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    Wyświetlanie 1-9 z 9
    Tytuł:
    Simulating an infinite mean waiting time
    Autorzy:
    Bartoszek, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/953256.pdf
    Data publikacji:
    2019
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    birth-death process
    infinite mean
    phylogenetic tree
    power-law distribution
    return time
    drzewo logenetyczne
    Opis:
    W pracy rozważany jest mieszany sposób symulowania czasu powrotu do stanu początkowego określonego krytycznego procesu narodzin i śmierci. Ten czas powrotu ma nieskończoną wartość oczekiwaną przy czym jego asymptotyczny rozkład jest potęgowy. Zatem dopóki symulowany czas nie przekroczy pewnej granicznej wartości proces jest symulowany bezpośrednio. W chwili przekroczenia tej wartości granicznej czas powrotu jest losowany z ogona tego rozkładu potęgowego.
    We consider a hybrid method to simulate the return time to the initial state in a critical-case birth-death process. The expected value of this return time is infinite, but its distribution asymptotically follows a power-law. Hence, the simulation approach is to directly simulate the process, unless the simulated time exceeds some threshold and if it does, draw the return time from the tail of the power law.
    Źródło:
    Mathematica Applicanda; 2019, 47, 1
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Diffusion approximation of the network with limited number of same type customers and time dependent service parameters
    Autorzy:
    Matalytski, M.
    Kopats, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/122463.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    queueing network
    birth and death process
    asymptotic analysis
    sieci kolejkowe
    analiza asymptotyczna
    proces losowy
    Opis:
    The article presents research of an open queueing network (QN) with the same types of customers, in which the total number of customers is limited. Service parameters are dependent on time, and the route of customers is determined by an arbitrary stochastic transition probability matrix, which is also dependent on time. Service times of customers in each line of the system is exponentially distributed. Customers are selected on the service according to FIFO discipline. It is assumed that the number of customers in one of the systems is determined by the process of birth and death. It generates and destroys customers with certain service times of rates. The network state is described by the random vector, which is a Markov random process. The purpose of the research is an asymptotic analysis of its process with a big number of customers, obtaining a system of differential equations (DE) to find the mean relative number of customers in the network systems at any time. A specific model example was calculated using the computer. The results can be used for modelling processes of customer service in the insurance companies, banks, logistics companies and other organizations.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 2; 77-84
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A continuum individual based model of fragmentation: dynamics of correlation functions
    Autorzy:
    Tanaś, Agnieszka
    Powiązania:
    https://bibliotekanauki.pl/articles/747252.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Configuration space
    individual-based model
    birth-and-death process
    correlation function
    scale of Banach spaces
    Ovcyannikov method.
    Opis:
    An individual-based model of an infinite system of point particles in Rd is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for this model is the set Γ of all locally finite subsets of Rd. The system's states are probability measures on  Γ the Markov evolution of which is described in terms of their  correlation functions in a scale of Banach spaces. The existence and uniqueness of solutions of the corresponding evolution equation are proved.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2015, 69, 2
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Asymptotic analysis of a closed G-network of unreliable nodes
    Autorzy:
    Rusilko, Tatiana
    Powiązania:
    https://bibliotekanauki.pl/articles/2175521.pdf
    Data publikacji:
    2022
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    G-network
    unreliable queueing systems
    positive customer
    negative customer
    birth-death process
    asymptotic analysis
    queueing network
    sieć G
    proces narodzin i śmierci
    analiza asymptotyczna
    sieci kolejkowe
    Opis:
    A closed exponential queueing G-network of unreliable multi-server nodes was studied under the asymptotic assumption of a large number of customers. The process of changing the number of functional servers in network nodes was considered as the birth-death process. The process of changing the number of customers at the nodes was considered as a continuous-state Markov process. It was proved that its probability density function satisfies the Fokker-Planck-Kolmogorov equation. The system of differential equations for the first-order and second-order moments of this process was derived. This allows us to predict the expectation, the variance and the pairwise correlation of the number of customers in the G-network nodes both in the transient and steady state.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 2; 91--102
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A multi-source fluid queue based stochastic model of the probabilistic offloading strategy in a MEC system with multiple mobile devices and a single MEC server
    Autorzy:
    Zheng, Huan
    Jin, Shunfu
    Powiązania:
    https://bibliotekanauki.pl/articles/2055156.pdf
    Data publikacji:
    2022
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    mobile edge computing
    probabilistic offloading strategy
    multi-source fluid queue
    birth and death process
    cumulative distribution function
    przetwarzanie mobilne
    proces narodzin i śmierci
    dystrybuanta
    Opis:
    Mobile edge computing (MEC) is one of the key technologies to achieve high bandwidth, low latency and reliable service in fifth generation (5G) networks. In order to better evaluate the performance of the probabilistic offloading strategy in a MEC system, we give a modeling method to capture the stochastic behavior of tasks based on a multi-source fluid queue. Considering multiple mobile devices (MDs) in a MEC system, we build a multi-source fluid queue to model the tasks offloaded to the MEC server. We give an approach to analyze the fluid queue driven by multiple independent heterogeneous finite-state birth-and-death processes (BDPs) and present the cumulative distribution function (CDF) of the edge buffer content. Then, we evaluate the performance measures in terms of the utilization of the MEC server, the expected edge buffer content and the average response time of a task. Finally, we provide numerical results with some analysis to illustrate the feasibility of the stochastic model built in this paper.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2022, 32, 1; 125--138
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Formulas for average transition times between states of the Markov birth-death process
    Autorzy:
    Zhernovyi, Yuriy
    Kopytko, Bohdan
    Powiązania:
    https://bibliotekanauki.pl/articles/2175497.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    birth-death process
    Markov models
    mean transition time
    mean time spent in the group of states
    queueing systems
    reliability model
    proces narodzin i śmierci
    modele Markova
    średni czas przejścia
    średni czas spędzony w grupie stanów
    systemy kolejkowe
    model niezawodności
    Opis:
    In this paper, we consider Markov birth-death processes with constant intensities of transitions between neighboring states that have an ergodic property. Using the exponential distributions properties, we obtain formulas for the mean time of transition from the state i to the state j and transitions back, from the state j to the state i. We found expressions for the mean time spent outside the given state i, the mean time spent in the group of states (0,...,i-1) to the left from state i, and the mean time spent in the group of states (i+1,i+2,...) to the right. We derive the formulas for some special cases of the Markov birth-death processes, namely, for the Erlang loss system, the queueing systems with finite and with infinite waiting room and the reliability model for a recoverable system.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 4; 99--110
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    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:
    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:
    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 1-9 z 9

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