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Stability in a non-homogeneous Markov chain model in manpower systems

Published online by Cambridge University Press:  14 July 2016

P.-C. G. Vassiliou
P.-C. G. Vassiliou*
Affiliation:
University of Ioannina
*
∗ Postal address: Department of Mathematics, University of Ioannina, Ioannina, Greece.
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Abstract

Necessary and sufficient conditions for stability, imposed firstly on the initial structure and the sequence of recruitment, and secondly on the initial structure and the sequence of expansion are provided in forms of two theorems. Also the limiting behaviour of the expected relative grade sizes is studied if we drop the conditions for stability imposed on the initial structure and keep the same sequence of expansion. Finally we examine the limiting behaviour of the expected grade sizes if we drop the assumption of a continuously expanding system.

Keywords

MANPOWER PLANNINGSTOCHASTIC POPULATION MODELSASYMPTOTIC BEHAVIOUR

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 924 - 930
Copyright
Copyright © Applied Probability Trust 1981 

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Footnotes

Part of this work was done while the author was at Imperial College, London.

References

Bartholomew, D. J. (1971) The statistical approach to manpower planning. Statistician 20, 3–26.Google Scholar
Bartholomew, D. J. (1973) Stochastic Models for Social Processes , 2nd edn. Wiley, New York.Google Scholar
Feichtinger, G. (1976) On the generalization of stable age distributions to Gani-type person flow models. Adv. App. Prob. 8, 433–145.Google Scholar
Feichtinger, G. and Mehlmann, A. (1976) The recruitment trajectory corresponding to particular stock sequences in Markovian person flow models. Math. Operat. Res. 1, 175–184.Google Scholar
Gantmacher, F. R. (1959) The Theory of Matrices. Chelsea, New York.Google Scholar
Isaacson, L. D. and Madsen, W. R. (1976) Markov Chains. Wiley, New York.Google Scholar
Seneta, E. (1973) Non-negative Matrices. Allen and Unwin, London.Google Scholar
Vassiliou, P-C. G. and Vassiliou, P. F. (1979) On the limiting structure of an expanding Markovian system with given size. Rev. Roum. Math. Pures Appl. 24, 1129–1136.Google Scholar
Young, A. and Vassiliou, P-C. G. (1974) A non-linear model on the promotion of staff. J. R. Statist. Soc. A 137, 584–595.Google Scholar