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    Wyświetlanie 1-6 z 6
    Tytuł:
    Single–server queueing system with limited queue, random volume customers and unlimited sectorized memory buffer
    Autorzy:
    Ziółkowski, Marcin
    Tikhonenko, Oleg
    Powiązania:
    https://bibliotekanauki.pl/articles/2173725.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    single-server queueing system
    queueing systems with random volume customers
    sectorized memory buffer
    total volume vector
    Laplace-Stieltjes transform
    system kolejkowy z jednym serwerem
    system kolejkowy z losowymi klientami
    bufor pamięci sektorowany
    wektor objętości całkowity
    transformata Laplace'a-Stieltjesa
    Opis:
    In the present paper, we analyze the model of a single–server queueing system with limited number of waiting positions, random volume customers and unlimited sectorized memory buffer. In such a system, the arriving customer is additionally characterized by a non– negative random volume vector whose indications usually represent the portions of unchanged information of a different type that are located in sectors of unlimited memory space dedicated for them during customer presence in the system. When the server ends the service of a customer, information immediately leaves the buffer, releasing resources of the proper sectors. We assume that in the investigated model, the service time of a customer is dependent on his volume vector characteristics. For such defined model, we obtain a general formula for steady–state joint distribution function of the total volume vector in terms of Laplace-Stieltjes transforms. We also present practical results for some special cases of the model together with formulae for steady–state initial moments of the analyzed random vector, in cases where the memory buffer is composed of at most two sectors. Some numerical computations illustrating obtained theoretical results are attached as well.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2022, 70, 6; art. no. e143647
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    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:
    Performance evaluation of unreliable system with infinite number of servers
    Autorzy:
    Tikhonenko, O.
    Ziółkowski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/201519.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    queueing systems with non-homogeneous customers
    unreliable queueing systems
    total volume
    loss probability
    Laplace–Stieltjes transform
    Opis:
    In the paper, we investigate queueing system M/G/∞ with non-homogeneous customers. By non-homogeneity we mean that each customer is characterized by some arbitrarily distributed random volume. The arriving customers appear according to a stationary Poisson process. Service time of a customer is proportional to his its volume. The system is unreliable, which means that all its servers can break simultaneously and then the repair period goes on for random time having an arbitrary distribution. During this period, customers present in the system and arriving to it are not served. Their service continues immediately after repair period termination. Time intervals of the system in good repair mode have an exponential distribution. For such system, we determine steady-state sojourn time and total volume of customers present in it distributions. We also estimate the loss probability for the similar system with limited total volume. An analysis of some special cases and some numerical examples are attached as well.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 2; 289-297
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    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
    Tytuł:
    Single-server queueing system with external and internal customers
    Autorzy:
    Tikhonenko, O.
    Ziółkowski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/199838.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    single-server queueing system with non-homogeneous customers
    random volume customers
    loss probability
    total volume distribution
    Laplace transform
    Laplace-Stieltjes transform
    RAM memory space
    prawdopodobieństwo straty
    transformacja Laplace'a
    transformata Laplace'a-Stieltjesa
    pamięć RAM
    Opis:
    In the paper, we investigate a single-server queueing system with unlimited memory space and non-homogeneous customers (calls) of the two following types: 1) external customers that are served by the system under consideration, 2) internal customers that arrive and interrupt the service process only when an external customer is being served. The external customers appear according to a stationary Poisson process. Customers of each of the above-mentioned types are characterized by some random volume. The customer service time depends arbitrarily on its volume. Two schemes of customer service organization are analyzed. The non-stationary and stationary distributions of the total volume of customers present in the system are determined in terms of Laplace and Laplace-Stieltjes transforms. The stationary first and second moments of total customers volume are also calculated. The obtained results are used to approximate loss characteristics in analogous systems with limited buffer space. Numerical examples illustrating theoretical results are attached as well.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 539-551
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
      Wyświetlanie 1-6 z 6

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