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    Wyświetlanie 1-5 z 5
    Tytuł:
    Markov chain model of phytoplankton dynamics
    Autorzy:
    Wieczorek, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/908138.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    dynamika fitoplanktonu
    koagulacja
    fragmentacja
    łańcuch Markowa
    phytoplankton dynamics
    coagulation
    fragmentation
    Markov chains
    Opis:
    A discrete-time stochastic spatial model of plankton dynamics is given. We focus on aggregative behaviour of plankton cells. Our aim is to show the convergence of a microscopic, stochastic model to a macroscopic one, given by an evolution equation. Some numerical simulations are also presented.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2010, 20, 4; 763-771
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Computing the Stackelberg/Nash equilibria using the extraproximal method: Convergence analysis and implementation details for Markov chains games
    Autorzy:
    Trejo, K. K.
    Clempner, J. B.
    Poznyak, A. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/329722.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    extraproximal method
    Stackelberg games
    convergence analysis
    Markov chains
    implementation
    gry Stackelberga
    analiza zbieżności
    łańcuchy Markowa
    Opis:
    In this paper we present the extraproximal method for computing the Stackelberg/Nash equilibria in a class of ergodic controlled finite Markov chains games. We exemplify the original game formulation in terms of coupled nonlinear programming problems implementing the Lagrange principle. In addition, Tikhonov's regularization method is employed to ensure the convergence of the cost-functions to a Stackelberg/Nash equilibrium point. Then, we transform the problem into a system of equations in the proximal format. We present a two-step iterated procedure for solving the extraproximal method: (a) the first step (the extra-proximal step) consists of a “prediction” which calculates the preliminary position approximation to the equilibrium point, and (b) the second step is designed to find a “basic adjustment” of the previous prediction. The procedure is called the “extraproximal method” because of the use of an extrapolation. Each equation in this system is an optimization problem for which the necessary and efficient condition for a minimum is solved using a quadratic programming method. This solution approach provides a drastically quicker rate of convergence to the equilibrium point. We present the analysis of the convergence as well the rate of convergence of the method, which is one of the main results of this paper. Additionally, the extraproximal method is developed in terms of Markov chains for Stackelberg games. Our goal is to analyze completely a three-player Stackelberg game consisting of a leader and two followers. We provide all the details needed to implement the extraproximal method in an efficient and numerically stable way. For instance, a numerical technique is presented for computing the first step parameter (λ) of the extraproximal method. The usefulness of the approach is successfully demonstrated by a numerical example related to a pricing oligopoly model for airlines companies.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2015, 25, 2; 337-351
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Influence of preconditioning and blocking on accuracy in solving Markovian models
    Autorzy:
    Bylina, B.
    Bylina, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/907654.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    kondycjonowanie
    równanie liniowe
    metoda blokowania
    łańcuch Markowa
    rozkład WZ
    preconditioning
    linear equations
    blocking methods
    Markov chains
    WZ factorization
    Opis:
    The article considers the effectiveness of various methods used to solve systems of linear equations (which emerge while modeling computer networks and systems with Markov chains) and the practical influence of the methods applied on accuracy. The paper considers some hybrids of both direct and iterative methods. Two varieties of the Gauss elimination will be considered as an example of direct methods: the LU factorization method and the WZ factorization method. The Gauss-Seidel iterative method will be discussed. The paper also shows preconditioning (with the use of incomplete Gauss elimination) and dividing the matrix into blocks where blocks are solved applying direct methods. The motivation for such hybrids is a very high condition number (which is bad) for coefficient matrices occuring in Markov chains and, thus, slow convergence of traditional iterative methods. Also, the blocking, preconditioning and merging of both are analysed. The paper presents the impact of linked methods on both the time and accuracy of finding vector probability. The results of an experiment are given for two groups of matrices: those derived from some very abstract Markovian models, and those from a general 2D Markov chain.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2009, 19, 2; 207-217
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Computing a mechanism for a Bayesian and partially observable Markov approach
    Autorzy:
    Clempner, Julio B.
    Poznyak, Alexander S.
    Powiązania:
    https://bibliotekanauki.pl/articles/24200692.pdf
    Data publikacji:
    2023
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    dynamic mechanism design
    partially observable Markov chains
    games with private information
    Bayesian equilibrium
    mechanizm dynamiczny
    łańcuchy Markova
    równowaga Bayesa
    Opis:
    The design of incentive-compatible mechanisms for a certain class of finite Bayesian partially observable Markov games is proposed using a dynamic framework. We set forth a formal method that maintains the incomplete knowledge of both the Bayesian model and the Markov system’s states. We suggest a methodology that uses Tikhonov’s regularization technique to compute a Bayesian Nash equilibrium and the accompanying game mechanism. Our framework centers on a penalty function approach, which guarantees strong convexity of the regularized reward function and the existence of a singular solution involving equality and inequality constraints in the game. We demonstrate that the approach leads to a resolution with the smallest weighted norm. The resulting individually rational and ex post periodic incentive compatible system satisfies this requirement. We arrive at the analytical equations needed to compute the game’s mechanism and equilibrium. Finally, using a supply chain network for a profit maximization problem, we demonstrate the viability of the proposed mechanism design.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2023, 33, 3; 463--478
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On three methods for bounding the rate of convergence for some continuous-time Markov chains
    Autorzy:
    Zeifman, Alexander
    Satin, Yacov
    Kryukova, Anastasia
    Razumchik, Rostislav
    Kiseleva, Ksenia
    Shilova, Galina
    Powiązania:
    https://bibliotekanauki.pl/articles/329966.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    inhomogeneous continuous time Markov chains
    weak ergodicity
    Lyapunov function
    differential inequalities
    forward Kolmogorov system
    łańcuchy Markowa z czasem ciągłym
    funkcja Lapunowa
    nierówność różniczkowa
    system Kołmogorowa
    Opis:
    Consideration is given to three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is particularly well suited to describe evolutions of the total number of customers in (in)homogeneous M/M/S queueing systems with possibly state-dependent arrival and service intensities, batch arrivals and services. One of the methods is based on the logarithmic norm of a linear operator function; the other two rely on Lyapunov functions and differential inequalities, respectively. Less restrictive conditions (compared with those known from the literature) under which the methods are applicable are being formulated. Two numerical examples are given. It is also shown that, for homogeneous birth-death Markov processes defined on a finite state space with all transition rates being positive, all methods yield the same sharp upper bound.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2020, 30, 2; 251-266
    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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