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Dudin, A.,Kim, C.,Dudina, O.,Dudin, S. Springer Science + Business Media 2016 Annals of operations research Vol.239 No.2
<P>A multi-server queueing system with a Markovian arrival process and finite and infinite buffers to model a call center with a call-back option is investigated. If all servers are busy during the customer arrival epoch, the customer may leave the system forever or move to the buffer (such a customer is referred to as a real customer), or, alternatively, request for call-back (such a customer is referred to as a virtual customer). During a waiting period, a real customer can be impatient and may leave the system without service or request for call-back (becomes a virtual customer). The service time of a customer and the dial time to a virtual customer for a server have a phase-type distribution. To simplify the investigation of the system we introduce the notion of a generalized phase-type service time distribution. We determine the stationary distribution of the system states and derive the Laplace-Stieltjes transforms of the sojourn and waiting time distributions for real and virtual customers. Some key performance measures are calculated and numerical results are presented.</P>
Recursive formulas for the moments of queue length in the BMAP/G/1 queue
Dudin, A.,Klimenok, V.,Lee, M. IEEE 2009 IEEE communications letters Vol.13 No.5
<P>We present recursive formulas for the moments of the joint distribution of the queue length and the state of the underlying process in the BMAP/G/1 at the service completion and arbitrary time epochs.</P>
Dina V. Dudina,Vyacheslav I. Mali,Alexander G. Anisimov,Natalia V. Bulina,Michail A. Korchagin,Oleg I. Lomovsky,Ivan A. Bataev,Vladimir A. Bataev 대한금속·재료학회 2013 METALS AND MATERIALS International Vol.19 No.6
We present several possible microstructure development scenarios in Ti3SiC2-Cu composites during mechanical milling and Spark Plasma Sintering (SPS). We have studied the effect of in situ consolidation during milling of Ti3SiC2 and Cu powders and melting of the Cu matrix during the SPS on the hardness and electrical conductivity of the sintered materials. Under low-energy milling, (3-5) vol.%Ti3SiC2-Cu composite particles of platelet morphology formed, which could be easily SPS-ed to 92-95% relative density. Under high-energy milling, millimeter-scale (3-5) vol.%Ti3SiC2-Cu granules formed as a result of in situ consolidation and presented a challenge to be sintered into a bulk fully dense sample; the corresponding SPS-ed compacts demonstrated a finer-grained Cu matrix and more significant levels of hardening compared to composites of the same composition processed by low-energy milling. The 3 vol.% Ti3SiC2-Cu in situ consolidated and Spark Plasma Sintered granules showed an extremely high hardness of 227 HV. High electrical conductivity of the Ti3SiC2-Cu composites sintered from the granules was an indication of efficient sintering of the granules to each other. Partial melting of the Cu matrix, if induced during the SPS, compromised the phase stability and uniformity of the microstructure of the Ti3SiC2-Cu composites and thus it is not to be suggested as a pathway to enhanced densification in this system.
A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items
Baek, Janghyun,Dudina, Olga,Kim, Chesoong UNIVERSITY OF ZIELONA GORA PRESS 2017 INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND C Vol.27 No.2
<P><B>Abstract</B></P><P>A single-server queueing system with a marked Markovian arrival process of heterogeneous customers is considered. Type-1 customers have limited preemptive priority over type-2 customers. There is an infinite buffer for type-2 customers and no buffer for type-1 customers. There is also a finite buffer (stock) for consumable additional items (semi-products, half-stocks, etc.) which arrive according to the Markovian arrival process. Service of a customer requires a fixed number of consumable additional items depending on the type of the customer. The service time has a phase-type distribution depending on the type of the customer. Customers in the buffer are impatient and may leave the system without service after an exponentially distributed amount of waiting time. Aiming to minimize the loss probability of type-1 customers and maximize throughput of the system, a threshold strategy of admission to service of type-2 customers is offered. Service of type-2 customer can start only if the server is idle and the number of consumable additional items in the stock exceeds the fixed threshold. Stationary distributions of the system states and the waiting time are computed. In the numerical example, we show some interesting effects and illustrate a possibility of application of the presented results for solution of optimization problems.</P>
Kim, Ji Soon,Dudina, Dina V,Kim, Jin Chun,Kwon, Young Soon,Park, Jin Ju,Rhee, Chang Kyu American Scientific Publishers 2010 Journal of Nanoscience and Nanotechnology Vol.10 No.1
<P>One of the possible reasons for low conductivity of in-situ produced dispersion strengthened copper matrix composites may be the incompleteness of the reaction between the initial reactants that remain in a state of solid solutions in the copper matrix. We report in-situ synthesis of TiB2-Cu composites starting from the powder mixtures with the limited content of copper ensuring a high probability of contact between the particles of titanium and boron and, as a result, their full conversion into the TiB2 phase. The nanoparticles were formed in a self-propagating mode in the ball milled Ti-B-Cu powder mixture corresponding to 57 vol.% TiB2-Cu composition. Afterwards, the system was 'diluted' with the required amount of the copper matrix using subsequent ball milling. Highly conductive 4.5 vol.% TiB2-Cu composites showing 82-87% IACS (International Annealed Copper Standard) conductivity were obtained by Spark Plasma Sintering (SPS) of the powders.</P>
TiB<sub>2</sub>-Cu Interpenetrating Phase Composites Produced by Spark-plasma Sintering
Kwon, Young-Soon,V. Dudina, Dina,I. Lomovsky, Oleg,A. Korchagin, Michail,Kim, Ji-Soon The Korean Powder Metallurgy Institute 2003 한국분말재료학회지 (KPMI) Vol.10 No.3
Interpenetrating phase composites of $TiB_2$-Cu system were produced via Spark-Plasma Sintering (SPS) oi nanocomposite powders. Under simultaneous action of pressure, temperature and electric current titanium diboride nanoparticles distributed in copper matrix move, agglomerate and form a fine-grained skeleton. Increasing SPS-temperature and he]ding time promote densification due to local melting of copper matrix When copper melting is avoided the compacts contain 17-20% porosity but titanium diboride skeleton is still formed representing the feature of SPS . High degree of densification and formation of titanium diboride network result in increased hardness of high-temperature SPS-compacts.
Queueing System Operating in Random Environment as a Model of a Cell Operation
Kim, Chesoong,Dudin, Alexander,Dudina, Olga,Kim, Jiseung Korean Institute of Industrial Engineers 2016 Industrial Engineeering & Management Systems Vol.15 No.2
We consider a multi-server queueing system without buffer and with two types of customers as a model of operation of a mobile network cell. Customers arrive at the system in the marked Markovian arrival flow. The service times of customers are exponentially distributed with parameters depending on the type of customer. A part of the available servers is reserved exclusively for service of first type customers. Customers who do not receive service upon arrival, can make repeated attempts. The system operation is influenced by random factors, leading to a change of the system parameters, including the total number of servers and the number of reserved servers. The behavior of the system is described by the multi-dimensional Markov chain. The generator of this Markov chain is constructed and the ergodicity condition is derived. Formulas for computation of the main performance measures of the system based on the stationary distribution of the Markov chain are derived. Numerical examples are presented.
Dudin, Sergey,Kim, Chesoong,Dudina, Olga,Baek, Janghyun Hindawi Limited 2013 Mathematical problems in engineering Vol.2013 No.-
<P>A multiserver queueing system with infinite and finite buffers, two types of customers, and two types of servers as a model of a call center with a call-back for lost customers is investigated. Type 1 customers arrive to the system according to a Markovian arrival process. All rejected type 1 customers become type 2 customers. Typer,r=1,2, servers serve typercustomers if there are any in the system and serve type<SUP>r′</SUP>,<SUP>r′</SUP>=1,2, <SUP>r′</SUP>≠r,customers if there are no type<I>r</I>customers in the system. The service times of different types of customers have an exponential distribution with different parameters. The steady-state distribution of the system is analyzed. Some key performance measures are calculated. The Laplace-Stieltjes transform of the sojourn time distribution of type 2 customers is derived. The problem of optimal choice of the number of each type servers is solved numerically.</P>
A tandem GI/PH/1→*/PH/1/0 queue with blocking
Klimenok, V.,Kim, C.,Dudina, O.,Dudin, A. Elsevier Science Ltd 2013 Applied mathematical modelling Vol.37 No.10
Tandem queues are widely used in mathematical modeling of random processes describing the operation of manufacturing systems, supply chains, computer and telecommunication networks. Although there exists a lot of publications on tandem queueing systems, analytical research on tandem queues with non-Markovian input is very limited. In this paper, the results of analytical investigation of two-node tandem queue with arbitrary distribution of inter-arrival times are presented. The first station of the tandem is represented by a single-server queue with infinite waiting room. After service at the first station, a customer proceeds to the second station that is described by a single-server queue without a buffer. Service times of a customer at the first and the second server have PH (Phase-type) distributions. A customer, who completes service at the first server and meets a busy second server, is forced to wait at the first server until the second server becomes available. During the waiting period, the first server becomes blocked, i.e., not available for service of customers. We calculate the joint stationary distribution of the system states at the embedded epochs and at arbitrary time. The Laplace-Stieltjes transform of the sojourn time distribution is derived. Key performance measures are calculated and numerical results presented.