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Methodology and Computing in Applied Probability

, Volume 14, Issue 3, pp 863–882 | Cite as

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

  • George Vasiliadis
Article

Abstract

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.

Keywords

Stochastic population systems Continuous time homogeneous Markov models Markov systems 

AMS 2000 Subject Classification

Primary 90B70 62E99; Secondary 91D35 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsAristotle University of ThessalonikiThessalonikiGreece

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