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The size order of the state vector of a continuous-time homogeneous Markov system with fixed size

Part of: Operations research and management science

Published online by Cambridge University Press:  14 July 2016

I. Kipouridis  and
G. Tsaklidis
I. Kipouridis*
Affiliation:
Aristotle University of Thessaloniki
G. Tsaklidis*
Affiliation:
Aristotle University of Thessaloniki
*
∗ Postal address: Department of Mathematics, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece.
∗ Postal address: Department of Mathematics, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece.
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Abstract

The variation of the state vectors p(t) = (pi(t)) of a continuous-time homogeneous Markov system with fixed size is examined. A specific time t0 after which the size order of the elements pi(t) becomes stable provides a criterion of the system's convergence rate. A method is developed to find t0 and a quickly evaluated lower bound for t0. This method is based on the geometric characteristics and the volumes of the attainable structures. Moreover, a condition concerning the selection of starting vectors p(0) is given so that the vector functions p(t) retain the same size order for every time greater than a given time t.

Keywords

Stochastic population systemshomogeneous Markov systemscontinuous time

MSC classification

Primary: 90B70: Theory of organizations, manpower planning
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 635 - 646
Copyright
Copyright © by the Applied Probability Trust 2001 

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References

Bartholomew, D. J. (1982). Stochastic Models for Social Processes, 3rd edn. John Wiley, New York.Google Scholar
Bartholomew, D. J., Forbes, A. F., and McClean, S. I. (1991). Statistical Techniques for Manpower Planning, 2nd edn. John Wiley, Chichester.Google Scholar
Davies, G. S. (1978). Attainable and maintainable regions in Markov chain control. In Recent Theoretical Development Control, ed. Gregson, M. J. Academic Press, London, pp. 371–381.Google Scholar
Hasani, H. (1980). Markov renewal models for manpower systems. Doctoral Thesis, University of London.Google Scholar
Huang, C., Isaacson, D. L., and Vinograde, B. (1976). The rate of convergence of certain nonhomogeneous Markov chains. Z. Wahrscheinlichkeitsth. 35, 141–146.Google Scholar
Isaacson, D. L., and Madsen, R. W. (1976). Markov Chains: Theory and Applications. John Wiley, New York.Google Scholar
Kipouridis, I., and Tsaklidis, G. (2001). The size order of the state vector of discrete-time homogeneous Markov systems. J. Appl. Prob. 38, 357–368.CrossRefGoogle Scholar
McClean, S. I. (1976). The two stage model of personnel behaviour. J. R. Statist. Soc. A 139, 205–217.CrossRefGoogle Scholar
McClean, S. I. (1978). Continuous-time stochastic models of a multigrade population. J. Appl. Prob. 15, 26–32.Google Scholar
McClean, S. I. (1986). Semi-Markov models for manpower planning. In Semi-Markov Models: Theory and Applications, ed. Janssen, J. Plenum Press, New York.Google Scholar
Tsaklidis, G. (1994). The evolution of the attainable structures of a homogeneous Markov system with fixed size. J. Appl. Prob. 31, 348–361.CrossRefGoogle Scholar
Vassiliou, P.-C. G. (1982). Asymptotic behaviour of Markov systems. J. Appl. Prob. 19, 851–857.CrossRefGoogle Scholar
Vassiliou, P.-C. G. (1997). The evolution of the theory of non-homogeneous Markov systems. Appl. Stoch. Models Data Anal. 13, 159–176.Google Scholar
Vassiliou, P.-C. G., and Papadopoulou, A.A. (1992). Non-homogeneous semi-Markov systems and maintainability of the state sizes. J. Appl. Prob. 29, 519–534.Google Scholar
Vassiliou, P.-C. G., Georgiou, A. C., and Tsantas, N. (1990). Control of asymptotic variability in non-homogeneous Markov systems. J. Appl. Prob. 27, 756–766.Google Scholar