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    Tytuł:
    Optimization of the service strategy in a queueing system with energy harvesting and customers’ impatience
    Autorzy:
    Dudin, A.
    Lee, M. H.
    Dudin, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/331226.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    energy harvesting
    threshold strategy
    optimization
    Markovian arrival process
    uzyskiwanie energii
    optymalizacja
    Markowski proces zgłoszeń
    Opis:
    A single-server queueing system with an infinite buffer is considered. The service of a customer is possible only in the presence of at least one unit of energy, and during the service the number of available units decreases by one. New units of energy arrive in the system at random instants of time if the finite buffer for maintenance of energy is not full. Customers are impatient and leave the system without service after a random amount of waiting time. Such a queueing system describes, e.g., the operation of a sensor node which harvests energy necessary for information transmission from the environment. Aiming to minimize the loss of customers due to their impatience (and maximize the throughput of the system), a new strategy of control by providing service is proposed. This strategy suggests that service temporarily stops if the number of customers or units of energy in the system becomes zero. The server is switched off (is in sleep mode) for some time. This time finishes (the server wakes up) if both the number of customers in the buffer and the number of energy units reach some fixed threshold values or when the number of energy units reaches some threshold value and there are customers in the buffer. Arrival flows of customers and energy units are assumed to be described by an independent Markovian arrival process. The service time has a phase-type distribution. The system behavior is described by a multi-dimensional Markov chain. The generator of this Markov chain is derived. The ergodicity condition is presented. Expressions for key performance measures are given. Numerical results illustrating the dependence of a customer’s loss probability on the thresholds defining the discipline of waking up the server are provided. The importance of the account of correlation in arrival processes is numerically illustrated.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2016, 26, 2; 367-378
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A queueing system with heterogeneous impatient customers and consumable additional items
    Autorzy:
    Baek, J.
    Dudina, O.
    Kim, C.
    Powiązania:
    https://bibliotekanauki.pl/articles/907646.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    marked Markovian arrival process
    consumable additional items
    phase type distribution
    impatient customer
    Markowski proces zgłoszeń
    system kolejkowy
    rozkład fazowy
    klient niecierpliwy
    Opis:
    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.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 2; 367-384
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    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
    Tytuł:
    Transient and stationary characteristics of a packet buffer modelled as an MAP/SM/1/b system
    Autorzy:
    Rusek, K.
    Janowski, L.
    Papir, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/330560.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    router interface
    Markovian arrival process
    semi Markov service time
    hidden Markov model
    finite buffer queue
    packet loss
    first passage time
    proces Markowiana
    model Markowa niejawny
    utrata pakietu
    Opis:
    A packet buffer limited to a fixed number of packets (regardless of their lengths) is considered. The buffer is described as a finite FIFO queuing system fed by a Markovian Arrival Process (MAP) with service times forming a Semi-Markov (SM) process (MAP/SM/1/b in Kendall’s notation). Such assumptions allow us to obtain new analytical results for the queuing characteristics of the buffer. In the paper, the following are considered: the time to fill the buffer, the local loss intensity, the loss ratio, and the total number of losses in a given time interval. Predictions of the proposed model are much closer to the trace-driven simulation results compared with the prediction of the MAP/G/1/b model.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 2; 429-442
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On truncations for weakly ergodic inhomogeneous birth and death processes
    Autorzy:
    Zeifman, A.
    Satin, Y.
    Korolev, V.
    Shorgin, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/330983.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    birth process
    death process
    weak ergodicity
    truncation
    forward Kolmogorov system
    nonstationary Markovian queueing model
    proces narodzin
    proces śmierci
    obcinanie
    system Kołmogorowa
    model Markowa
    Opis:
    We investigate a class of exponentially weakly ergodic inhomogeneous birth and death processes. We consider special transformations of the reduced intensity matrix of the process and obtain uniform (in time) error bounds of truncations. Our approach also guarantees that we can find limiting characteristics approximately with an arbitrarily fixed error. As an example, we obtain the respective bounds of the truncation error for an Mt/Mt/S queue for any number of servers S. Arbitrary intensity functions instead of periodic ones can be considered in the same manner.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 3; 503-518
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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