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    Wyświetlanie 1-11 z 11
    Tytuł:
    Application of a z-transforms method for investigation of Markov G-networks
    Autorzy:
    Matalytski, M.
    Naumenko, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/122773.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    open G-network
    positive and negative messages
    expected incomes
    z-transforms method
    dochody oczekiwane
    Opis:
    The purpose of this research paper is to find the expected incomes in open Markov queueing networks with incomes, positive and negative messages at any time by the multidimensional transformations. Investigations were carried out in cases when incomes from the network transitions between the states are deterministic functions not dependent on network states and time. It is assumed that all network systems are one-line. It was proved the theorem on the expression for the multidimensional z-transform. An algorithm was proposed for calculation of expected incomes. It is calculated an example on the PC.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 1; 61-73
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Finding the expected revenues in Markov networks with positive and negative customers at a stationary regime
    Autorzy:
    Matalytski, M.
    Kopats, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/122624.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    G-network
    positive and negative customers
    signals
    expected revenues
    stationary regime
    sieć G
    pozytywny klient
    negatywny klient
    system kolejkowy
    Opis:
    Finding the expected revenues in the queueing systems (QS) of open Markov G-networks of two types, with positive and negative customers and with positive customers and signals, has been described in the paper. A negative customer arriving to the system destroys one positive customer if at least one is available in the system, thus reducing the number of positive customers in the system by one. The signal, coming into an empty system (where there are no positive customers), does not have any impact on the network and immediately disappears from it. Otherwise, if the system is not empty, when it receives a signal, the following events can occur: the incoming signal instantly moves the positive customer from one QS into another with a certain probability, or with the other probability, the signal is triggered as a negative customer.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 1; 49-60
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Finding the probabilistically-temporal characteristics of Markov G-network with batch removal of positive customers
    Autorzy:
    Matalytski, M.
    Naumenko, V.
    Kopats, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/122998.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    G-network
    positive and negative customers
    customers batch removal
    nonstationary regime
    generation function
    state probabilities
    teoria kolejek
    systemy kolejkowe
    pozytywny klient
    Opis:
    The investigation of a Markov queueing network with positive and negative customers and positive customers batch removal has been carried out in the article. The purpose of the research is analysis of such a network at the non-stationary regime, finding the time-dependent state probabilities and mean number of customers. In the first part of this article, a description of the G-network operation is provided with one-line queueing systems. When a negative customer arrives to the system, the count of positive customers is reduced by a random value, which is set by some probability distribution. Then for the non-stationary state probabilities a Kolmogorov system was derived of differencedifferential equations. A technique for finding the state probabilities and the mean number of customers of the investigated network, based on the use of an apparatus of multidimensional generating functions has been proposed. The theorem about the expression for the generating function has been given. A model example has been calculated.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 4; 125-136
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    About one method of finding expected incomes in HM-queueing network with positive customers and signals
    Autorzy:
    Matalytski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/122974.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    HM-queueing network
    positive and negative customers
    signals
    expected incomes
    ransient regime
    kolejkownie sieci
    systemy kolejkowe
    pozytywny klient
    negatywny klient
    teoria kolejek
    Opis:
    In the paper an open Markov HM(Howard-Matalytski)-Queueing Network (QN) with incomes, positive customers and signals (G(Gelenbe)-QN with signals) is investigated. The case is researched, when incomes from the transitions between the states of the network are random variables (RV) with given mean values. In the main part of the paper a description is given of G-network with signals and incomes, all kinds of transition probabilities and incomes from the transitions between the states of the network. The method of finding expected incomes of the researched network was proposed, which is based on using of found approximate and exact expressions for the mean values of random incomes. The variances of incomes of queueing systems (QS) was also found. A calculation example, which illustrates the differences of expected incomes of HM-networks with negative customers and QN without them and also with signals, has been given. The practical significance of these results consist of that they can be used at forecasting incomes in computer systems and networks (CSN) taking into account virus penetration into it and also at load control in such networks.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 1; 87-98
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of the queueing network with a random bounded waiting time of positive and negative customers at a non-stationary regime
    Autorzy:
    Matalytski, M.
    Naumenko, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/122455.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    G-network
    positive and negative customers
    random bounded waiting time of customers
    non-stationary regime
    generation function
    non-stationary state probabilities
    expected revenues
    sieć G
    pozytywny klient
    negatywny klient
    teoria kolejek
    czas oczekiwania
    Opis:
    In the first part of the article, an investigation of an open Markov queueing network with positive and negative customers (G-networks) has been carried out. The network receives two exponential arrivals of positive and negative customers. Negative customers do not receive service. The waiting time of customers of both types in each system is bounded by a random variable having an exponential distribution with different parameters. When the waiting time of a negative customer in the queue is over it reduces the number of positive customers per unit if the system has positive customers. The Kolmogorov system of difference-differential equations for non-stationary state probabilities has been derived. The method for finding state probabilities of an investigated network, based on the use of apparatus of multidimensional generating functions has been proposed. Expressions for finding the mean number of positive and negative customers in the network systems have also been found. In the second part the same network has been investigated, but with revenues. The case when revenues from the network transitions between states are random variables with given mean values has been considered. A method for finding expected revenues of the network systems has been proposed. Obtained results may be used for modeling of computer viruses in information systems and networks and also for forecasting of costs, considering the viruses penetration.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 1; 97-108
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Investigation of G-networks with restart at a non-stationary mode and their application
    Autorzy:
    Matalytski, Mikhail
    Naumenko, Victor
    Kopats, Dmitry
    Powiązania:
    https://bibliotekanauki.pl/articles/122538.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    queueing network
    G-network
    positive and negative customers
    non-stationary regime
    multiple type customers
    signals
    restart
    nonstationary state probabilities
    successive approximation method
    sieć kolejkowa
    sieć G
    sygnały
    metoda aproksymacji
    aproksymacja
    teoria kolejek
    pozytywny klient
    negatywny klient
    Opis:
    This article discusses the question of restarting the script, when restart is used by many users of the information network, which can be modelled as a G-network. Negative claims simulate the crash of the script and the re-sending of the request. Investigation of an open queuing network (QN) with several types of positive customers with the phase type of distribution of their service time and one type of negative customers have been carried out. Negative customers are signals whose effect is to restart one customers in a queue. A technique is proposed for finding the probability of states. It is based on the use of a modified method of successive approximations, combined with the method of a series. The successive approximations converge with time to a stationary distribution of state probabilities, the form of which is indicated in the article, and the sequence of approximations converges to the solution of the difference-differential equations (DDE) system. The uniqueness of this solution is proved. Any successive approximation is representable in the form of a convergent power series with an infinite radius of convergence, the coefficients of which satisfy recurrence relations, which is convenient for computer calculations. A model example illustrating the finding of time-dependent probabilities of network states using the proposed technique is also presented.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 41-51
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of HM-network with positive and negative claims for finding of memory volumes in information systems
    Autorzy:
    Matalytski, Mikhail
    Zając, Paweł
    Powiązania:
    https://bibliotekanauki.pl/articles/122992.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    HM-networks
    information systems
    volume of claim
    positive claims
    negative claims
    sieci HM
    systemy informacyjne
    roszczenie pozytywne
    roszczenie negatywne
    Opis:
    To solve the problem of determining the volume of memory of information systems (IS), it was suggested to use a stochastic model based on the use of HM (Howard-Matalytski) - a queueing network with revenues. This model allows you to take into account the dependencies of the processing times of messages (claims) on their volumes, the possibility of changing the volume of messages over time, and also the possibility of getting computer viruses into it. In such cases the processing of messages in nodes can be interrupted for some random time. Expressions are obtained for the mean (expected) values of the total message volumes in the IS nodes.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 1; 41-51
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of HM-networks with positive and negative heterogeneous requests for finding memory volume in information systems
    Autorzy:
    Matalytski, Mikhail
    Zajac, Pawel
    Kopats, Dmitry
    Powiązania:
    https://bibliotekanauki.pl/articles/1839809.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    HM-network
    information systems
    volumes of requests
    positive heterogeneous request
    negative heterogeneous request
    sieć HM
    sieć kolejkowa
    system informacyjny
    pojemność pamięci
    Opis:
    To determine the memory volume of information systems (IS), it was proposed to use a stochastic model, based on the use of a queueing network with bypasses, known as an HM-network. This model includes the servicing of heterogeneous requests along with their volumes, the ability to change the volume of such requests with their passage of time and the possibility of finding computer viruses in them, and therefore servicing requests can be interrupted at some random time. The expressions were obtained for the expected total values of the volume of requests in IS nodes.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 67-77
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of HM-networks with positive and negative heterogeneous requests for finding memory volume in information systems
    Autorzy:
    Matalytski, Mikhail
    Zajac, Pawel
    Kopats, Dmitry
    Powiązania:
    https://bibliotekanauki.pl/articles/122732.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    HM-network
    information systems
    volumes of requests
    positive heterogeneous request
    negative heterogeneous request
    sieć HM
    sieć kolejkowa
    system informacyjny
    pojemność pamięci
    Opis:
    To determine the memory volume of information systems (IS), it was proposed to use a stochastic model, based on the use of a queueing network with bypasses, known as an HM-network. This model includes the servicing of heterogeneous requests along with their volumes, the ability to change the volume of such requests with their passage of time and the possibility of finding computer viruses in them, and therefore servicing requests can be interrupted at some random time. The expressions were obtained for the expected total values of the volume of requests in IS nodes.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 67-77
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Asymptotic analysis of a closed G-network of unreliable nodes
    Autorzy:
    Rusilko, Tatiana
    Powiązania:
    https://bibliotekanauki.pl/articles/2175521.pdf
    Data publikacji:
    2022
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    G-network
    unreliable queueing systems
    positive customer
    negative customer
    birth-death process
    asymptotic analysis
    queueing network
    sieć G
    proces narodzin i śmierci
    analiza asymptotyczna
    sieci kolejkowe
    Opis:
    A closed exponential queueing G-network of unreliable multi-server nodes was studied under the asymptotic assumption of a large number of customers. The process of changing the number of functional servers in network nodes was considered as the birth-death process. The process of changing the number of customers at the nodes was considered as a continuous-state Markov process. It was proved that its probability density function satisfies the Fokker-Planck-Kolmogorov equation. The system of differential equations for the first-order and second-order moments of this process was derived. This allows us to predict the expectation, the variance and the pairwise correlation of the number of customers in the G-network nodes both in the transient and steady state.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 2; 91--102
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of the queueing network with a random waiting time of negative customers at a non-stationary regime
    Autorzy:
    Naumenko, V.
    Matalytski, M.
    Kopats, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/122923.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    G-network
    positive customers
    negative customers
    random waiting time
    heavy-traffic regime
    state probabilities
    mean characteristics
    non-stationary regime
    sieci kolejkowe
    sieć G
    pozytywny klient
    negatywny klient
    czas oczekiwania
    równania różniczkowe
    Opis:
    In the article a queueing network (QN) with positive customers and a random waiting time of negative customers has been investigated. Negative customers destroy positive customers on the expiration of a random time. Queueing systems (QS) operate under a heavy-traffic regime. The system of difference-differential equations (DDE) for state probabilities of such a network was obtained. The technique of solving this system and finding mean characteristics of the network, which is based on the use of multivariate generating functions was proposed.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 3; 111-122
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-11 z 11

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