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    Tytuł:
    M/M/n/m queueing systems with non-identical servers
    Autorzy:
    Ziółkowski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/121808.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
    Tematy:
    queueing theory
    queueing systems
    teoria kolejkowania
    system kolejkowania
    Opis:
    M/M/n/m queueing systems with identical servers are well known in queueing theory and its applications. The analysis of these systems is very simple thanks to the fact that the number of customers ɳ(t) in the system at arbitrary time instant t forms a Markov chain. The main purpose of this paper is to analyse the M/M/n/m system under assumption that its servers are different, i.e. they have different parameters of service time.
    Źródło:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2011, 16; 163-168
    2450-9302
    Pojawia się w:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Queueing systems with random volume customers and a sectorized unlimited memory buffer
    Autorzy:
    Tikhonenko, Oleg
    Ziółkowski, Marcin
    Kempa, Wojciech M.
    Powiązania:
    https://bibliotekanauki.pl/articles/2055163.pdf
    Data publikacji:
    2021
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    queueing system
    random volume customers
    sectorized memory buffer
    total volume vector
    Laplace transform
    Laplace–Stieltjes transform
    multivariate L’Hospital rule
    system kolejkowania
    wektor objętości
    transformata Laplace'a
    transformata Laplace'a-Stieltjesa
    Opis:
    In the present paper, we concentrate on basic concepts connected with the theory of queueing systems with random volume customers and a sectorized unlimited memory buffer. In such systems, the arriving customers are additionally characterized by a non-negative random volume vector. The vector’s indications can be understood as the sizes of portions of information of a different type that are located in the sectors of memory space of the system during customers’ sojourn in it. This information does not change while a customer is present in the system. After service termination, information immediately leaves the buffer, releasing its resources. In analyzed models, the service time of a customer is assumed to be dependent on his volume vector characteristics, which has influence on the total volume vector distribution. We investigate three types of such queueing systems: the Erlang queueing system, the single-server queueing system with unlimited queue and the egalitarian processor sharing system. For these models, we obtain a joint distribution function of the total volume vector in terms of Laplace (or Laplace-Stieltjes) transforms and formulae for steady-state initial mixed moments of the analyzed random vector, in the case when the memory buffer is composed of two sectors. We also calculate these characteristics for some practical case in which the service time of a customer is proportional to the customer’s length (understood as the sum of the volume vector’s indications). Moreover, we present some numerical computations illustrating theoretical results.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2021, 31, 3; 471--486
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Calculating steady-state probabilities of single-channel closed queueing systems using hyperexponential approximation
    Autorzy:
    Zhernovyi, Yuriy
    Kopytko, Bohdan
    Powiązania:
    https://bibliotekanauki.pl/articles/1839796.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    single-channel closed queueing system
    arbitrary distributions
    hyperexponential approximation
    system kolejkowania
    rozkład prawdopodobieństwa
    aproksymacja wykładnicza
    Opis:
    In this paper we propose a method for calculating steady-state probability distributions of the single-channel closed queueing systems with arbitrary distributions of customer generation times and service times. The approach based on the use of fictitious phases and hyperexponential approximations with parameters of the paradoxical and complex type by the method of moments. We defined conditions for the variation coefficients of the gamma distributions and Weibull distributions, for which the best accuracy of calculating the steady-state probabilities is achieved in comparison with the results of simulation modeling.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 113-120
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Calculating steady-state probabilities of single-channel closed queueing systems using hyperexponential approximation
    Autorzy:
    Zhernovyi, Yuriy
    Kopytko, Bohdan
    Powiązania:
    https://bibliotekanauki.pl/articles/122348.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    single-channel closed queueing system
    arbitrary distributions
    hyperexponential approximation
    system kolejkowania
    rozkład prawdopodobieństwa
    aproksymacja wykładnicza
    Opis:
    In this paper we propose a method for calculating steady-state probability distributions of the single-channel closed queueing systems with arbitrary distributions of customer generation times and service times. The approach based on the use of fictitious phases and hyperexponential approximations with parameters of the paradoxical and complex type by the method of moments. We defined conditions for the variation coefficients of the gamma distributions and Weibull distributions, for which the best accuracy of calculating the steady-state probabilities is achieved in comparison with the results of simulation modeling.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 113-120
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    M/G→ /n/0 Erlang queueing system with heterogeneous servers and non-homogeneous customers
    Autorzy:
    Ziółkowski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/199840.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    multi-server queueing systems
    queueing systems with non-homogeneous customers
    queueing systems with heterogeneous servers
    total volume distribution
    Laplace–Stieltjes transform
    system kolejkowania
    transformata Laplace'a-Stieltjesa
    dystrybucja
    Opis:
    In the present paper, we investigate a multi-server queueing system with heterogeneous servers, unlimited memory space, and non-homogeneous customers. The arriving customers appear according to a stationary Poisson process. Service time distribution functions may be different for every server. Customers are additionally characterized by some random volume. On every server, the service time of the customer depends on their volume. The number of customers distribution function is obtained in the classical model of the system. In the model with non-homogeneous customers, the stationary total volume distribution function is determined in the term of Laplace–Stieltjes transform. The stationary first and second moments of a total customers volume are calculated. An analysis of some special cases of the model and some numerical examples are also included.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 1; 59-66
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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