On the Distributions of the State Sizes of the Continuous Time Homogeneous Markov System with Finite State Capacities

Autor:	George Vasiliadis
Rok vydání:	2012
Předmět:	Statistics and Probability Combinatorics Distribution (mathematics) Markov kernel Markov chain General Mathematics Discrete phase-type distribution Interval (mathematics) Statistical physics State (functional analysis) Time point Transition rate matrix Mathematics
Zdroj:	Methodology and Computing in Applied Probability. 14:863-882
ISSN:	1573-7713 1387-5841
DOI:	10.1007/s11009-012-9284-9
Popis:	In the present paper we study the evolution of a continuous time homogeneous Markov system whose states have finite capacities. We assume that the members of the system who overflow, due to the finite state capacities, leave the system. In order to investigate the variability of the state sizes we provide the evaluation of the intensity matrix for any time point and then we derive a formula concerning the derivate of the moments of the state sizes. As a consequence the distributions of the state sizes can be evaluated. Moreover, an alternative method of calculating the distributions of the state sizes by means of the interval transition probabilities is given. Finally we examine the distribution of the time needed for the leavers to leave the system. The theoretical results are illustrated by a numerical example.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b6ef53f7c80b0fbd9e03109ada85c5ed https://doi.org/10.1007/s11009-012-9284-9 Zobrazit plný text záznamu Plný text ve formátu PDF