On certain aspects of non-homogeneous Markov systems in continuous time

Abstract

In the present paper we study three aspects in the theory of non-homogeneous Markov systems under the continuous-time formulation. Firstly, the relationship between stability and quasi-stationarity is investigated and conditions are provided for a quasi-stationary structure to be stable. Secondly, the concept of asymptotic attainability is studied and the possible regions of asymptotically attainable structures are determined. Finally, the cyclic case is considered, where it is shown that for a system in a periodic environment, the relative structure converges to a periodic vector, independently of the initial distribution. Two numerical examples illustrate the above theoretical results.

A procedure for distributing recruits in manpower systems

“…The aggregate-fractional flow balance equations are obtained by setting ( (8) It is important to mention here that when () t  xD in Eq. 8, then the model is akin to the system in [1].…”

On the dynamics of workforce-mix in a manpower system

“…Guerry [17], Kipouridis & Tsaklidis [22] and Vassiliou & Tsantas [40] analysed graded manpower systems using discrete-time Markov chains. The semi-Markov models [37,39] and the continuous-time Markov models [15,29] have also been used to describe graded manpower systems. More details on the use of Markov models for manpower planning may be found in [5,32].…”

Non-homogeneous Markov Processes for Biomedical Data Analysis

“…Some methods have been proposed by different authors to fit non-homogeneous Markov models in continuous time (Kalbfleisch and Lawless, 1985;Gerontidis, 1990;Billard and Zhao, 1994). In short, there are two methodologies that are commonly used in these types of process:…”

“…In 1990's some theoretic aspects as stability or quasi-stationarity were analysed (Gerontidis, 1990) and some studies about non-homogeneous Markov processes in a stochastic environment have been shown (Tsantas and Vassiliou, 1993). However, few methods have been proposed for estimating nonhomogeneous processes under incomplete observations (Frydman, 1992).…”