- 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