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    Tytuł:
    Analysis of an MMAP/PH1, PH2/N/∞ queueing system operating in a random environment
    Autorzy:
    Kim, C.
    Dudin, A.
    Dudin, S.
    Dudina, O.
    Powiązania:
    https://bibliotekanauki.pl/articles/330607.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    random environment
    marked Markovian arrival process
    phase type distribution
    Laplace–Stieltjes transform
    rozkład fazowy
    transformata Laplace'a-Stieltjesa
    system operacyjny
    system kolejkowy
    Opis:
    A multi-server queueing system with two types of customers and an infinite buffer operating in a random environment as a model of a contact center is investigated. The arrival flow of customers is described by a marked Markovian arrival process. Type 1 customers have a non-preemptive priority over type 2 customers and can leave the buffer due to a lack of service. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. The criterion of ergodicity for a multi-dimensional Markov chain describing the behavior of the system and the algorithm for computation of its steady-state distribution are outlined. Some key performance measures are calculated. The Laplace–Stieltjes transforms of the sojourn and waiting time distributions of priority and non-priority customers are derived. A numerical example illustrating the importance of taking into account the correlation in the arrival process is presented.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 3; 485-501
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    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
      Wyświetlanie 1-2 z 2

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