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The size order of the state vector of discrete-time homogeneous Markov systems

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 size order problem of the probability state vector elements of a homogeneous Markov system is examined. The time t0 is evaluated, after which the order of the state vector probabilities remains unchanged, and a formula to quickly find a lower bound for t0 is given. A formula for approximating the mode of the state sizes ni(t) as a function of the means Eni(t), and a relation to evaluate P(ni(t) = x+1) by means of certain terms which constitute P(ni(t) = x) are derived.

Keywords

stochastic population systemshomogeneous Markov systemsdiscrete time

MSC classification

Primary: 90B70: Theory of organizations, manpower planning
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 2 , June 2001 , pp. 357 - 368
Copyright
Copyright © 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
Gantmacher, F. R. (1977). The Theory of Matrices. Chelsea, New York.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
McClean, S. I. (1976). The two stage model of personnel behaviour. J. R. Statist. Soc. A. 139, 205–217.Google 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
Pollard, J. H. (1966). On the use of the direct matrix product in analysing certain stochastic population models. Biometrika 53, 397–415.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.Google Scholar
Vassiliou, P.-C. G. (1982). Asymptotic behaviour of Markov systems. J. Appl. Prob. 19, 851–857.Google Scholar
Vassiliou, P.-C. G. (1986). Asymptotic variability of non-homogeneous Markov systems under cyclic behaviour. Eur. J. Operat. Res. 27, 215–228.Google 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., Georgiou, A. C., and Tsantas, N. (1990). Control of asymptotic variability in non-homogeneous Markov systems. J. Appl. Prob. 27, 756–766.Google Scholar
Young, A. (1971). Demographic and ecological models in manpower planning. In Aspects of Manpower Planning, eds Bartholomew, D. G. and Morris, B. R. English Universities Press, London, pp. 75–97.Google Scholar