Исследование многофазных стохастических систем с орбитой для оценки производительности беспроводных сетей линейной топологии / Retrial multiphase queueing system with orbit for performance evaluation of wireless networks with linear topology тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Данг Минь Конг

• Данг Минь Конг
• кандидат наук
• 2025

Оглавление диссертации кандидат наук Данг Минь Конг

Contents

Pg.

Introduction

Chapter 1. Literature review

1.1 Wireless networks along Transportation systems

1.2 Multiphase queueing systems and Retrial Multiphase queueing systems

1.3 Machine learning methods for Performance evaluation of Queueing systems

1.4 Conclusion of the first chapter

Chapter 2. Retrial multiphase queueing system

2.1 System with Poisson input and exponential distributed service times

2.1.1 Balance equations

2.1.2 Performance characteristics

2.2 System with Markovian arrival process input and Phase type

distributed service times

2.3 Analysis of two stations model

2.3.1 Markov chain

2.3.2 Ergodicity condition

2.3.3 Stationary distribution and Performance characteristics

2.4 Conclusion of the second chapter

Chapter 3. Performance evaluation of Retrial multiphase queueing

system using Machine learning methods

3.1 Generation of Synthetic dataset by Simulation model

3.2 Gradient Boosting

3.3 Random Forest

3.4 Neural Network

3.5 Numerical examples for system with two stations

Pg.

3.6 Comparison of execution time

3.7 Conclusion of the third chapter

Chapter 4. Programs Complex

4.1 Analytical Module

4.2 Simulation Module

4.2.1 Event Management

4.2.2 Network Elements

4.2.3 Simulation Algorithm

4.2.4 Statistical Collection

4.2.5 Convergence Detection

4.3 Machine Learning Module

4.3.1 Data Preprocessing

4.3.2 Models Training

4.4 Conclusion of the fourth chapter

Conclusion

Acknowledgments

List of Abbreviations

References

List of Figures

List of Tables

Appendix A. Source code of the main modules

Appendix B. Certificates of State Registration of Computer Program

Appendix C. Certificate on the Utilization of the Results of the Dissertation

Введение диссертации (часть автореферата) на тему «Исследование многофазных стохастических систем с орбитой для оценки производительности беспроводных сетей линейной топологии / Retrial multiphase queueing system with orbit for performance evaluation of wireless networks with linear topology»

Introduction

Relevance of the Research Topic. Wireless telecommunication networks have become an important part of modern societies, playing a significant role in the way societies communicate, operate, and innovate. With the development of technologies such as 5G, WiFi 6, and the proliferation of smart wireless devices, autonomous vehicles, etc., the degree of importance of wireless networks in modern infrastructure is even higher. Hence, research topics in the field of wireless networks deserve great attention.

Wireless networks with linear topology are a class of networks, where all stations are arranged in a line, and packets are transmitted from station to station sequentially. Although simple, they have practical applications in scenarios where terrain restricts station deployment, such as highways, bridges, etc. In [1; 2], Professor V.M. Vishnevsky et al. designed a wireless network system with linear topology for traffic monitoring, along with using a multiphase queueing system to model and evaluate the performance of the network. Multiphase queueing systems (or tandem queues) are a type of system that consists of multiple queues working in sequence. Customers enter the system at the first queue; after finishing service at a queue, they move to the next queue in the sequence, and so on until they finish service at the last queue. For a network with linear topology, a multiphase queueing system (or tandem queue) is a suitable model, where each phase of the multiphase system corresponds to a station in the wireless network, the queue buffer before each server corresponds to the data packet buffer of a station, and the service time of each server corresponds to the transmission time of a data link.

However, the wireless network researched in [1; 2] did not consider the mechanism of retransmission. When a packet arrives at a station with a full buffer, it is lost permanently from the system. Therefore, in this dissertation, a simple protocol for retransmission of lost packets from the first station of a network with linear topology is considered. With the addition of a retransmission mechanism, the original multiphase queue must also change correspondingly. In queueing theory, there is a class of retrial queueing systems, where customers that cannot be serviced at the moment will not leave permanently, but stay in a waiting area called orbit, and attempt to retry again at a later

time. Consider a retrial multiphase queueing system with a common orbit for all queues. Packets that cannot enter at any queue are directed to stay at the orbit and attempt to restart again at the first queue after some waiting time. This queueing system can model accurately the networks with linear topology and retransmission protocol mentioned above, where the orbit corresponds to the retransmission buffer. However, retrial multiphase queueing systems are complicated to investigate, as analytical methods are infeasible in the case of a large number of queues, and simulation methods can be slow in some cases. For this reason, machine learning methods can be used as an alternative to evaluate the performance of the system. Thus, the topics of this dissertation center around a retrial multiphase queueing system with a common orbit and the use of machine learning methods to evaluate the performance of the system — an approach that is particularly relevant for next-generation network design and optimization.

State of the art. Both multiphase queueing systems and retrial queues separately are popular topics and have been exhaustively researched in the literature. However, much less attention has been focused on retrial multiphase queueing systems. Many studies only consider systems with two queues, or only consider an orbit for the first queue instead of a common orbit for all queues. Notable is the research of A. Avrachenko and U. Yechiali [3], in which, motivated by studying TCP data flows in the Internet, the authors also investigated a retrial multiphase queueing system with a common orbit using approximation methods.

In this dissertation, aside from the mathematical analysis of a retrial multiphase queueing system, a significant portion is devoted to the problem of using machine learning methods to evaluate system performance. In the field of queueing theory, the use of machine learning methods is a relatively new topic, which has garnered much attention from researchers due to the popularity of machine learning research. Therefore, many recent studies have been devoted to applying machine learning to study queueing systems; with each study focusing on a specific kind of queueing system. The closest one to this dissertation topic is the paper [4] by V.M. Vishnevsky et al., in which multiphase queueing systems without a retrial orbit are studied.

Aim of the Dissertation. The aim of this dissertation is to research a new retrial multiphase queueing system with a common orbit for the purpose of performance evaluation of wireless networks with linear topology and retransmission mechanism. To

achieve this goal, the dissertation sets out to complete a comprehensive set of objectives, including:

1. Mathematical analysis of a retrial multiphase queueing system, to derive its stationary performance characteristics, along with the development of a numerical program to calculate analytical results;

2. Development of a simulation program, to evaluate performance characteristics of the retrial multiphase queueing system, with results are verified by analytical results in limited cases;

3. Employment of machine learning methods to estimate the average sojourn time of the retrial multiphase queueing system, using the results from the simulation program as training data;

4. Comparison of results obtained from machine learning, simulation and analytical methods, to assess their strengths and limitations.

Scientific Novelty. As mentioned above, the subject of retrial multiphase queueing systems has not been sufficiently investigated. In this dissertation, there are certain new developments as follows:

1. Investigation of a new retrial multiphase queueing system with a common orbit, correlated arrival flow (Markovian arrival process), and Phase-type distributed service times;

2. Application of machine learning methods to evaluate the performance of the retrial multiphase queueing system;

3. A programs complex combining numerical, simulation and machine learning methods to evaluate the performance of the retrial multiphase queueing system.

Practical Significance of this dissertation is as follows:

1. Development of new methods and models: The methods and models for analyzing the retrial multiphase queueing system developed in this dissertation enable better performance evaluation for wireless networks with linear topology and retransmission mechanism;

2. Creation of a programs complex: The developed programs complex in this dissertation provides a tool for the practical application of theoretical results;

3. Application in network design: The results of this dissertation can be applied in designing wireless networks with linear topology, improving their performance, reliability, and resource efficiency;

4. Contribution to theoretical development: The obtained results expand the theoretical foundation in the field of retrial multiphase queueing systems and can be used for further research in this area.

Methodology and Research Methods. To address the tasks at hand, methods from probability theory, queueing theory, computational mathematics, stochastic processes, simulation modeling, and machine learning are employed. Keypoints to be Defended:

1. Mathematical method for investigating the retrial multiphase queueing system with a common orbit;

2. Application of machine learning methods for performance evaluation of the retrial multiphase queueing system with a common orbit;

3. Comparative analysis of various methods, affirming the strengths, limitations, and practicality of the methods;

4. Development of a programs complex for the realization of the tasks addressed in this dissertation.

Reliability of the obtained results is determined by the rigorous proofs of the derived formulae for calculating the performance characteristics of the retrial multiphase queueing system with a common orbit, and the comparison of results from numerical calculation, simulation modeling, and machine learning methods.

Approbation. The main results of the research on the topic of this dissertation were presented and discussed at the following conferences and meetings:

1. 26th International Conference on "Distributed Computer and Communication Networks: Control, Computation, Communications" (DCCN2023, Moscow).

2. X International Conference on "Engineering & Telecommunication" (En&T

2023, Moscow).

3. XIV All-Russian Conference on Control Problems (VSPU-2024, Moscow).

4. XI International Conference on "Engineering & Telecommunication" (En&T

2024, Moscow).

The results obtained in this dissertation were used in conducting fundamental research on the topic "Theory and methods of development of technical means for control systems, computing and communication" No. 122041300130-3 (2022-2024) at the V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences.

Personal contribution. The author has actively worked on the tasks of this dissertation under the direct guidance of the scientific supervisor and the scientific consultant. The main contribution of the author lies in the investigation of various methods for performance evaluation of retrial multiphase queueing systems with a common orbit, as well as in the development of a programs complex for implementing of those methods. The author has presented the results of this dissertation at international scientific conferences and published them in scientific journals.

Publications. The main research results on the topics of this dissertation have been published in 8 publications, including 1 paper [5] in scientific journals included in the list of Higher Attestation Committee of the Russian Federation, 2 papers [6; 7] in scientific publications indexed by Scopus and Web of Science, 2 certificates of State Registration of computer program [8; 9], and 3 conference proceedings [10—12].

Volume and Structure of the Work. The dissertation consists of an introduction, 4 chapters, conclusion, and 3 appendices. The total volume of the disseratation is 155 pages, including 9 figures and 12 tables. The list of references contains 89 items.

Introduction. This chapter describes the relevance of the dissertation, defines the goals and objectives of the research, formulates the scientific novelty of the work, reviews the degree of study of the topic in the scientific literature, and outlines the practical value of the dissertation. The main scientific propositions to be defended are presented, along with information on the approbation of the obtained results and publications on the research topic.

Chapter 1: "Literature review." This chapter provides a short review of the core subjects related to the research topics, i.e. wireless networks along transport roads, multiphase queueing systems, and machine learning methods for evaluating the performance of queueing systems. Previous works on these subjects form the theoretical and practical basis for the topic of the dissertation.

Chapter 2: "Retrial multiphase queueing system." This chapter describes the mathematical model of a retrial multiphase queueing system, in both variants, one with a

Poisson input flow and exponential distributed service times, the other with a Markovian arrival process (MAP) input flow and Phase-type (PH) distributed service times. Analytical methods are carried out to obtain the formulae for calculating stationary performance characteristics of the system.

Chapter 3: "Performance evaluation of Retrial multiphase queueing system using Machine learning methods." This chapter describes the method of generating training data through simulation and using them to train machine learning models. A comparison between different methods is performed to evaluate the accuracy and effectiveness of the machine learning methods.

Chapter 4: "Programs Complex." This chapter describes the architecture and key parts of the programs complex, which includes a numerical program in Python for calculating the stationary characteristics of the retrial multiphase queueing system, a simulation program written in C++ programming language, as well as a machine learning program implemented using the Scikit-learn and PyTorch frameworks.

Conclusion. This chapter summarizes the main results of the dissertation research.

Заключение диссертации по теме «Другие cпециальности», Данг Минь Конг

Conclusion

In this dissertation, a little-studied type of retrial multiphase queueing system with a common orbit is investigated by a wide range of methods: analytical method, and simulation modeling in combination with various machine learning methods. The main motivation of the research is extending the queueing theory approach of performance evaluation into the case of wireless networks with linear topology and retransmission mechanism, for which requires the study of retrial multiphase queueing system. Wireless networks with linear topology have important roles in the development of communication networks for transportation road systems, and thus the development of methods for performance evaluation of such systems is still a relevant task.

The main results of this dissertation are as follows:

1. Mathematical models of a novel retrial multiphase queueing system with a common orbit, MAP input, PH distributed service times, and arbitrary finite number of stations is developed;

2. Analytical method for evaluating system performance is carried out for the case of limited conditions (two stations);

3. A Monte Carlo simulation model for the retrial multiphase queueing system has been developed and verified with results from analytical results;

4. A combination approach of using simulation model to generate data for training machine learning models is proposed, in order to evaluate system performance using machine learning models; its effectiveness is validated in comparison with simulation model;

5. A software implementation of the presented methods above for evaluating the performance of the retrial multiphase queueing system is provided.

Список литературы диссертационного исследования кандидат наук Данг Минь Конг, 2025 год

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