Paper Title (use style: paper title)

Study of the parameters of the multimedia stream of a telecommunications
network
Kamila Sherjanova
Department of training scientific and pedagogical personnel
Tashkent University of Information Technologies named after
Muhammad al-Khwarizmi Tashkent, Uzbekistan
sherjanovak@gmail.com
Abstract — In this article we discuss about the problem of studying non-
Puasson traffic, which is obtained during the procedure for removing statistical
characteristics at given packet arrival rates, is considered. The assay MSM (mass
service means) of the intensity of the load of the total flow of transmitted packets at any
moment of time is determined by those software products that will serve outgoing
requests, as well as the ratio of the number of requests, taking into account these software
products. Using the spectral method for solving the Lindley integral equation for the
G/G/1 queuing system, we obtained the values for the average packet delay time in the
network and the queue length. The accuracy of the solution is determined by the
accuracy of the approximation of the used distributions with a "heavy" tail.
Keywords — multimedia, stream, approximation, Lindley integral equations,
“heavy” tail, average delay time, quality of service.
I.INTRODUCTION.
Modern studies of traffic transmitted in telecommunication networks show that
its statistical properties and hapacteptics differ from those that are typical in the
classical theory of mass service means. (MSM). The existing multiservice networks set
a number of questions on the impact of the statistical traffic type of the Internet
multimedia applications, on the characteristics of the quality of listening to the network
devices. Analysis of the telecommunications network, this possibility will encounter the
unknown of various network parameters, such as packet delay, transmission speed, and
the bandwidth of the communication channels used. All this determines the activity,
novelty and significance of the task addressed in this article. The effectiveness of the
interaction of modern computer networks can be estimated by applying mathematical
models of different MSMs. Modern systems that handle non-Puasson traffic are
described by MSM G/G/1 models from the G/G/n group. The specificity of the study of
telecom traffic, which has the property of self-similarity, lies in the practical absence of
the study of network parameters. These parameters include the duration of packets, the
time intervals between packets. This feature is important, since the listed parameters
are used to investigate network traffic using MSM.
The article analyzes the statistical parameters of network traffic, based on
previously known studies of self-similar flows; The article analyzes the statistical
parameters of network traffic, based on previously known studies of self-similar flows;
a choice of mathematical models of flows was made and methods for determining flow
parameters (average waiting time in the queue and queue length of MSM G/G/1) were
proposed, using approximation in the form of a sum of damped exponents to search for
a solution to the Lindley integral equation by the spectral method. In order to improve
the quality of service for network traffic and present a forecast of its behavior, it seems
appropriate to estimate the average waiting time of a network packet, taking into
account statistical analysis of data.
The analysis of the average traffic parameters, which has the properties of fractal
processes, self-similarity, has been relatively studied in modern telecommunication
networks [1–2]. Scientific publications devoted to the study of the degree of influence
of self-similar information flows on the quality of service in network nodes [3–13],
their statistical characteristics, lead to the validity of the choice of mathematical
models of flows using simulation or analytical models [6–8]. The method of
parametric synthesis for determining the parameters of information network flows
when they are combined, taking into account the properties of self-similarity, is
reliable, which is confirmed by the results of simulation modeling. Basically, when
modeling, the intervals of arrival of packets and the time intervals between packets in
the server buffer, the sizes of transferred files are used [3]. In [7;9] it is stated that they
are closest to the real distributions in the node for processing incoming packets and are
most often used for to study the network parameters of a distribution with a ―heavy‖
tail [9–21].
The peculiarity of NT is that they show a high degree of variability, and in the
traffic of multiservice networks they explain the reasons for its self-similarity. The
degree of self- similarity is determined by the Hurst parameter n. Estimation of the
Herpt parameter depends on a number of factors, such as the estimation method, sample
size, time scale, correlation structure.
Methods for estimating the Hurst parameter in time series are known, but the
analysis statistics is simpler and more informative. The study of the variability of
various statistical phenomena led to the development of a normalized dimensionless
quantity capable of describing the variability. This value is called the normalized R/S
range. The result of the analysis of publications related to the study of network traffic in
networks using IP technologies [9; 12; 13], is the presented classification of network
traffic with a comparison of the laws of distribution for each type of traffic. To estimate
the required buffer size of a device that provides a certain pre-necessary quality of
service using the values of loss probabilities, an expression was written taking into
account the necessary additional simplifications.
A method is considered for determining the average waiting time of a claim in a
queue in the case when the unknown parameter refers to the gamma distribution, which
characterizes random time intervals between arrivals of claims to enter a node. In [14],
for the Pareto model Pa/M/1 and the hyperexponential model n 2/M/1 received
estimates of the quality of service in terms of the delay time of the application in the
system; estimating the level of decrease in the timeliness of service in terms of the
delay time for the formation of an updated flow through the connection with the
dispersion index of the studied sequence, taking into account the correlation of random
intervals (namely, the Erlang distributions, hyperexponential distributions, Daghym
distributions), and the solution of the known Lindley integral equation, the average
value of the Lindley average was obtained the waiting time for an application in the
queue.
According to the results of the analysis of publications [2; 4; 14; 15], devoted
to the study of the statistical characteristics of network traffic of multimedia
telecommunication networks, within the framework of the tasks solved in this article, it
can be noted that when approximating the parameters of the traffic flow, it is possible to
achieve results that allow determining the average packet delay time in the queue by the
analytical method for special and general cases, and then spawn with simulation results.
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