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    Wyświetlanie 1-3 z 3
    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
    Tytuł:
    Ergodicity and perturbation bounds for inhomogeneous birth and death processes with additional transitions from and to the origin
    Autorzy:
    Zeifman, A.
    Korotysheva, A.
    Satin, Y.
    Korolev, V.
    Shorgin, S.
    Razumchik, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/331214.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    inhomogeneous birth process
    inhomogeneous death process
    ergodicity bound
    perturbation bound
    Opis:
    Service life of many real-life systems cannot be considered infinite, and thus the systems will be eventually stopped or will break down. Some of them may be re-launched after possible maintenance under likely new initial conditions. In such systems, which are often modelled by birth and death processes, the assumption of stationarity may be too strong and performance characteristics obtained under this assumption may not make much sense. In such circumstances, time-dependent analysis is more meaningful. In this paper, transient analysis of one class of Markov processes defined on non-negative integers, specifically, inhomogeneous birth and death processes allowing special transitions from and to the origin, is carried out. Whenever the process is at the origin, transition can occur to any state, not necessarily a neighbouring one. Being in any other state, besides ordinary transitions to neighbouring states, a transition to the origin can occur. All possible transition intensities are assumed to be non-random functions of time and may depend (except for transition to the origin) on the process state. To the best of our knowledge, first ergodicity and perturbation bounds for this class of processes are obtained. Extensive numerical results are also provided.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2015, 25, 4; 787-802
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services
    Autorzy:
    Zeifman, A.
    Razumchik, R.
    Satin, Y.
    Kiseleva, K.
    Korotysheva, A.
    Korolev, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/330534.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    inhomogeneous birth process
    inhomogeneous death process
    weak ergodicity
    rate of convergence
    sharp bounds
    logarithmic norm
    forward Kolmogorov system
    proces narodzin
    proces śmierci
    stopień konwergencji
    norma logarytmiczna
    system Kołmogorowa
    Opis:
    In this paper we present a method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically, we consider an inhomogeneous M/M/S queueing system with possible state-dependent arrival and service intensities, and additionally possible batch arrivals and batch service. A unified approach based on a logarithmic norm of linear operators for obtaining sharp upper and lower bounds on the rate of convergence and corresponding sharp perturbation bounds is described. As a side effect, we show, by virtue of numerical examples, that the approach based on a logarithmic norm can also be used to approximate limiting characteristics (the idle probability and the mean number of customers in the system) of the systems considered with a given approximation error.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2018, 28, 1; 141-154
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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