- 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