- 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