Mathematical Model of the Delay in Communication Networks Based on QS with a Time Lag

In the mathematical modeling of modern computer networks, telecommunication networks, traffic flows, logistics and many others, the methods of queuing theory are widely used. In turn, in studies of queuing systems (QS) G/G/1 with arbitrary distribution laws of intervals between adjacent requirements of the incoming flow and their service time, the spectral decomposition method (MSD) of solving the Lindley integral equation is often used. This method is based on the search for zeros and poles of the constructed spectral decomposition in the form of some fractional-rational function using numerical methods to determine the roots of polynomials. In this case, the coefficients of the polynomial in the numerator of the expansion are expressed through the unknown parameters of the distribution laws used to describe the QS. In the case of teletraffic research, usually these unknown parameters of the distribution laws can be determined through the numerical characteristics of the intervals between traffic packets by the method of moments. The purpose of this article is to present a fundamentally new mathematical model of a system formed by two flows with distribution laws shifted to the right. This is possible only for those probability distribution laws whose density functions are Laplace transformable. The main advantages of such systems, let us call them time lag systems, are that they provide less queue latency compared to conventional systems, and that they extend the range of traffic parameters. The article presents the results obtained on the average delay of requests in the queue for a system with exponential and hyper-Erlang distributions, an algorithm for calculating the average delay and the results of computational experiments in the Mathcad package.

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Mathematical model of delay based on a system with gamma distribution

Physics of Wave Processes and Radio Systems ◽

10.18469/1810-3189.2021.24.2.62-67 ◽

2021 ◽

Vol 24 (2) ◽

pp. 62-67

Author(s):

Veniamin N. Tarasov

Keyword(s):

Gamma Distribution ◽

Spectral Decomposition ◽

Queuing Theory ◽

Queuing System ◽

Arbitrary Distribution ◽

Distribution Law ◽

Average Delay ◽

Switched Networks ◽

Packet Delays ◽

Distribution Laws

This article is devoted to the analysis of a queuing system formed by two flows with density functions of the gamma distribution law in order to derive a solution for the average delay of requests in the queue, which is the main characteristic for any queuing system. According to this characteristic, for example, packet delays in packet-switched networks are estimated when they are modeled using the queuing system. In queuing theory, studies of G/G/1 systems are especially relevant because there is no solution in the final form for the general case. Therefore, in the study of such systems, various particular distribution laws are used as an arbitrary distribution law for G. In the study of G/G/1 systems, an important role is played by the method of spectral decomposition of the solution of the Lindley integral equation, and most of the results in the theory of queuing were obtained using this method. The article presents the derivation of the calculation formula for the average delay of requests in the queue in the system under consideration, also based on the spectral decomposition method.

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MODELING DATA TRANSMISSION SYSTEMS USING MODERN INFORMATION TECHNOLOGIES

T-Comm ◽

10.36724/2072-8735-2021-15-8-52-57 ◽

2021 ◽

Vol 15 (8) ◽

pp. 52-57

Author(s):

Eleonora G. Akhmetshina ◽

Keyword(s):

Data Transmission ◽

Simulation Modeling ◽

Queuing Theory ◽

Analytical Modeling ◽

Telecommunication Networks ◽

Erlang Distribution ◽

Transmission Systems ◽

Average Delay ◽

Distribution Laws ◽

Modeling Data

When modeling data transmission systems for various purposes, including computer and telecommunication networks, both components of mathematical modeling are widely used. These are simulation modeling and analytical modeling based on queuing theory. At the same time, researchers can always compare the results obtained by means of simulation and analytical modeling. From modern technologies of simulation modeling, one can single out the IT GURU Academic Edition technologies, represented by the Opnet Modeler and Riverbed Modeler software products with powerful graphical editors. Graphic editors allow you to create simulation models of data transmission systems of any complexity, and launch and run their models to obtain statistics of the main performance indicators of these systems. Comparison of the simulation results with the results of queuing systems (QS) of the G/G/1 type makes it possible to assess the adequacy of those and other mathematical models. This article summarizes the results of the author’s publications on G/G/1 systems based on time-shifted distribution laws such as exponential, hyperexponential, and Erlang distribution. Thus, these distribution laws for the random variables used provide the coefficients of variation less than, equal or greater than one. This fact is important from the point of view of the queuing theory, because the average delay of claims in the system directly depends on the coefficients of variations in the time intervals for the arrival and servicing of claims.

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MATHEMATICAL DELAY MODEL BASED ON SYSTEMS WITH HYPERERLANGIAN AND ERLANGIAN DISTRIBUTIONS

Radio Electronics Computer Science Control ◽

10.15588/1607-3274-2021-1-9 ◽

2021 ◽

Vol 1 (1) ◽

pp. 87-96

Author(s):

V. N. Tarasov

Keyword(s):

Integral Equation ◽

Closed Form ◽

Service Time ◽

Spectral Decomposition ◽

Queuing Theory ◽

Input Flow ◽

Average Delay ◽

Spectral Expansions ◽

Wide Range ◽

Two Systems

Context. Studies of G/G/1 systems in queuing theory are relevant because such systems are of interest for analyzing the delay of data transmission systems. At the same time, it is impossible to obtain solutions for the delay in the final form in the general case for arbitrary laws of distribution of the input flow and service time. Therefore, it is important to study such systems for particular cases of input distributions. We consider the problem of deriving a solution for the average queue delay in a closed form for two systems with ordinary and shifted hypererlangian and erlangian input distributions. Objective. Obtaining a solution for the main characteristic of the system – the average delay of requests in the queue for two queuing systems of the G/G/1 type with ordinary and with shifted hypererlangian and erlangian input distributions. Method. To solve this problem, we used the classical method of spectral decomposition of the solution of the Lindley integral equation. This method allows to obtaining a solution for the average delay for systems under consideration in a closed form. The method of spectral decomposition of the solution of the Lindley integral equation plays an important role in the theory of systems G/G/1. For the practical application of the results obtained, the well-known method of moments of probability theory is used. Results. For the first time, spectral expansions of the solution of the integral Lindley equation for two systems are obtained, with the help of which calculation formulas for the average delay in a queue in a closed form are derived. Thus, mathematical models of queuing delay for these systems have been built. Conclusions. These formulas expand and supplement the known queuing theory formulas for the average delay G/G/1 systems with arbitrary laws distributions of input flow and service time. This approach allows us to calculate the average delay for these systems in mathematical packages for a wide range of traffic parameters. In addition to the average delay, such an approach makes it possible to determine also moments of higher orders of waiting time. Given the fact that the packet delay variation (jitter) in telecommunications is defined as the spread of the delay from its average value, the jitter can be determined through the variance of the delay.

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TELECOMMUNICATION NETWORKS AS A BASE FOR BRIDGING THE DIGITAL DIVIDE BETWEEN RUSSIAN FEDERATION REGIONS

Электросвязь ◽

10.34832/elsv.2021.21.8.003 ◽

2021 ◽

Author(s):

Н.А. ЧИСТОВА ◽

А.С. БОРОДИН ◽

А.Е. КУЧЕРЯВЫЙ

Keyword(s):

Digital Divide ◽

Communication Networks ◽

Russian Federation ◽

Educational Process ◽

Telecommunication Networks ◽

Gross Regional Product ◽

Planning And Design ◽

The Russian Federation ◽

Regional Product ◽

The Relationship

Статья посвящена анализу возможностей сетей связи для сокращения цифрового разрыва между регионами Российской Федерации. Основным результатом статьи является установление взаимосвязи валового регионального продукта и доли занятых в сфере информатизации и связи в общем числе занятых во всех отраслях. Результаты статьи могут быть использованы заинтересованными министерствами и ведомствами при реализации программы цифровой экономики, научными и проектными организациями при планировании и проектировании сетей связи, а также университетами в учебном процессе. The article is devoted to the analysis of the capabilities of telecommunication networks with ultralow latency to reduce the digital divide between the regions of the Russian Federation. The main result of the article is to establish the relationship between the gross regional product and the share of people employed in the field of informatization and communications in the total number of people employed in all industries. The results of the article can be used by interested ministries and departments in the implementation of the digital economy program, scientific and design organizations in the planning and design of communication networks, as well as by universities in the educational process.

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Mathematical Model of Information and Communication Networks

2018 International Conference on Actual Problems of Electron Devices Engineering (APEDE) ◽

10.1109/apede.2018.8542330 ◽

2018 ◽

Author(s):

M.S. Svetlov ◽

A.A. L'vov ◽

D.A. Mishchenko ◽

N.S. Vagarina

Keyword(s):

Mathematical Model ◽

Communication Networks ◽

Information And Communication

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Cooperative Problem Solving in Telecommunication Network

INTERNATIONAL JOURNAL OF MANAGEMENT & INFORMATION TECHNOLOGY ◽

10.24297/ijmit.v4i3.4548 ◽

2013 ◽

Vol 4 (3) ◽

pp. 388-392

Author(s):

Shanu K Rakesh ◽

Bharat Choudhary ◽

Rachna Sandhu

Keyword(s):

Communication Network ◽

Problem Solving ◽

Distributed Control ◽

Communication Networks ◽

Foraging Behaviour ◽

Telecommunication Network ◽

Telecommunication Networks ◽

Control Problems ◽

Engineering Systems ◽

Biologically Inspired

Swarm intelligence, as demonstrated by natural biological swarms, has numerous powerful properties desirable in many engineering systems, such as telecommunication. Communication network management is becoming increasingly difficult due to the increasing size, rapidly changing topology, and complexity of communication networks. This paper describes how biologically-inspired agents can be used to solve control problems in telecommunications. These agents, inspired by the foraging behaviour of ants, exhibit the desirable characteristics of simplicity of action and interaction. The colle ction of agents, or swarm system, deals only with local knowledge and exhibits a form of distributed control with agent communication effected through the environment. In this paper we explore the application of ant-like agents to the problem of routing in telecommunication networks.

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Parallel Network Simulation With OMNeT++

Research and Development on Information and Communication Technology ◽

10.32913/mic-ict-research.v3.n5.320 ◽

2009 ◽

Author(s):

András Varga ◽

Ahmet Y. Şekercioğlu Şekercioğlu

Keyword(s):

Communication Networks ◽

Large Scale ◽

Distributed Simulation ◽

Discrete Event ◽

Rare Event ◽

Telecommunication Networks ◽

Event Simulation ◽

Parallel And Distributed Simulation ◽

Simulation Protocol ◽

Parallel Network

This paper reports a new parallel and distributed simulation architecture for OMNeT++, an open-source discrete event simulation environment. The primary application area of OMNeT++ is the simulation of communication networks. Support for a conservative PDES protocol (the Null Message Algorithm) and the relatively novel Ideal Simulation Protocol has been implemented.Placeholder modules, a novel way of distributing the model over several logical processes (LPs) is presented. The OMNeT++ PDES implementation has a modular and extensible architecture, allowing new synchronization protocols and new communication mechanisms to be added easily, which makes it an attractive platform for PDES research, too. We intend touse this framework to harness the computational capacity of highperformance cluster computersfor modeling very large scale telecommunication networks to investigate protocol performance and rare event failure scenarios.

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Decision Choice Optimization With Genetic Algorithm in Communication Networks

Research Anthology on Multi-Industry Uses of Genetic Programming and Algorithms ◽

10.4018/978-1-7998-8048-6.ch017 ◽

2021 ◽

pp. 328-343

Author(s):

Driss Ait Omar ◽

Mohamed El Amrani ◽

Hamid Garmani ◽

Mohamed Baslam ◽

Mohamed Fakir

Keyword(s):

Mathematical Modeling ◽

Genetic Algorithm ◽

Inverse Problem ◽

Decision Support ◽

Communication Networks ◽

Service Providers ◽

Telecommunication Networks ◽

Essential Tool ◽

Decision Choice

Optimization is an essential tool in the field of decision support. In this chapter, the authors study an inverse problem applied in the telecommunication networks. Indeed, in the telecommunication networks, service providers have subscription offers to customers. Since competition is strong in this sector, most of these advertising offerings, totally or partially ambiguous, are prepared to attract the attention of consumers. For this reason, customers face problems in making decisions about the choice of the operators that gives them a better report price/QoS. Mathematical modeling of this decision support problem led to the resolution of an inverse problem. More precisely, the inverse problem is to find the function of the QoS real knowing the QoS theoretical or advertising. This model will help customers who seek to know the degree of sincerity of their operators, and it is an opportunity for operators who want to maintain their resources so that they gain the trust of customers.

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