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

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