Alexander Rumyantsev

Alexander Rumyantsev
Karelian Research Centre of the Russian Academy of Sciences | Karelian Research Centre of RAS · Institute of Applied Mathematical Research

PhD

About

58
Publications
3,026
Reads
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165
Citations
Additional affiliations
September 2015 - May 2020
Petrozavodsk State University
Position
  • Professor (Assistant)
February 2010 - present
Karelian Research Centre of the Russian Academy of Sciences
Position
  • Senior Researcher
Education
September 2008 - December 2012
Karelian Research Centre of the Russian Academy of Sciences
Field of study
  • Applied Mathematics, Numerical Methods and Software
September 2006 - June 2008
Petrozavodsk State University
Field of study
  • Applied Mathematics and Informatics
September 2002 - June 2006
Petrozavodsk State University
Field of study
  • Applied Mathematics and Informatics

Publications

Publications (58)
Article
Full-text available
In this paper we study a simultaneous service multiserver system which we call speed-scaling supercomputer, where speed-scaling is used to address the performance/power demand tradeoff. We treat the system by three-level modeling approach, using matrix-analytic method, generalized semi-Markov processes and small-scale technical system as the three...
Chapter
Full-text available
We consider a single-server system with energy saving inactive state, non-zero setup, shutoff and hot reserve state. Matrix-analytic method is used to obtain the steady-state performance and average power demand, as well as study the energy-performance tradeoff in explicit way. Numerical results illustrate the model’s properties.
Chapter
The convergence of a recently proposed tabu-enhanced quantum annealing algorithm depends critically on the finiteness of memory of the related stochastic process. We discuss the background of quantum annealing and the convergence issues of the tabu-enhanced algorithm. Given the details of the tabu data structure, the so-called tabu matrix, we consi...
Article
Full-text available
In this paper we consider a single server queueing model with under general bulk service rule with infinite upper bound on the batch size which we call group clearance. The arrivals occur according to a batch Markovian point process and the services are generally distributed. The customers arriving after the service initiation cannot enter the ongo...
Article
Full-text available
In this paper, we consider a queuing inventory system with heterogeneous customers of K types arriving according to a marked Markovian arrival process. Each class of customers differs by nature of the service they seek and different priorities are assigned for each class resulting in different levels of inventory admitted to exhaust for customers o...
Conference Paper
In this paper we obtain sufficient conditions for the multiclass multiserver model with automata-type transitions to have a product-form type explicit form of the stability criterion. We use the method to obtain stability conditions of an interesting simultaneous service multiserver model describing a supercomputer, both in case of phase-dependent...
Conference Paper
We study certain properties of the function space of autocorrelation functions of unit, as well as finite state space Continuous Time Markov Chains (CTMCs). It is shown that under particular conditions, the L p norm of the autocorrelation function of arbitrary finite state space CTMCs is infinite. Several interesting inferences are made for point p...
Chapter
The paper describes a discrete event simulation model of a Desktop Grid system. Firstly, we present a stochastic model of a volunteer computing project. We then employ the event simulation approach based on the generalized semi-Markov processes to develop a discrete event simulation model. Finally, using the simulation model, we describe a performa...
Article
The effect of site preparation (mixed mounding and removal of the humus layer) under a shelterwood of mixed boreal forest along a forest interior-edge gradient on Norway spruce (Picea abies) seedlings was studied two years after planting. Mounds had a positive effect on root development, ectomycorrhiza formation and the absorption of nitrogen (N) a...
Preprint
Full-text available
In this paper the simultaneous service multiserver queueing model with a small number of servers is studied. The customer occupies and releases a random number of servers simultaneously. The system admits speed scaling technique: both servers switch the service rate at arrival/departure instants according to randomized asynchronous speed scaling me...
Chapter
In this paper, motivated by an increasing interest in Cognitive Radio wireless transmission systems, we study a stochastic model of a single node of such a system with underlay transmission and balking. The considered model is essentially a single-server system with an ON–OFF type environment governing the service time intensity and triggering the...
Article
Full-text available
The motivation of mixing distributions in communication/queueing systems modeling is that some input data (e.g., service time in queueing models) may follow several distinct distributions in a single input flow. In this paper, we study the sensitivity of performance measures on proximity of the service time distributions of a multiserver system mod...
Article
Full-text available
In this work, we consider an approximation of the so-called far-end-tail distribution of processes describing quality of service (QoS) performance of queueing systems. This approximation is based on the asymptotic equivalence between the excess distribution over a high threshold and the generalized Pareto distribution, for a wide class of the gover...
Conference Paper
Full-text available
The paper deals with simultaneous service multi-server system, where customer occupies a random number of servers. The system also admits speed scaling mechanism by switching speed regimes at arrival/departure instants according to the corresponding transition probability matrices. Stability conditions for Markovian case of such a model were derive...
Article
Queueing-inventory models have many practical applications and have been studied extensively in the literature. Most of the studies focus on models in which the the demands occur singly. Only a very few papers analyze models wherein the demands occur in batches. In this paper we consider batch demands in the context of two models, both of which ass...
Chapter
In this work, we discuss various (stochastic) orderings between random variables, with focus on the failure rate comparison. Then these results are applied to construct a coupling of random variables. In particular, it is shown how to compare the failure rates of various distributions, including Exponential, Weibull, Pareto and Burr distributions....
Chapter
A common approach to performance estimation of queueing system models is based on point estimators. Confidence intervals provide more insight on the system performance, and basically a regenerative structure of the studied process is required. However, classical regeneration epochs (arrivals into empty system) are too rare (or even might not exist)...
Article
Exponential growth of the amount of data stored worldwide together with high level of data redundancy motivates the active development of data deduplication techniques. The overall increasing popularity of solid-state drives (SSDs) as primary storage devices forces the adaptation of deduplication techniques to technical peculiarities of this type o...
Article
In this paper, we consider a single-server retrial model with multiple classes of customers. Arrival of customers follow independent Poisson rule. A new customer, facing a busy server upon his arrival, may join the corresponding (class-dependent) orbit queue with a class-dependent probability, or leaves the system forever (balks). The orbit queues...
Conference Paper
Full-text available
We give a simple proof of the well-known property PASTA for the workload and queue size process in the queueing systems with Poisson input. The proof is based on a relation connecting the workload process at an arbitrary instants and the arrival instants of the customers and, in particular, yields famous Pollaczeck-Khintchine equality. It is then s...
Article
Full-text available
We present regeneration techniques for perfomance estimation of multiserver system characteristics. Providing a necessary background of classical and weak regeneration notions, we focus on less well-known and mainly new construction of artificial classical regeneration, as well as recent method of regenerative envelopes for modeling modern energy e...
Article
Full-text available
In this research paper we consider the matrix polynomial equation arising naturally in the equilibrium analysis of a structured G∕M∕1-type Markov process. We obtain an explicit expression for the unknown rate matrix R being 2 × 2 matrix. The method is based on symbolic solution of the determinantal polynomial equation. Using Cayley–Hamilton theorem...
Article
Cloud computing is continuing to prove its flexibility and versatility in helping industries and businesses as well as academia as a way of providing needed computing capacity. As an important alternative to cloud computing, desktop grids allow to utilize the idle computer resources of an enterprise/community by means of distributed computing syste...
Article
Full-text available
A stochastic model of a multiserver queueing system with simultaneous service of a customer by a random number of servers and threshold-based (hysteretic) control of the service rate is presented. The performance and quality-of-service measures of the model are defined. Numerical results of experiments studying the dependence of performance/energy...
Article
Full-text available
In this paper, we study a multiserver system in which each customer requires a random number of servers simultaneously and a random but identical service time at all occupied servers. This model describes the dynamics of modern high performance clusters. Stability criteria of this system (under exponential assumptions) have been proved earlier for...
Conference Paper
Full-text available
In this paper, we study the stability conditions of the multiserver system in which each customer requires a random number of servers simultaneously and a random service time, identical at all occupied servers. We call it cluster model since it describes the dynamics of the modern multicore high performance clusters (HPC). Stability criterion of an...
Chapter
In this paper, we consider a model of communication system with state-dependent service rate. This mechanism allows to change service rate to increase the efficiency of the system. Motivation of such a system is discussed as well. Then we present the regenerative proof of the sufficient stability conditions of the system which is based on the negat...
Conference Paper
In this paper we develop a novel approach to confidence estimation of the stationary measures in high performance multiserver queueing systems. This approach is based on construction of the two processes which are, respectively, upper and lower (stochastic) bounds for the trajectories of the basic queue size process in the original system. The main...
Conference Paper
Full-text available
We continue to develop a novel approach for confidence estimation of the stationary measures in the model describing high performance multiserver queueing systems, such as high performance clusters (HPC). We call this model cluster model. This model is described by a stochastic process, and in the framework of the approach, we construct two envelop...
Conference Paper
Full-text available
We propose a new approach which allows to accelerate verification of the stability criterion of a multiserver model with simultaneous service for large number of servers. This approach reduces a state space related to calculation of a basic normalization constant included in the stability condition. Moreover, this result allows to obtain a stable c...
Data
Full-text available
Conference Paper
In this paper, we consider a state-dependent mechanism which can be used to reduce mean power consumption in modern communication and computer systems. This mechanism allows to change flexibly the service rate so as to increase the energy efficiency of the system. We focus on computer systems with sojourn time dependent service rate, and present a...
Conference Paper
Full-text available
The workload model of a high-performance cluster is considered in the context of an upgrade (increase the computational power) or downgrade (save energy) problems. Analytical solutions are found that provide stochastic stability of the workload. The results of numerical experiments with log-files of a real workload are presented.
Presentation
Full-text available
Some recent results presented at Aalto University, including the stability criterion and it’s accelerated version, exact solution for a single-server green computing model, some tasks in the volunteer computing research
Conference Paper
Full-text available
A multiserver model with simultaneous service as a model of a high performance computing cluster is viewed. The stability criterion of the model under the assumptions of i. i. d. exponentially distributed driving sequences is considered. The condition is applied to the problem of optimal task deadline selection. Simulation results are presented, th...
Article
Full-text available
A multi-server model with simultaneous service and concurrent server release is considered. A stability condition of the model (under exponential assumptions) is presented. A method for fast evaluation of the stability criterion is obtained. The condition allows to verify the stability of a supercomputer at design time, provided that the governing...
Conference Paper
We give a short survey of the moment properties of the basic regenerative queueing processes. Moreover, we show applicability of the regenerative simulation to estimate a steady-state performance measure of the positive recurrent basic process possessing long-range dependence. The moment properties of the embedded renewal process of regenerations p...

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Projects

Projects (4)
Project
Object and subject of research: Performance and energy efficiency in stationary (long-term operation) and transient (time-dependent characteristics) modes of models of advanced systems and storage and data processing networks, such as supercomputers, computer networks from personal computers, wireless data transmission systems, data storage systems based on solid state drives. Mathematical class of objects: in the field of queuing theory, the systems under consideration belong to the following three classes: - systems with multidimensional clients; - systems and networks with redundancy; - systems with group admission / group service. In all three classes, as a rule, systems are multi-server and multi-class, service disciplines can also be special. In a number of cases, taking into account additional constraints, a system of the service-reserve type is considered (when a resource, for example, memory, slots for access to a communication channel, is considered as a renewable stock consumed when servicing claims). The study of each class consists of the following main stages: 1) study of the stationarity of the model; 2) building a consistent three-tier model and researching its performance / efficiency; 3) solving the problem of finding the optimal system configuration with constraints on performance / efficiency. At the same time, translated systems of parallel service, such as high-performance computing clusters, systems of distributed computing and distributed data storage, telecommunication systems, quantum computers, act as both an object and a tool for conducting research.
Project
This is a joint RFBR (Russia) - DST (India) project of an international collaboration group from Karelian Research Centre of RAS, Federal Research Centre "Computer Science and Control" of RAS from Russian side; Anna University Chennai, Mahindra Ecole Centrale from Indian side. High-Performance and Distributed Computing systems are widely used to equip science and business to perform computationally intensive applications. To fulfill this unsaturated demand, Ubiquitous Computing attempts to utilize idle resources of nonspecific computational resources enabled by modern telecommunication technologies such as Internet of Things. To guarantee high rate of data transmission in the high-performance infrastructure, various media are used at network level, including the wired/wireless transmission systems. In such systems the variable transmission quality is leveraged by means of Automatic Repeat Request technologies and Error Control. These technologies bring up issues of reliability, performance, efficiency and stability of such systems. Of specific interest is the energy efficiency issue, which is open for all the aforementioned system classes, despite their heterogeneity. Random and unpredictable characteristics of workload submit to necessity of stochastic models in the performance analysis of these systems. In the field of such models, all the aforementioned system classes are related to the so-called multiserver queueing systems, however possessing very specific features. Large scale of real-world applications and sophisticated system structure lead to dramatic increase of analysis complexity. A separate difficulty is related to transfer of the theoretical results towards practical applications. The proposed project is targeted to solve the problem of analysis and performance estimation of high-performance, distributed and ubiquitous computing systems, as well as modern telecommunication systems with automatic repeat request and error control. The new methodology of validated three level stochastic modeling (at analytical, simulation and technical levels) of stationary performance and transient behavior in transient and steady-state regimes is implemented in the project. At analytical level the queueing theory is applied, utilizing the enhanced matrix-analytic and regenerative methods (in particular, applied jointly). At the simulation level it is assumed to apply the discrete event simulation technique (based on the so-called piecewise deterministic Markov chains), regenerative simulation (including confidence estimation), applying the novel regenerative envelops method, variance reduciton techniques (e. g. antithetic variables) as well as stochastic recursions. Finally, the results of technical level modeling are expected from the mockup real-life experiments based on open source software and multicore devices, wireless network devices and appropriate measurement devices (for energy efficiency).