Information Technologies and Mathematical Modelling. Queueing Theory and Applications: 21st International Conference, ITMM 2022, Karshi, Uzbekistan, ... in Computer and Information Science)

✍ Scribed by Alexander Dudin (editor), Anatoly Nazarov (editor), Alexander Moiseev (editor)

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 250
• Category: Library

✦ Synopsis

This book constitutes the refereed proceedings of the 21st International Conference on Information Technologies and Mathematical Modelling. Queueing Theory and Applications, ITMM 2022, held in Karshi, Uzbekistan, during October 25–29, 2022.
The 19 full papers included in this book were carefully reviewed and selected from 89 submissions. The papers are devoted to new results in queueing theory and its applications. Its target audience includes specialists in probabilistic theory, random processes, mathematical modeling as well as engineers engaged in logical and technical design and operational management of data processing systems, communication, and computer networks.

✦ Table of Contents

Preface
Organization
Contents
Limit Theorems for the Positive Recurrent Q-process
1 Introduction
1.1 Preliminaries
1.2 Main Results
2 Proof of the Results
References
Numerical Analysis of Shortest Queue Problem for Time-Scale Queueing System with a Small Parameter
1 Introduction
2 Time-Scale Queueing Systems Model
3 Time-Scale Queueing Systems Model with a Small Parameter
4 Truncated System of Differential Equations and Numerical Analysis
5 Conclusion
References
Mathematical Modeling of Virtual Machine Life Cycle Using Branching Renewal Process
1 Introduction
2 Mathematical Model
3 Probability Distribution of the Number of Simultaneously Performed Phases
4 Total Volume V of Resources Occupied by All Virtual Machines
5 Performance Metrics of Cloud System
5.1 Special Case: Branching Process with Three Phases
5.2 Special Case: Branching Process with Five Phases
6 Conclusion
References
On Modeling a Section of a Single-Track Railway Network Based on Queuing Networks
1 Introduction
2 Problem Statement
3 Methodology
4 The Northern Section of the Ulaanbaatar Railway
5 Mathematical Model
6 Computational Experiment
7 Discussion and Conclusions
References
Asymptotic Analysis of a Multiserver Retrial Queue with Disasters in the Service Block
1 Introduction
2 Model Description
3 Asymptotic Analysis
3.1 The First Order Asymptotics
3.2 The Second Order Asymptotics
4 Numerical Analysis
5 Conclusions
References
Refined Limit Theorems for the Critical Continuous-Time Markov Branching Systems
1 Introduction and Results
1.1 Preliminaries on Slow Variation
1.2 Background, Basic Assumptions and Purpose
1.3 Results
2 Auxiliaries
3 Proof of the Results
References
Retrial Queue MMPP/M/1 with Server Switching
1 Introduction
2 Mathematical Model
3 Asymptotic Analysis Under Heavy Load
4 Numerical Examples
5 Conclusions
References
Account of Disasters in Analysis of Queueing Systems Modeled by the Quasi-Birth-and-Death-Process
1 Introduction
2 Problem Formulation
3 The Main Result
4 Level-Independent QBD
5 Consideration of the System Described by the Level-Independent QBD that is Influenced by the Disasters
6 Conclusion
References
Retrial Queue with Two-Way Communication and Collisions
1 Introduction
2 Model Description
3 Kolmogorov System
4 Asymptotic-Diffusion Method
5 Numerical Example
6 Conclusion
References
Real Waiting Time in Single-Server Resource Queue with Markovian Arrival Process
1 Introduction
2 Model Description
3 Amount of Information in the Buffer
4 Virtual Waiting Time
5 Real Waiting Time
6 Numerical Example
7 Conclusion
References
Controlled Queueing Systems G/G/1 with Time Shift
1 Introduction
2 The Nature of the Change in the Numerical Characteristics and Parameters of Distributions with a Shift in Time
3 Theorem on the Spectral Expansion
4 Examples of Systems with a Time Shift
4.1 E2/M/1 System with Time Shift
4.2 M/E2/1 System with Time Shift
4.3 M/M/1 System with Time Shift
5 Results of Numerical Experiments
6 Simulation Results
7 Conclusion
References
Analysis of Retrial Queueing System with Two-Way Communication in Different Scenarios Using Simulation
1 Introduction
2 System Model
3 Simulation Results
3.1 First Scenario
3.2 Second Scenario
4 Conclusion
References
An Explicit Solution for an Inventory Model with Server Interruption and Retrials
1 Mathematical Model
2 Analysis of the Model
2.1 Stability Condition
2.2 Computation of Steady State Vector
3 System Performance Measures
3.1 Expected Number of Interruptions Encountered by a Customer
3.2 Expected Duration of an Interrupted Service
3.3 Other Performance Measures
4 Numerical Illustration
5 Graphical Illustration
6 Conclusion
References
Asymptotic Analysis of the M/M/1/N-1 Retrial System with Priority and Feedback
1 Introduction
2 The Mathematical Model
3 Kolmogorov Equations
4 First Order Asymptotics
5 Second Order Asymptotics
6 Numerical Results
7 Conclusion
References
Modelling of a MAP/PH(1),PH(2)/2 Production Inventory System with Multiple Servers and Production Vacations
1 Introduction
2 Model Description
3 Analysis
3.1 Stability Analysis
3.2 Steady State Probability Vector
4 Measures of Effectiveness
5 Cost Analysis
6 Numerical Experiments
References
A Discrete Time Perishable Inventory System Under (s, S) policy and Age-Dependent-Requests
1 Mathematical Modelling and Analysis
2 Stability Condition
3 Steady-State Analysis
4 System Performance Measures
5 Cost Analysis
6 Numerical Illusration
6.1 Effect of a on Various Performane Measures
6.2 Effect of b on Various Performane Measures
6.3 Effect of c on Various Performane Measures
7 (s, S) Pair
8 Graphical Illustration
References
N-Policy on a Retrial Inventory System
1 Introduction
2 Mathematical Modelling and Analysis of the Problem
3 Steady State Analysis
3.1 System Stability
3.2 Steady State Probability Vector
3.3 System Performance Measures
3.4 Cost Function
4 Numerical and Graphical Illustrations
5 Concluding Remarks
References
Research of Dynamic RQ System M/M/1 with Unreliable Server
1 Introduction
2 Description of the Mathematical Model
3 Method of Generating Functions
4 Method of Characteristic Functions
5 Asymptotic Analysis
6 Numerical Example
7 Conclusion
References
Estimating the Distribution Function Using Parametric Methods in Informative Model of Random Censorship from Both Sides
1 Informative Model of Random Censorship from Both Sides
2 Investigations on How the Estimator Is Influenced by Unknown Parameters of Censorship
3 Estimating the Parameters of the Exponential Distribution
References
Author Index