Valentina Klimenok
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Valentina Klimenok has a total of 33 co-authors. Here are the top co-authors by number of shared publications:
- Alexander Dudin
Belarusian State University, Minsk, Belarus
28 shared publications - Vladimir Vishnevsky
V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
15 shared publications - Chesoong Kim
Sangji University
9 shared publications - Olga Dudina
Belarusian State University, Minsk, Belarus
5 shared publications - Sergey Dudin
Belarusian State University, Minsk, Belarus
4 shared publications - Aleksandr Sokolov
V.A. Trapeznikov Institute of Control Sciences Russian Academy of Sciences
2 shared publications
Latest Publications
- 16 February 2025
- Published by Springer Nature
- p. 203-218
Tandem Retrial Queueing System with Markovian Arrival Process and Common Orbit
- 16 February 2025
- Published by Springer Nature
- p. 203-218
Tandem Retrial Queueing System with Markovian Arrival Process and Common Orbit
- Open Access
- 15 July 2024
- Published by MDPI AG in Mathematics
- Vol. 12 (14) , 2214
Stability of Queueing Systems with Impatience, Balking and Non-Persistence of Customers
The operation of many queueing systems is adequately described by the structured multidimensional continuous-time Markov chains. The most well-studied classes of such chains are level-independent Quasi-Birth-and-Death processes, type and type Markov chains, generators of which have the block tri-diagonal, lower- and upper-Hessenberg structure, respectively. All these classes assume that the matrices of transition rates are quasi-Toeplitz. This property greatly simplifies their analysis but makes them inappropriate for the study of many important systems, e.g., retrial queues with a retrial rate depending on the number of customers in orbit, queues with impatient customers, etc. The importance of such systems attracts significant interest to their analysis. However, in the literature, there is a methodological gap relating to the ergodicity condition of the corresponding Markov chains. To fulfill this gap and facilitate the analysis of a wide range of such systems, we show that under non-restrictive assumptions, the following hold true: (i) if the customers can balk or are impatient or non-persistent, then the Markov chain describing the behavior of the system belongs to the class of asymptotically quasi-Toeplitz Markov chains; (ii) this chain is ergodic; (iii) known algorithms can be applied for the calculation of the stationary distribution of the corresponding queueing system.- 15 July 2024
- Published by MDPI AG in Mathematics
- Vol. 12 (14) , 2214
Open AccessStability of Queueing Systems with Impatience, Balking and Non-Persistence of Customers
The operation of many queueing systems is adequately described by the structured multidimensional continuous-time Markov chains. The most well-studied classes of such chains are level-independent Quasi-Birth-and-Death processes, type and type Markov chains, generators of which have the block tri-diagonal, lower- and upper-Hessenberg structure, respectively. All these classes assume that the matrices of transition rates are quasi-Toeplitz. This property greatly simplifies their analysis but makes them inappropriate for the study of many important systems, e.g., retrial queues with a retrial rate depending on the number of customers in orbit, queues with impatient customers, etc. The importance of such systems attracts significant interest to their analysis. However, in the literature, there is a methodological gap relating to the ergodicity condition of the corresponding Markov chains. To fulfill this gap and facilitate the analysis of a wide range of such systems, we show that under non-restrictive assumptions, the following hold true: (i) if the customers can balk or are impatient or non-persistent, then the Markov chain describing the behavior of the system belongs to the class of asymptotically quasi-Toeplitz Markov chains; (ii) this chain is ergodic; (iii) known algorithms can be applied for the calculation of the stationary distribution of the corresponding queueing system. - Open Access
- 23 February 2024
- Published by MDPI AG in Mathematics
- Vol. 12 (5) , 659
Investigation of the Fork–Join System with Markovian Arrival Process Arrivals and Phase-Type Service Time Distribution Using Machine Learning Methods
This paper presents a study of fork–join systems. The fork–join system breaks down each customer into numerous tasks and processes them on separate servers. Once all tasks are finished, the customer is considered completed. This design enables the efficient handling of customers. The customers enter the system in a MAP flow. This helps create a more realistic and flexible representation of how customers arrive. It is important for modeling various real-life scenarios. Customers are divided into tasks and assigned to different subsystems. The number of tasks matches the number of subsystems. Each subsystem has a server that processes tasks, and a buffer that temporarily stores tasks waiting to be processed. The service time of a task by the k-th server follows a PH (phase-type) distribution with an irreducible representation (, ), . An analytical solution was derived for the case of when the input MAP flow and service time follow a PH distribution. We have efficient algorithms to calculate the stationary distribution and performance characteristics of the fork–join system for this case. In general cases, this paper suggests using a combination of Monte Carlo and machine learning methods to study the performance of fork–join systems. In this paper, we present the results of our numerical experiments.- 23 February 2024
- Published by MDPI AG in Mathematics
- Vol. 12 (5) , 659
Open AccessInvestigation of the Fork–Join System with Markovian Arrival Process Arrivals and Phase-Type Service Time Distribution Using Machine Learning Methods
This paper presents a study of fork–join systems. The fork–join system breaks down each customer into numerous tasks and processes them on separate servers. Once all tasks are finished, the customer is considered completed. This design enables the efficient handling of customers. The customers enter the system in a MAP flow. This helps create a more realistic and flexible representation of how customers arrive. It is important for modeling various real-life scenarios. Customers are divided into tasks and assigned to different subsystems. The number of tasks matches the number of subsystems. Each subsystem has a server that processes tasks, and a buffer that temporarily stores tasks waiting to be processed. The service time of a task by the k-th server follows a PH (phase-type) distribution with an irreducible representation (, ), . An analytical solution was derived for the case of when the input MAP flow and service time follow a PH distribution. We have efficient algorithms to calculate the stationary distribution and performance characteristics of the fork–join system for this case. In general cases, this paper suggests using a combination of Monte Carlo and machine learning methods to study the performance of fork–join systems. In this paper, we present the results of our numerical experiments. - Open Access
- 29 September 2023
- Published by United Institute of Informatics Problems of the National Academy of Sciences of Belarus in Informatics
- Vol. 20 (3) , 50-60
Performance characteristics of the fork-join queuing system
Objectives. The problem of investigating a fork-join queuing system is considered. It is required to build the process of the system functioning, to find the condition for the existence of a stationary distribution, and propose algorithms for calculating the stationary distribution and the main stationary performance characteristics. The special interest of the study is to obtain the lower and upper bounds of the mean sojourn time of a customer in the system.Methods. Methods of probability theory, queuing theory and matrix theory are used.Results. The functioning of the system is described in terms of a multidimensional Markov chain. A constructive condition for the existence of a stationary distribution is found, and algorithms for calculating the stationary distribution and stationary performance characteristics of the system are proposed. Analytical expressions are obtained for the lower and upper bounds of the mean sojourn time of customers in the system.Conclusion. The functioning of the fork-join queuing system with a stationary Poisson flow has been studied. Each of the arriving customers forks into two tasks that go to two subsystems, each of which consists of a server and a buffer. We assume that the buffer to one of the servers is unlimited, and to the second server has a finite volume. Service times have, generally speaking, different phase distributions (PH-Phase type distributions). For this system, a condition for the existence of a stationary distribution is obtained, algorithms for calculating the stationary distribution and a number of stationary performance measures of the system are proposed. Analytical expressions for the lower and upper bounds of the mean sojourn time of a customer in the system from the moment it enters the system to the moment of synchronization, which is a critical performance indicator of the fork-join queues, are obtained. The results of the study can be used for modeling various computer and communication systems, in particular, systems that perform parallel computing, customer processing in distributed databases, and parallel disk access.
- 29 September 2023
- Published by United Institute of Informatics Problems of the National Academy of Sciences of Belarus in Informatics
- Vol. 20 (3) , 50-60
Open AccessPerformance characteristics of the fork-join queuing system
Objectives. The problem of investigating a fork-join queuing system is considered. It is required to build the process of the system functioning, to find the condition for the existence of a stationary distribution, and propose algorithms for calculating the stationary distribution and the main stationary performance characteristics. The special interest of the study is to obtain the lower and upper bounds of the mean sojourn time of a customer in the system.Methods. Methods of probability theory, queuing theory and matrix theory are used.Results. The functioning of the system is described in terms of a multidimensional Markov chain. A constructive condition for the existence of a stationary distribution is found, and algorithms for calculating the stationary distribution and stationary performance characteristics of the system are proposed. Analytical expressions are obtained for the lower and upper bounds of the mean sojourn time of customers in the system.Conclusion. The functioning of the fork-join queuing system with a stationary Poisson flow has been studied. Each of the arriving customers forks into two tasks that go to two subsystems, each of which consists of a server and a buffer. We assume that the buffer to one of the servers is unlimited, and to the second server has a finite volume. Service times have, generally speaking, different phase distributions (PH-Phase type distributions). For this system, a condition for the existence of a stationary distribution is obtained, algorithms for calculating the stationary distribution and a number of stationary performance measures of the system are proposed. Analytical expressions for the lower and upper bounds of the mean sojourn time of a customer in the system from the moment it enters the system to the moment of synchronization, which is a critical performance indicator of the fork-join queues, are obtained. The results of the study can be used for modeling various computer and communication systems, in particular, systems that perform parallel computing, customer processing in distributed databases, and parallel disk access.
- 22 October 2022
- Published by Springer Nature in Annals of Operations Research
- Vol. 331 (2) , 839-866
Analysis of MAP/G/1 queue with inventory as the model of the node of wireless sensor network with energy harvesting
- 22 October 2022
- Published by Springer Nature in Annals of Operations Research
- Vol. 331 (2) , 839-866
Analysis of MAP/G/1 queue with inventory as the model of the node of wireless sensor network with energy harvesting
- 24 June 2022
- Published by Springer Nature
- p. 157-171
Queueing System with Two Types of Customers and Limited Processor Sharing
- 24 June 2022
- Published by Springer Nature
- p. 157-171
Queueing System with Two Types of Customers and Limited Processor Sharing
- Open Access
- 18 March 2022
- Published by United Institute of Informatics Problems of the National Academy of Sciences of Belarus in Informatics
- Vol. 19 (2) , 56-67
A retrial queueing system with processor sharing and impatient customers
Objectives. The problem of constructing and investigating a mathematical model of a stochastic system with processor sharing, repeated calls, and customer impatience is considered. This system is formalized in the form of a queueing system. The operation of the queue is described in terms of multi-dimensional Markov chain. A condition for the existence of a stationary distribution is found, and algorithms for calculating the stationary distribution and stationary performance characteristics of the system are proposed.Methods. Methods of probability theory, queueing theory and matrix theory are used.Results. The steady state operation of a queueing system with repeated calls, processor sharing and two types of customers arriving in a marked Markovian arrival process is studied. The channel bandwidth is divided between two types of customers in a certain proportion, and the number of customers of each type simultaneously located on the server is limited. Customers of one of the types that have made all the channels assigned to them busy leave the system unserved with some probability and, with an additional probability, go to the orbit of infinite size, from where they make attempts to get service at random time intervals. Customers of the second type, which caused all the channels assigned to them to be busy, are lost. Customers in orbit show impatience: each of them can leave orbit forever if the time of its stay in orbit exceeds some random time distributed according to an exponential law. Service times of customers of different types are distributed according to the phase law with different parameters. The operation of the system is described in terms of a multi-dimensional Markov chain. It is proved that for any values of the system parameters this chain has a stationary distribution. Algorithms for calculating the stationary distribution and a number of performance measures of the system are proposed. The results of the study can be used to simulate the operation of a fixed capacity cell in a wireless cellular communication network and other real systems operating in the processor sharing mode.
- 18 March 2022
- Published by United Institute of Informatics Problems of the National Academy of Sciences of Belarus in Informatics
- Vol. 19 (2) , 56-67
Open AccessA retrial queueing system with processor sharing and impatient customers
Objectives. The problem of constructing and investigating a mathematical model of a stochastic system with processor sharing, repeated calls, and customer impatience is considered. This system is formalized in the form of a queueing system. The operation of the queue is described in terms of multi-dimensional Markov chain. A condition for the existence of a stationary distribution is found, and algorithms for calculating the stationary distribution and stationary performance characteristics of the system are proposed.Methods. Methods of probability theory, queueing theory and matrix theory are used.Results. The steady state operation of a queueing system with repeated calls, processor sharing and two types of customers arriving in a marked Markovian arrival process is studied. The channel bandwidth is divided between two types of customers in a certain proportion, and the number of customers of each type simultaneously located on the server is limited. Customers of one of the types that have made all the channels assigned to them busy leave the system unserved with some probability and, with an additional probability, go to the orbit of infinite size, from where they make attempts to get service at random time intervals. Customers of the second type, which caused all the channels assigned to them to be busy, are lost. Customers in orbit show impatience: each of them can leave orbit forever if the time of its stay in orbit exceeds some random time distributed according to an exponential law. Service times of customers of different types are distributed according to the phase law with different parameters. The operation of the system is described in terms of a multi-dimensional Markov chain. It is proved that for any values of the system parameters this chain has a stationary distribution. Algorithms for calculating the stationary distribution and a number of performance measures of the system are proposed. The results of the study can be used to simulate the operation of a fixed capacity cell in a wireless cellular communication network and other real systems operating in the processor sharing mode.
- Open Access
- 16 January 2022
- Published by MDPI AG in Mathematics
- Vol. 10 (2) , 269
Retrial BMAP/PH/N Queueing System with a Threshold-Dependent Inter-Retrial Time Distribution
In this paper, we study a multi-server queueing system with retrials and an infinite orbit. The arrival of primary customers is described by a batch Markovian arrival process (), and the service times have a phase-type () distribution. Previously, in the literature, such a system was mainly considered under the strict assumption that the intervals between the repeated attempts from the orbit have an exponential distribution. Only a few publications dealt with retrial queueing systems with non-exponential inter-retrial times. These publications assumed either the rate of retrials is constant regardless of the number of customers in the orbit or this rate is constant when the number of orbital customers exceeds a certain threshold. Such assumptions essentially simplify the mathematical analysis of the system, but do not reflect the nature of the majority of real-life retrial processes. The main feature of the model under study is that we considered the classical retrial strategy under which the retrial rate is proportional to the number of orbital customers. However, in this case, the assumption of the non-exponential distribution of inter-retrial times leads to insurmountable computational difficulties. To overcome these difficulties, we supposed that inter-retrial times have a phase-type distribution if the number of customers in the orbit is less than or equal to some non-negative integer (threshold) and have an exponential distribution in the contrary case. By appropriately choosing the threshold, one can obtain a sufficiently accurate approximation of the system with a distribution of the inter-retrial times. Thus, the model under study takes into account the realistic nature of the retrial process and, at the same time, does not resort to restrictions such as a constant retrial rate or to rough truncation methods often applied to the analysis of retrial queueing systems with an infinite orbit. We describe the behavior of the system by a multi-dimensional Markov chain, derive the stability condition, and calculate the steady-state distribution and the main performance indicators of the system. We made sure numerically that there was a reasonable value of the threshold under which our model can be served as a good approximation of the queueing system with the distribution of inter-retrial times. We also numerically compared the system under consideration with the corresponding queueing system having exponentially distributed inter-retrial times and saw that the latter is a poor approximation of the system with the distribution of inter-retrial times. We present a number of illustrative numerical examples to analyze the behavior of the system performance indicators depending on the system parameters, the variance of inter-retrial times, and the correlation in the input flow.- 16 January 2022
- Published by MDPI AG in Mathematics
- Vol. 10 (2) , 269
Open AccessRetrial BMAP/PH/N Queueing System with a Threshold-Dependent Inter-Retrial Time Distribution
In this paper, we study a multi-server queueing system with retrials and an infinite orbit. The arrival of primary customers is described by a batch Markovian arrival process (), and the service times have a phase-type () distribution. Previously, in the literature, such a system was mainly considered under the strict assumption that the intervals between the repeated attempts from the orbit have an exponential distribution. Only a few publications dealt with retrial queueing systems with non-exponential inter-retrial times. These publications assumed either the rate of retrials is constant regardless of the number of customers in the orbit or this rate is constant when the number of orbital customers exceeds a certain threshold. Such assumptions essentially simplify the mathematical analysis of the system, but do not reflect the nature of the majority of real-life retrial processes. The main feature of the model under study is that we considered the classical retrial strategy under which the retrial rate is proportional to the number of orbital customers. However, in this case, the assumption of the non-exponential distribution of inter-retrial times leads to insurmountable computational difficulties. To overcome these difficulties, we supposed that inter-retrial times have a phase-type distribution if the number of customers in the orbit is less than or equal to some non-negative integer (threshold) and have an exponential distribution in the contrary case. By appropriately choosing the threshold, one can obtain a sufficiently accurate approximation of the system with a distribution of the inter-retrial times. Thus, the model under study takes into account the realistic nature of the retrial process and, at the same time, does not resort to restrictions such as a constant retrial rate or to rough truncation methods often applied to the analysis of retrial queueing systems with an infinite orbit. We describe the behavior of the system by a multi-dimensional Markov chain, derive the stability condition, and calculate the steady-state distribution and the main performance indicators of the system. We made sure numerically that there was a reasonable value of the threshold under which our model can be served as a good approximation of the queueing system with the distribution of inter-retrial times. We also numerically compared the system under consideration with the corresponding queueing system having exponentially distributed inter-retrial times and saw that the latter is a poor approximation of the system with the distribution of inter-retrial times. We present a number of illustrative numerical examples to analyze the behavior of the system performance indicators depending on the system parameters, the variance of inter-retrial times, and the correlation in the input flow. - 1 January 2022
- Published by Springer Nature
- p. 257-269
On the Distribution of the Number of Consecutively Lost Customers in the BMAP/PH/1/N System
- 1 January 2022
- Published by Springer Nature
- p. 257-269
On the Distribution of the Number of Consecutively Lost Customers in the BMAP/PH/1/N System
- Open Access
- 14 December 2021
- Published by MDPI AG in Mathematics
- Vol. 9 (24) , 3236
Performance Evaluation of the Priority Multi-Server System MMAP/PH/M/N Using Machine Learning Methods
In this paper, we present the results of a study of a priority multi-server queuing system with heterogeneous customers arriving according to a marked Markovian arrival process (MMAP), phase-type service times (PH), and a queue with finite capacity. Priority traffic classes differ in PH distributions of the service time and the probability of joining the queue, which depends on the current length of the queue. If the queue is full, the customer does not enter the system. An analytical model has been developed and studied for a particular case of a queueing system with two priority classes. We present an algorithm for calculating stationary probabilities of the system state, loss probabilities, the average number of customers in the queue, and other performance characteristics for this particular case. For the general case with K priority classes, a new method for assessing the performance characteristics of complex priority systems has been developed, based on a combination of machine learning and simulation methods. We demonstrate the high efficiency of the new method by providing numerical examples.
- 14 December 2021
- Published by MDPI AG in Mathematics
- Vol. 9 (24) , 3236
Open AccessPerformance Evaluation of the Priority Multi-Server System MMAP/PH/M/N Using Machine Learning Methods
In this paper, we present the results of a study of a priority multi-server queuing system with heterogeneous customers arriving according to a marked Markovian arrival process (MMAP), phase-type service times (PH), and a queue with finite capacity. Priority traffic classes differ in PH distributions of the service time and the probability of joining the queue, which depends on the current length of the queue. If the queue is full, the customer does not enter the system. An analytical model has been developed and studied for a particular case of a queueing system with two priority classes. We present an algorithm for calculating stationary probabilities of the system state, loss probabilities, the average number of customers in the queue, and other performance characteristics for this particular case. For the general case with K priority classes, a new method for assessing the performance characteristics of complex priority systems has been developed, based on a combination of machine learning and simulation methods. We demonstrate the high efficiency of the new method by providing numerical examples.