# Study of the Process of Packet Arrival at a Multiservice Node  
[PERSON]  
1 Faculty of Information Technologies, L.N. Cumilyov Eurasian National University,  
Nur-Sultan 010000, Kazakhstan; [EMAIL_ADDRESS] (D.S.); [EMAIL_ADDRESS] (Z.A.); [EMAIL_ADDRESS] (G.U.); [EMAIL_ADDRESS] (L.R)  
[PERSON]  
1 Faculty of Information Technologies, L.N. Cumilyov Eurasian National University,  
Nur-Sultan 010000, Kazakhstan; [EMAIL_ADDRESS] (D.S.); [EMAIL_ADDRESS] (Z.A.); [EMAIL_ADDRESS] (G.U.); [EMAIL_ADDRESS] (L.R)  
[PERSON]  
2 Faculty of Infocommunication Networks and Systems, The Bonch-Bruevich Saint-Petersburg State University of Telecommunications, 19323 Saint Petersburg, Russia; [EMAIL_ADDRESS] 2  
[PERSON]  
3 LLC Scientific and Technical Center \"Protei\", 19404 Saint Petersburg, Russia; [EMAIL_ADDRESS] 3  
[PERSON]  
1 Faculty of Information Technologies, L.N. Cumilyov Eurasian National University,  
Nur-Sultan 010000, Kazakhstan; [EMAIL_ADDRESS] (D.S.); [EMAIL_ADDRESS] (Z.A.); [EMAIL_ADDRESS] (G.U.); [EMAIL_ADDRESS] (L.R)  
[PERSON]  
1 Faculty of Information Technologies, L.N. Cumilyov Eurasian National University,  
Nur-Sultan 010000, Kazakhstan; [EMAIL_ADDRESS] (D.S.); [EMAIL_ADDRESS] (Z.A.); [EMAIL_ADDRESS] (G.U.); [EMAIL_ADDRESS] (L.R)  
Footnote 10: https://www  
the queuing theory [3; 4]. This name is used because the request can stay in the buffer memory (in other words, in the queue) waiting for servicing.  
Measurements of traffic parameters in telephone networks showed that the CDF \(A(t)\) in most cases obeys the exponential law [5] with the parameter \(\lambda\):  
\[A(t)=1-e^{-\lambda t}. \tag{1}\]  
The value of the parameter \(\lambda\) is inversely proportional to the average value of the interval between the moments of arrival of requests \(A^{(1)}\). The queuing theory calls the value \(\lambda\) the intensity of the arriving request flow. An exponential distribution of the form (1) indicates that the request flow is of a Poisson process [3; 4]. For a Poisson flow, the probability of arrival of exactly \(k\) requests over a time interval with duration of \(t\), denoted as \(p_{k}(t)\), is determined by the following formula:  
\[p_{k}=\frac{(\lambda t)^{k}}{k!}e^{-\lambda t}. \tag{2}\]  
Note that as the product of \(\lambda t\) increases, the function \(p_{k}(t)\) becomes close to symmetric.  
With the formation of multiservice networks, in which all types of information (speech, data, and video) are transmitted as a sequence of packets, the Poisson flow hypothesis became unacceptable. CDF \(A(t)\) that differed from (1) began to be used. Note that the coefficient of variation is equal to the ratio of the standard deviation to the mean of a random variable. Typically, these distributions have a coefficient of variation, \(C_{A}\), greater than one. For a Poisson flow, this coefficient is equal to one. Moreover, self-similar processes began to be used to describe the function \(A(t)\)[6].  
Modern telecommunication equipment allows the collection of statistical data, based on which a histogram \(a(t)\) is being built. It allows highly reliable assessments to be obtained that are able to reveal the nature of the arriving request flow. For this purpose, it is necessary to develop a method for analyzing the function \(a(t)\). The solution to such a problem is the main topic of this paper.