depends on the sampling frequency of the sound, the bitness of the analog-to-digital conversion, the number of audio channels, as well as on a degree of data compression by the audio codec.

Experimentally, a data flow rate (the amount of data transmitted per unit of time) can be estimated using a network analyzer. In this work we used the software network

analyzer Wireshark, version 2.4.3. Schematic of the experiment is shown in Fig. 1.

A server of multimedia contains a video file with a resolution of 320x240 pixels, a refresh rate of 15 frames per second, a video flow rate of 144 Kbps, an audio stream rate of 99 kbps, a total flow rate of 243 Kbps.

At the client side, the video file is displayed in the browser; in this case, all traffic between the server and the client was captured by the buffer of the network analyzer.

Fig. 1. Schematic of experiment on the analysis of a multimedia stream traffic

The volume of data that we measured, sent from the server to the client over a time interval 7=30 s, was divided by the duration of this interval 7. Thus, we experimentally obtained the observed values for the multimedia data stream rate Ci, i = 1, n, where i is the number of experiment, n is the number of experiments. The total number of experiments in this paper is n=50. A block diagram of the method for the experimental estimation of multimedia data flow rate in a computer network is shown in Fig. 2.

Fig. 2. Block diagram of method for the experimental estimation of a multimedia data flow rate in a computer network

The obtained set of observed values for a random variable of the multimedia data stream rate {Ci} (Table 1) was statistically processed in accordance with the method shown in Fig. 3, based on the methods of mathematical statistics [19].

Rate of multimedia data of 320x240 and a frame experimentally

stream with a video resolution rate of 15 frames/s, measured in the interval of 30 s

No. of experiment C value, bps

1 304 682

2 291 286

3 266 304

4 298 214

5 282 938

6 290 186

7 291 526

8 301 041

9 291 707

10 271 824

11 318 396

12 302 515

13 309 254

14 290 548

15 294 600

16 294 607

17 297 436

18 297 461

19 303 862

20 294 056

21 293 319

22 289 996

23 305 730

24 299 295

25 300 335

26 281 088

27 291 584

28 300 474

29 295 331

30 293 133

31 286 363

32 279 721

33 282 793

34 287 527

35 301 595

36 290 244

37 295 595

38 294 607

39 291 075

40 293 508

41 302 768

42 301 811

43 286 100

44 278 613

45 299 197

46 294 951

47 283 472

48 305 631

49 293 440

50 303 486

Ordered statistical population based on the results of experiments given in Table 1

Fig. 3. Block diagram of the algorithm for statistical processing of results of the experiment

First, based on the results of experiment, given in Table 1, we construct an ordered statistical population of the observed values for a random variable of the rate of multimedia data stream Ci (Table 2). For this purpose, the observed values of a random variable Ci are arranged in ascending order. Next, we determine a minimum Cm;n and a maximum Cmax of the observed values for the multimedia data stream rate Ci. Then we define the limits of range DC of the observed values Ci by using expression

DC= Cmax— Cmin. (1)

In this case,

Cmin=266 304 bps;

Cmax=318 396 bps;

DC=52 092 bps.

Nest, range DC is divided into k intervals of equal length dC =DC

where sign [" ] denotes rounding to a larger integer (Fig. 4). In this case, k=\\0, 5C=5 210 bps.

i C value, bps

1 266 304

2 271 824

3 278 613

4 279 721

5 281 088

6 282 793

7 282 938

8 283 472

9 286 100

10 286 363

11 287 527

12 289 996

13 290 186

14 290 244

15 290 548

16 291 075

17 291 286

18 291 526

19 291 584

20 291 707

21 293 133

22 293 319

23 293 440

24 293 508

25 294 056

26 294 600

27 294 607

28 294 607

29 294 951

30 295 331

31 295 595

32 297 436

33 297 461

34 298 214

35 299 197

36 299 295

37 300 335

38 300 474

39 301 041

40 301 595

41 301 811

42 302 515

43 302 768

44 303 486

45 303 862

46 304 682

47 305 631

48 305 730

49 309 254

50 318396

Number of interval j

1 23456789 10 c

H-I-1-1-1-1-1-1-1-1-h^

(Table 4). Once a grouped statistical series is built, we construct a statistical distribution function of a random variable C (Table 4) using formula

c c c c c c c c c

•JO CO •jO CO •JO CO CO •JO

CO 2 3 4 5 6 7 8 9

E E E E E E &Ü E E &Ü

c c c c c c c c c c

F*(C,)= P*{C < C,}= £P*(C).

Fig. 4. Division of the range of the observed values for a random variable C into intervals

Then we count the number of cases a random variable C hits the j-th interval (Table 3) (Fig. 5).

Each interval can be assigned with a single value for a random variable C, equal, for example, to the midpoint of interval Cj. The hit rate of random variable C in the j-th interval can be derived from formula

Grouped statistical series, a statistical distribution function F*(Cj and the density of frequency /*(Cy) for a random variable C

C, • Cj+\\

0 1 2 3 4 5 6 7 8 9 10 11

P*{C,<C<Cj+i} 0 0.02 0.02 0.06 0.1 0.2 0.26 0.2 0.1 0.02 0.02 0

F*(Cj)= =P*{C<C,} 0 0.02 0.04 0.1 0.2 0.4 0.66 0.86 0.96 0.98 1 1

f*(Cj), X10-5 0 0 0.38 0.38 1.15 1.92 3.84 4.99 3.84 1.92 0.38 0

p * (Cj )=p * c < c < Cj+1}=n

where nj is the number of hits in the j-th interval; n is the total number of experiments.

Quantity and frequency of cases when a random variable C hits the j-th interval

Number of interval j Left bound of the interval Interval midpoint Cj Right bound of the interval Number of cases when C hits the j-th interval nj Frequency of cases when C hits interval P*(Cj)

1 266 304 268 909 271 514 1 0.02

2 271 514 274 119 276 724 1 0.02

3 276 724 279 329 281 934 3 0.06

4 281 934 284 539 287 144 5 0.10

5 287 144 289 749 292 354 10 0.20

6 292 354 294 959 297 564 13 0.26

7 297 564 300 169 302 774 10 0.20

8 302 774 305 379 307 984 5 0.10

9 307 984 310 589 313 194 1 0.02

10 313 194 315 799 318 405 1 0.02

Fig. 5. Histogram of the number of cases a random variable C hits the j-th interval

Next, based on the data obtained, we construct a grouped statistical distribution series for random variable C

F*(266 304)=P*{C<266 304}=0;

F*(271 514)=P*{C<271 514}= = P*{C<266 304}+_P*{266 304<C<271 514}= = 0+0.02=0.02;

and so on.

A statistical distribution density (frequency density) for a random variable C can be derived by dividing the frequency of hits of a Cj value in each of the intervals by the length of this interval 5Cj (Table 4)

f * (C, )=^

Charts of statistical distribution function F*(C) and a hypothetical distribution function F(C) are shown in Fig. 6. Fig. 7 shows charts of frequency density f *(C) and the probability density f(C).

If we assume that a random variable C of the multimedia data stream rate is continuous, that is it can take fractional values (which, in practice, can be rounded), the character of the distribution curve suggests that a continuous random variable C of the multimedia data stream rate is distributed by the normal law (Gaussian law).

Fig. 6. Charts of the statistical distribution function F*(C) and the hypothetical distribution function F(C) for the video with a resolution of 320x240

&*Cn ___

= ICf *(C ) = 293813.

Root-mean-square deviation o*C takes the form

c = JX(C -m*c) ■ P*(C,) = 9041.

To determine the expected probability P(Cj) (Table 5), we apply formula

P(C, <C <Cj+i) = o

1 x t1

0(x) = -;= i e Tdt.

The expected probability of cases when a random variable C hits the j-th interval

Number of interval j Left bound of interval Cj Right bound of interval Cj+1 Frequency of C hitting interval P*(Cj+1) Expected probability of C hitting interval P(Cj+1)

1 266 304 271 514 0.02 0.00683

2 271 514 276 724 0.02 0.02255

3 276 724 281 934 0.06 0.06507

4 281 934 287 144 0.10 0.13593

5 287 144 292 354 0.20 0.20552

6 292 354 297 564 0.26 0.22498

7 297 564 302 774 0.20 0.17830

8 302 774 307 984 0.10 0.10230

9 307 984 313 194 0.02 0.04249

10 313 194 318 405 0.02 0.01277

To test the proposed hypothesis H0 that assumes that a random variable for the multimedia data stream rate C is distributed by the normal law, we can use the Pearson c2 consensus criterion

* (p * (c, )- p (c, ))2

2 = nf\\ I &) I >)) = 2.99483.

£ P (C,)

Fig. 7. Charts of the frequency density f*(C) and the probability density f(C) for the video with a resolution of 320x240

Next, we estimate statistical characteristics of the random variable C distribution law, that is, mathematical expectation m*C and mean deviation o*C. Mathematical expectation m*C takes the form

The significance level in this case is set at a=0,01. The number of degrees of freedom r in this case is equal to the number of intervals k=10 minus the number of independent conditions imposed on frequencies. Such conditions are as follows: - the experiment covers a complete group of events

IP * (C, ) = 1

- statistical mean m*C and hypothetical mathematical expectation mC coincide

mc = m *c = ±CJP * (C,);

- statistical and hypothetical root-mean-square deviation o*C coincide

-K* = 0Ci-m*c) P*(C,).

where ®(x) is a Laplace function, calculated from known formula

Hence, r=10-3=7.

Based on values r=7 and c2=2.99483, we find the probability that a random variable, distributed according to the c2 law, exceeds a given value. This probability can be found using the tables, given in literature [19], or using specialized mathematical programs. A value for the significance level, ^=0.88548, derived in a given experiment, significantly exceeds the assigned a=0.01. This means that the probability that the proposed hypothesis Ho on that the character of a random variable C distribution is contrary to experimental data, is very low. Thus, one could argue that the hypothesis on that the random variable C of multimedia data stream rate is in line with the normal law of distribution is consistent with the experimental data.

5. Results of the experimental estimation of multimedia data flow rate in a computer network

By analogy with the above calculations, we obtained values for numerical characteristics of the random variable C and tested hypotheses about the normal character of its distribution for other experiments. The results are given in Table 6. The total bit rate of video and audio data is taken from the video file attributes and is the original data.

Fig. 8-15 show charts of statistical distribution function F*(C), a hypothetical distribution function F(C), the density of frequency f*(C) and the probability density f(C) for experiments with multimedia data streams with the parameters of video given in Table 6.

2

Fig. 8. Charts of the statistical distribution function F*(C) and the hypothetical distribution function F(C) for the video with a resolution of 382x288

Fig. 12. Charts of the statistical distribution function F*(C) and the hypothetical distribution function F(C) for the video with a resolution of 1280x720

Fig. 9. Charts of the frequency density f*(C) and the probability density f(C) for the video with a resolution of 382x288

Fig. 13. Charts of the frequency density f*(C and the probability density f(C) for the video with a resolution of 1280x720

I_¡Distribution function F*(Cj)

---Distribution function F(Cj)

Fig. 10. Charts of the statistical distribution function F*(C) and the hypothetical distribution function F(C) for the video with a resolution of 640x480

Fig. 14. Charts of the statistical distribution function F*(C) and the hypothetical distribution function F(C) for the video with a resolution of 1920x1080

Results of the experimental estimation of multimedia data flow rate

-Frequency density f*(Cj) - Probability density f(Cj)

Fig. 11. Charts of the frequency density f*(C) and the probability density f(C) for the video with a resolution of 640x480

Video parameters Total rate of video and audio data flow, bps Experimental estimation C, bps Significance level p

Resolution Frame rate/s m*c s c

320x240 15 243 000 293 813 9 041 0.89

384x288 25 2 983 000 3 100 172 43 272 0.50

640x480 25 2 689 000 2 793 076 105 424 0.39

1,280x720 30 9 097 000 9 369 508 892 616 0.33

1,920x1,080 25 9 160 000 9 850 610 1 779 069 0.74

Probability density f(Cj)

Fig. 15. Charts of the frequency density f*(C) and the probability density f(C) for the video with a resolution of 1,920x1,080

In all the cases considered, the value of multimedia data stream rate estimates exceeded values, given in test files, by 3...20 %. Significance level p in all experiments is significantly larger than the preset value a=0.01. This means that the proposed hypothesis H0 about the character of distribution of the random variable C for the multimedia data stream rate is consistent with experimental data with a probability of 99 %.

6. Discussion of results of the experimental estimation of multimedia data flow rate in a computer network

The character of statistical distribution functions F *(C) (Fig. 6, 8, 10, 12, 14) and the frequency density f*(C) (Fig. 7, 9, 11, 13, 15) for a random variable of the multimedia data stream rate in a computer network, derived from the experiment, allows us to assume that the random variable is governed by the normal distribution law.

In our work, we obtained results of the experimental estimation of multimedia data flow rate in a computer network in the form of numerical characteristics of a random variable, distributed by the normal distribution law, specifically mathematical expectation m*C and root-mean-square deviation s*C for the data flow rate. Based on these characteristics, we derived analytical expressions for the distribution function F(C) and probability density f(C). The hypothesis on that the random variable obeys a normal distribution law was tested based on the Pearson C2 consensus criterion, and, with a probability of 99 %, is consistent with experimental data.

The developed method for the experimental estimation of multimedia data flow rate in a computer network differs from methods based on queueing theory or the theory of self-similar processes by using, as the law of distribution of a random variable of data flow rate, the normal law as a superposition to disparate laws of distribution.

Using the proposed method makes it possible to obtain scientifically sound values of the range of values of multimedia data stream rate with a high confidence probability. According to the rule of "three s" [19], a value of the random variable for multimedia data flow rate deviates from its mathematical expectation by the magnitude not exceeding 3s, with a probability of 0.0027. Thus, with probability P=1-0.0027=0.9973, one can argue that the transmission of video with a resolution of 320x240 and a refresh rate of 15 frames per second would require a throughput from 266 689 to 320 937 bps. These calculations suggest that the transmission of video with a theoretically required rate of 243 Kbps in practice would require a rate of 321 Kbps, which is 20 % higher. This may be due to the redundancy of protocols at the transportation, network, and channel levels, which, depending on the TCP segment useful load, may range from 4 % to 30 % [6]. At a large number of user connections, the divergence may increase. Therefore, in the process of designing new, and upgrading existing, network segments, values for the required throughput should be increased by 20 %.

7. Conclusions

1. We have designed an experiment that includes a client computer, which captures traffic from a multimedia data stream, a media server, and the communication equipment Gigabit Ethernet in a local computer network. The software WireShark, version 2.4.3, was used as a network analyzer. We conducted an experiment to capture traffic at five different sets of parameters for multimedia, which resulted in the sets of observed values for a random variable of multimedia data stream rate in a computer network at different video settings.

2. A method for the experimental estimation of multimedia data stream rate in a computer network was developed, based on the methods of mathematical statistics. The devised method, in contrast to the existing ones, is based on considering the rate of multimedia data stream as a random variable that obeys the normal distribution law. The method makes it possible to obtain a reliable estimate of rate C in the form of numerical characteristics of a random variable its expected value and a standard deviation. One can also calculate the probability of any value for the rate of multimedia data stream P(C); we built its probability distribution function F(C) and a probability density function f(C).

3. By using the developed method, we analyzed the derived results of multimedia data stream rate in a computer network at different values of resolution and video frame rate (Table 6). The results of analysis clearly showed that the actual rate of data flow exceeds the theoretical one by 3...20 %, which could exert a significant impact on the performance of a computer network. This fact should be taken into consideration by the designers of computer networks and network integrators when developing projects of networks.

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АНАЛИЗ СЕТЕВОГО ТРАФИКА СТАТИСТИЧЕСКАЯ ОБРАБОТКА РЕЗУЛЬТАТОВ ЭКСПЕРИМЕНТА СКОРОСТЬ ПОТОКА ДАННЫХ network traffic analysis statistical processing of results of experiment data flow rate

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