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Testing of Software for Calculating a Multichannel Queuing System with "Cooling" and E2-approximation
Khalil M. M.
Emperor Alexander I Petersburg State Transport University
St. Petersburg, Russia maadalomar@gmail.com
Andruk A. A.
Emperor Alexander I Petersburg State Transport University St. Petersburg, Russia aaandruk@gmail.com
Abstract. An application for the cloud-based system with a web interface and the use of filters, filter estimated impact on the performance of cloud services. Calculations are based on queuing theory and synthesis of multi-channel systems models with "cooling" and not an approximation of Markov processes with the help of phase-type distributions. Describes charts and transitions matrix microstates multichannel queuing system for modelling application with a web interface, a diagram to calculate the stationary distribution of the number of requests in the system and developed a JAVA program that implements a filter for the data encryption. The scheme of mutual validation of models of multi-channel service delivery systems with a "cooling" is presented.
Keywords: servlets, filters, cloud computing, cooling, web interface, queuing theory.
Introduction
With more and more devices getting connected to the internet every day, and by moving from the internet of computers to the internet of things, with a big demand that devices get smaller, lighter and more powerful with fast connectivity all at the same time. It all heads for the need of faster connections so that a request from a client doesn't consume a large bandwidth or memory, and an efficient way to deal with the request once it is on the server's side.
In order to connect with devices that are different in size, shape, capacity, power, user language and operating system, a very simple and global interface is needed, that can connect to devices using very simple protocols. Today almost any device can be connected to the internet and communicate via a web interface, that's why if you need to move your applications and data to the cloud, it would be easier and better if the applications had a web interface, as the whole idea of moving to the cloud is so that you can have access anytime from any device with maximum reliability and unlimited computing power.
In this paper a cloud system application with a java based web interface using filters is examined and tested to calculate how filters effect on the overall performance of the cloud service, as performance is one of the key factors for moving to the cloud. It based on queuing theory and extend its applications by studying the multichannel systems with "cooling" and phasetype approximation of Markovian and non-Markovian processes. Transition diagrams and matrices for the microstates of a sample application with Web interface model described, and a scheme for computing the stationary probability distributions for requests number and waiting time is developed.
Servlet filters are powerful tools that are available to web application developers using the Servlet 2.3 specification or above. Filters are designed to be able to manipulate a request or response (or both) that is sent to a web application, yet provide this functionality in a method that won't affect servlets and JSPs being used by the web application unless that is the desired effect. A good way to think of servlet filters is as a chain of steps that a request and response must go through before reaching a servlet, JSP, or static resource such as an HTML page in a web application. However this consumes time, and the time it consumes shall be calculated to see the overall effect of performance.
Cloud Computing Using A Web Interface Common Characteristics
Cloud computing is a number of computing resources that are delivered as a service over a network connection (usually the internet). Therefore Cloud computing relies on sharing a pool of physical and/or virtual resources, rather than deploying local or personal hardware and software. A user is able to connect into a supply of computing resources rather than managing, operating, maintaining, securing and servicing the equipment needed to generate it themselves; just as the same way as a consumer tapping into the national electricity supply, instead of running their own electric generator. Thereby the service is billed likewise where you pay for the amount of service that you consume.
Also likewise cloud computing is more reliable, flexible, scalable and most importantly more economical. You can choose between different types of clouds depending on the amount of security that you demand for your business, these types are: public, private and hybrid cloud. You can also choose the type of service that you need for your business, the major types of services are: SaaS (Software as a service); PaaS (Platform as a service) and IaaS (Infrastructure as a service).
In order to connect with devices that are different in size, shape, capacity, power, user language and operating system, a very simple and global interface is needed, that can connect to devices using very simple protocols. Today almost any device can be connected to the internet and use different protocols to communicate, that's why if you need to move your applications and data to the cloud, it would be easier and better if the applications had a web interface, as the whole idea of moving to the cloud is so that you can have access anytime from any device with maximum reliability and unlimited computing power.
Internet connections use protocols to connect between different devices, so that after every handshake every device knows what it should do and how to do it. A Web service, in very broad terms, is a method of communication between two applications or electronic devices over the WWW. Web services are of two kinds: Simple Object Access Protocol (SOAP) and Representational State Transfer (REST).
Applications with Web interface on Java platform used serv-lets and applets. Servlet is a Java-program running on the server side and expand server functionality. The servlet communicates with clients by processing HTTP requests. Filters allow performing actions on the request before it is processed by the servlet or on the response after its formation. Filters implement model "interceptor request", and for each resource in the web application has its own filter chain can be arranged.
The client can use any device he likes, as long as that device has a connection to the internet and a web browser. Almost no or very little amount of data need to be stored or computed in the client side, all the data is stored and processed in the cloud's side.
Servlets
Servlets provide a component-based, platform-independent method for building Web-based applications, without the performance limitations of CGI programs. Servlets have access to the entire family of Java APIs, including the JDBC API to access enterprise databases.
A servlet is a small program that runs on a server. The term usually refers to a Java applet that runs within a Web server environment.
Using Servlets, you can collect input from users through web page forms, present records from a database or another source, and create web pages dynamically.
Java Servlets often serve the same purpose as programs implemented using the Common Gateway Interface (CGI). But Servlets offer several advantages in comparison with the CGI:
• performance is significantly better;
• servlets execute within the address space of a Web server. It is not necessary to create a separate process to handle each client request;
• servlets are platform-independent because they are written in Java;
• java security manager on the server enforces a set of restrictions to protect the resources on a server machine;
• the full functionality of the Java class libraries is available to a servlet. It can communicate with applets, databases, or other software via the sockets and RMI mechanisms that you have seen already.
Servlets Architecture:
Following diagram shows the position of Servlets in a Web Application (fig. 1).
The Http Servlet class reads the HTTP request, and determines if the request is an HTTP GET, POST, PUT, DELETE, HEAD etc. and calls one the corresponding method.
Let us consider how possible modelling peculiar properties of the process functioning of application with Web interface using models of queuing theory.
Fig. 1. Position of Servlets in a Web Application
Filters
A filter is an object that intercepts requests to a servlet, JSP, or static file in a web application. The filter has the opportunity to modify the request before passing it along to the underlying resource and can capture and modify the response before sending it back to the client. Since filters can be specified declara-tively using the web application deployment descriptor, they can be inserted into existing web applications without altering any of the existing code.
There are many cases where some pre-processing of the request for servlets would be useful. In addition, it is sometimes useful to modify the response from a class of servlets. One example is encryption. A servlet, or a group of servlets in an application, might generate response data that is sensitive and should not go out over the network in clear-text form, especially when the connection has been made using a non-secure protocol such as HTTP. A filter can encrypt the responses.
Servlet filters are useful for many purposes, including logging, user authentication, data compression and encryption. Many filters can be chained together, each performing one specific task.
A filter is where you want to apply pre-processing or postprocessing to requests or responses for a group of servlets, not just a single servlet, so when your application is working in a cloud environment filters are very useful tools. Filters are designed to be able to manipulate a request or response (or both) that is sent to a web application, yet provide this functionality in a method that won't affect servlets and JSPs being used by the web application unless that is the desired effect.
A good way to use filters is as a chain of steps that a request and response must go through before reaching a servlet, JSP, or static resource such as an HTML page in a web application. Fig. 2 shows the commonly used illustration of this concept.
Possible main usage of filter include following:
• recording all incoming requests;
• logs the IP addresses of the computers from which the requests originate;
• conversion;
• data compression;
• encryption and decryption;
• input validation etc.
Testing Approaches Simulation Modelling
In our test we used an encryption filter to illustrate the effect of cooling, as encryption is very common and widely used after main processing so that the response is encrypted before
Web Interface Based on Java Platform
a
Fig. 2. Using filters with servlets
sending it back over the internet. Following is the filter that we used in our test:
public class EncryptFilter implements Filter {
private static final boolean debug = true; private FilterConfig filterConfig = null;
public Encrypt() { }
public void doFilter(ServletRequest request, ServletResponse response, FilterChain chain)
throws lOException, ServletException {
long start = System.nanoTime();
String text = request.getProtocol(); String keyWord = "text"; byte[] arr = text.getBytes(); byte[] keyarr = keyWord.getBytes(); byte[] result = new byte[arr.length];
for(int i = 0; i< arr.length; i++) {
result[i] = (byte) (arr[i] A keyarr[i % keyarr.length]);
}
long finish = System.nanoTime(); long res = finish - start;
System.out.println("Bpei™ работы фильтра " +
res);
}
As can be seen from fig. 2 the filter or filter chain can run before call of servlet (or JSP, or HTML) and/or after finishing servlet execution. In first case (at the entry of servlet) filter can make any preparatory work (for example, decompression of data), that named by "warming-up" or "warm-up". In second case (after returning from servlet) filter can make any final work (for example, data compression), that named by "cooling".
The request then reaches the servlet container in the web application to be processed, the servlet must process the request and generate as much of the response as the application requires.
Relative Checking Models
It is easy to show that the distribution of Erlang k order Ek is a special case of distribution of k order Cox Ck. Hk-distribution can be transformed to the form equivalent Ck distribution. Equiv-
}
alent transformations used for selecting parameters in solving the problem of the approximation of an arbitrary distribution of phase type distributions in the case where the parameters of the approximation expresses analytically one kind of distribution, but doesn't express the others. Solution of the equivalent transformation Hk-distribution to the form Ck is reduced to solving a system of differential equations. Thus, between the probability distributions of phase type Ck, Hk and Ek there is a link that allows you to establish a relationship between them. Note, however, that a direct comparison of Ek and Hk, is impossible, since Ek-distribution is not an equivalent hyperexponential distribution of k-th order.
Scheme perform mutual authentication results using various types of distributions illustrated in fig. 3, which shows the pattern realized on the generality from the left most basic general distribution to the exponential using a two-stage Cox.
Common Queuing System Models with "Cooling"
M/M/M/n Ej/M/M/n H2/M/M/n Cj/M/M/n C2/M/C2/n
M/M/E2/n M/M/H2/n M/M/C2/n
Fig. 3. Common queuing system models with "cooling"
Existing models
For queuing theory Kendall's notation is the standard system to describe and classify a queuing node. It uses three factors written A/S/n, where A denotes the time between arrivals to the queue, S - the service time distribution and n denotes the number of servers at the node. It been extended to A/S/n/K/N/D, where K and D mean the capacity of the queue and queuing discipline and N denotes the size of the population of jobs to be served. Best studied QS M/M/n - with channels, service time distribution and the distribution for the time between arrivals follow an exponential distribution. Because of the assumptions made, such models known as Markov models, have limited appliance and do not fit for most practical systems.
The most examined are the relatively simple M/M/n models. The simplest example is M/M/1 queue, for which textbooks pertaining to performance evaluation usually present the results to compute the steady state distribution of number of requests. Well studied class of one-channel models with specific flow characteristics, discussed e. g. by Ryzhikov in [1] or Eremin [2], which analyse the behaviour QS with determined delay in starting the service.
The biggest interest was recently been focused on the investigations in multichannel non-Markovian queues where flows are approximated by phase-type distributions. For example, Bub-nov in [3] models to forecast software reliability characteristics, such as number of corrected errors, required debugging time, etc. Brandwajn and Begin in [4] propose a semi-numerical approach to compute the steady-state probability distribution for the number of requests at arbitrary and at arrival time instants in Ph/M/c-like systems.
Cox showed in [5] that an arbitrary distribution of length of a random variable can be represented by a compound of exponential stages or phase-type distribution. The advantage of such a representation is that it ensures convenience of approximation
of the random process to a Markov process and gives the power of creating and solving the system of equations describing the behaviour of the corresponding model.
Described here multichannel non-Markovian QS with warm-up require more complex mathematical description, compared to the Markov models, e. g. the request flow can be recurrent or represented by an arbitrary stochastic function. Examples of previous works addressing QS with warm-up are by Kolahi in [6] or by Kreinin in [7] for the characteristics of single channel QS, or by Bin Sun, A. N. Dudin in [1] studying the MAP/PH/n multichannel QS with warm-up and broadcasting service discipline. Mao and Humphrey in [8] examine the influence of the warm-up during virtual machine startup in the cloud system.
Examples of early works on cloud performance subject can be found in [2] and [9]. In a fairly recent work of several authors investigate questions of evaluation of performance of cloud and other systems on the basis of models of multi-channel queuing systems with warming [10] and cooling [11, 12].
Models with "cooling"
To study the cloud systems with described "cooling" it is useful to introduce an enhanced notation A/S/C/n, which compared to original Kendall's notation contains additional C denoting the cooling time distribution.
Let's describe the parameters of a model which is set up. To approximate the distribution of the cooling time we propose to apply a generalized Erlang distribution of the second order, which refers to the distributions of phase type and consists of two consecutive phases with exponential distribution delays in each of them. This distribution allows with reasonable accuracy [13]. This distribution allows with reasonable accuracy to approximate random variables with a coefficient of variation u £ [0,7; 1), which corresponds to the many practice areas. For the case when the coefficient of variation of u > 1, can be applied hyperexponential distribution of second order, as was done in article [14]. Received QS M/M/E2/n with cooling has the microstate diagram, shown in the fig. 4.
The cooling process has two parameters and -intensities of "cooling".
The leftmost column in the diagram shows the current number of customers in the system and indicates the number of the state. Each tier system is in one of three states: a service state and two phase cooling states. In this model, the duration of cooling is characterized by a generalized second order Erlang distribution. After the last service the request moves to the first phase of the cooling with intensity ^ then to the second phase with intensity ^c2, and after that system goes into service state. Service proceeds with intensity multiplied by the number of occupied service channels. At full occupation (in tiers with the numbers more than n) the diagram stabilizes at all the lower tiers.
Based on Markovian QS transition diagram a matrix of transition intensities are constructed and vector-matrix balance equations of transitions between microstates are solved.
Denote as Sj the set of system microstates when exactly j requests are served, and by oj - number of elements in Sj Then from the microstates diagram, analytically the following matrices describing the system are defined:
• Aj [ct j x ct j+1] - in Sj_1 (request arrival);
• Bj[ctj x ctj-1] - in S (request service completion);
• Cj[ctj xctj] - in S- (request service in progress);
• Dj [ctj xctj ] - leaving microstates of tier j (a diagonal matrix).
For each tier j denote by vectors y j = (y j j, y j,i,..., Y j, ct } the probability that a QS is in microstate (j, i), j = 0,1,.. Then it is possible to write the system of vector-matrix balance equations describing transitions between microstates:
Y o Do = Y oCo + YlBl,
Y jDj = Yj-i Aj-i + Y jCj + Y j+iBj+i, j = 1,2,...
An iterative numerical method introduced by Takahashi and Takami in [i0] is then used to solve the system and find the steady-state microstates probability distribution.
Mutual model checking
Java program has been developed to implement the described numeric method. it has been designed to perform actions on matrices in general, and therefore it allows obtaining results for both presented models as well as for models of other systems within the comparable classes of phase-type distributions.
The initial data has been produced from test statistics gathered for a sample cloud system as shown on fig. i. To collect it a simulation performance testing in an Apache JMeter tool was
Service Cooiing
Phase 2 Phase 1
t t +
Fig. 4. Diagram for M/M/E2/n QS with "cooling"
run with 300 threads in parallel and independently performing queries of various kinds.
The following computational resources were used to perform the testing:
Application servers have the following characteristics:
• CPU Intel Xeon X7560 (2.26 GHz), 8 cores;
• hyperthreading disabled;
• 512Gb RAM;
• memory allocated in the range of 6-8 Gb per node;
• average CPU load in the range 0.3-0.5 per core.
Network segments have the following characteristics:
• nodes reside in the same logical network segment;
• 100/1000 Mbps Ethernet ports are used.
It is useful to experiment with the model parameters under different scenarios and determine the conditions for receiving the desired QoS level.
We considered the following inputs - the intensity of the incoming stream X = 3; the average cooling time a1 = 1; service rate p. = 1,5; the number of channels n = 3. We calculated for different cooling coefficients of variation u = {0.7, 0.8, 0.9, 1.0}. These stationary probabilities of states of the system are shown in fig. 5.
Fig. 5. Probabilities of stationary states QS M/M/EJ3 with "cooling"
The graph shows a significant effect of the variation coefficient on the probability of the system states.
The study demonstrates the influence of the cooling patterns on the performance and shows the need to collect data and examine cooling patterns to assure that the system capabilities are appropriate for significantly different levels and patterns of demand that might be relevant during a given time period.
Conclusion
With the use of a multichannel queuing system model with "cooling" our paper demonstrates the effects filters have on the
performance when the filter is used after the return from the servlet. Where a Java program was developed to simulate a cloud computing system with a java web-interface using filters.
The further study is to focus on:
• Expanding the characteristic distribution function of the described models on to the networks of QS with multiple nodes.
• Expanding the research on Hyper exponential distribution case with complex coefficients.
References
1. Ryzhikov Yu. I. Raspredelenie chisla trebovanii v sisteme massovogo obsluzhivaniia s "razogrevom" [Distribution of the Number of Requests in a Queuing System with warm-up], Prob-lemyperedachi informatsii [Probl. Peredachi Inf.], 1973, Vol. 9, no. 1, pp. 88-97.
2. Eremin A. S. A Queuing System with Determined Delay in Starting the Service, Intellectual Technologies on Transport, 2015, no. 4, pp. 23-26.
3. Bubnov V. P., Tyrva A. V., Khomonenko A. D. Model ofre-liability of the software with coxian distribution of length of intervals between the moments of detection of errors. Proc. 34th Annual IEEE Comput. Software and Appl. Conf. (COMPSAC 2010), Seoul, Korea, 19-23 July 2010, Seoul, 2010, pp. 238243.
4. Brandwajn A., Begin T. A recurrent solution of Ph/M/c/ N-like and Ph/M/c-like queues, J. Appl. Probab, 2012, Vol. 49, no. 1, pp. 84-99.
5. Cox D. R. A use of complex probabilities in the theory of stochastic processes, Proc. Cambr. Phil. Soc., 1955. Vol. 51, no. 2, pp. 313-319.
6. Kolahi S. S. Simulation Model, Warm-up Period, and Simulation Length of Cellular Systems, Second Int. Conf. Intell. Syst., Model. Simul. (ISMS), 2011, pp. 375-379.
7. Kreinin Ya. Single-channel queuing system with warm up, Autom. Remote Control, 1980, Vol. 41, no. 6, pp. 771-776.
8. Mao M., Humphrey M. A performance study on the vm startup time in the cloud, IEEE 5th Int. Conf. on Cloud Comput. (CLOUD), IEEE Press, 2012, pp. 423-430.
9. Takahashi y, Takami Y. A numerical method for the steady-state probabilities of a GI/G/c queuing system in a general class, J. Operat. Res. Soc. Jpn., 1976, Vol. 19, no. 2, pp. 147-157.
10. Khomonenko A. D., Gindin S. I. Stochastic models for cloud computing performance evaluation, Proc. 10th Central and Eastern European Software Eng. Conf. in Russia, NY, USA, 2014; Moscow, 23-25 Oct. 2014. Available at: http://dl.acm. org/citation.cfm?id=2687233.
11. Khomonenko A. D., Khalil M. M., Gindin S. I. A cloud computing model using multi-channel queuing system with control, XIXIEEE Int. Conf. Soft Comput. and Meas. (SCM), 2016, pp. 103-106.
12. Lokhvitsky V.A., Ulanov A. V. The numerical analyses of queuing system with hyperexponential distribution of cooling time [Chislennyi analiz sistemy massovogo obsluzhivaniia s gipereksponentsial'nym «okhlazhdeniem»], Vestnik-tomskogo-gosudarstvennogo-universiteta-upravlenie-vychislitelnaya-tekh-nika-i-informatika [Tomsk State Univ. J. Control and Comput. Sci.], 2016. no. 4 (37). pp. 36-43.
13. Gindin S. I., Khomonenko A. D., Matveev S. V. Software For Calculation The Characteristics of Multichannel Queueing Systems With "Warm-Up" And Approach For Its Testing [Pro-grammnyi kompleks rascheta kharakteristik mnogokanal'nykh sistem massovogo obsluzhivaniia s «razogrevom» i podkhod k ego testirovaniiu], Sovremennye problemy nauki i obrazovaniia [Modern problems of science and education], 2014, no. 4, pp. 152. Available at: http://www.science-education.ru/118-13872.
14. http://www.tutorialspoint.com/servlets/servlets_overview. htm.
Тестирование программного комплекса расчета многоканальных систем массового обслуживания с «охлаждением» и E2-аппроксимацией
Халил М. М. Петербургский Государственный Университет Путей Сообщения Императора Александра I Санкт-Петербург, Россия maadalomar@gmail.com
Андрук А. А. Петербургский Государственный Университет Путей Сообщения Императора Александра I Санкт-Петербург, Россия aaandruk@gmail.com
Аннотация. Рассмотрено приложение для облачной системы с веб-интерфейсом с использованием фильтров. Оценивается влияние фильтров на производительность облачных сервисов. Расчеты основаны на теории массового обслуживания и обобщении моделей многоканальных систем с «охлаждением» и аппроксимацией не Марковских процессов с помощью распределений фазового типа. Описаны диаграммы переходов и матрицы микросостояний многоканальной системы массового обслуживания для моделирования приложения с веб-интерфейсом, показана схема для вычисления стационарных распределений числа запросов в системе и разработана JAVA программа, реализующая фильтр для шифрования данных. Приведена схема взаимной проверки моделей многоканальных систем обслуживания с «охлаждением».
Ключевые слова: сервлеты, фильтры, облачные вычисления, охлаждение, веб-интерфейс, теория массового обслуживания.
Литература
1. Рыжиков Ю. И. Распределение числа требований в системе массового обслуживания с «разогревом» / Ю. И. Рыжиков // Проблемы передачи информации. - 1973. - Т. 9, № 1. - С. 88-97.
2. Еремин А. С. Система массового обслуживания с детерминированными задержками запуска службы / А. С. Еремин // Интеллектуальные технологии на транспорте. - 2015. -№ 4. С. 23-26.
3. Bubnov V. P. Model of reliability of the software with Cox-ian distribution of length of intervals between the moments of detection of errors / V. P. Bubnov, A. V. Tyrva, A. D. Khomonen-ko // Proc. 34th Annual IEEE Comput. Software and Appl. Conf. (COMPSAC 2010), Seoul, Korea, 19-23 July 2010. - Seoul, 2010. - P. 238-243.
4. Brandwajn A. A recurrent solution of Ph/M/c/N-like and Ph/M/c-like queues / A. Brandwajn, T. Begin // J. Appl. Probab. -2012. - Vol. 49, № 1. P. 84-99.
5. Cox D. R. A use of complex probabilities in the theory of stochastic processes / D. R. Cox // Proc. Cambr. Phil. Soc. -1955. - Vol. 51, № 2. P. 313-319.
6. Kolahi S. S. Simulation Model, Warm-up Period, and Simulation Length of Cellular Systems / S. S. Kolahi // Second Int. Conf. Intell. Syst., Modeling and Simulation (ISMS), 2011. -2011. - P. 375-379.
7. Kreinin Ya. Single-channel queuing system with warm up / Ya. Kreinin // Autom. Remote Control. - 1980. - Vol. 41, № 6. - P. 771-776.
8. Mao M. A performance study on the vm startup time in the cloud / M. Mao, M. Humphrey // IEEE 5th Int. Conf. Cloud Comput. (CLOUD). - IEEE Press, 2012. - P. 423-430.
9. Takahashi У. A numerical method for the steady-state probabilities of a GI/G/c queuing system in a general class / У Takahashi, Y. Takami // J. Operat. Res. Soc. Jpn. - 1976. - Vol. 19, № 2. - P. 147-157.
10. Khomonenko A. D. Stochastic models for cloud computing performance evaluation / A. D. Khomonenko, S. I. Gindin // Proc. 10th Central and Eastern European Software Eng. Conf. in Russia, 23-25 Oct. 2014. - NY, USA: ACM New York; Moscow, 2014 - URL: http://dl.acm.org/citation.cfm?id=2687233.
11. Хомоненко А. Д. Модель облачных вычислений с использованием многоканальной системы массового обслуживания с управлением / А. Д. Хомоненко, M. M. Халил, С. И. Гиндин // Мягкие вычисления (SCM), XIX междунар. конф., СПб., 25-27 мая 2016; Т. 1, Секция 2. - СПб., 2016. - С. 247-251.
12. Лохвицкий В. А. Численный анализ системы массового обслуживания с гиперэкспоненциальным «охлаждением» / В. А. Лохвицкий, А. В. Уланов // Вестн Томск. гос. ун-та. Управление, вычислительная техника и информатика. - 2016. - № 4 (37). - С. 36-43.
13. Гиндин С. И. Программный комплекс расчета характеристик многоканальных систем массового обслуживания с «разогревом» и подход к его тестированию / С. И. Гиндин, А. Д. Хомоненко, С. В. Матвеев // Соврем. проблемы науки и образования. - 2014. - № 4. С. 152. URL: http://www.science-education.ru/118-13872 (дата обращения 09.07.2014).
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