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Control of asymptotic variability in non-homogeneous Markov systems

Published online by Cambridge University Press:  14 July 2016

P.-C. G. Vassiliou ,
A. C. Georgiou  and
N. Tsantas
P.-C. G. Vassiliou
Affiliation:
University of Thessaloniki
A. C. Georgiou
Affiliation:
University of Thessaloniki
N. Tsantas*
Affiliation:
University of Thessaloniki
*
∗ Postal address for all authors: Statistics and Operations Research Section, Mathematics Department, University of Thessaloniki, Thessaloniki, Greece.
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Abstract

In this paper we provide two basic results. First, we find the set of all the limiting vectors of expectations, variances and covariances in an NHMS which are possible provided that we control the limit vector of the sequence of vectors of input probabilities. Secondly, under certain conditions easily met in practice we find the distribution of the limiting vector of expectations, variances and covariances to be multinomial with probabilities the corresponding limiting expected populations in the various states of the NHMS.

Keywords

MANPOWER MODELSCONTROL BY RECRUITMENT
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 4 , December 1990 , pp. 756 - 766
Copyright
Copyright © Applied Probability Trust 1990 

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References

Bartholomew, D. J. (1973) Stochastic Models for Social Processes, 2nd edn. Wiley, Chichester.Google Scholar
Bartholomew, D. J. (1982) Stochastic Models for Social Processes, 3nd edn. Wiley, Chichester.Google Scholar
Gantmacher, R. F. (1959) Applications of the Theory of Matrices. Interscience, London.Google Scholar
Huang, C.-C, Isaacson, D. and Vinograde, B. (1976) The rate of convergence of certain nonhomogeneous Markov chains. Z. Wahrscheinlichkeitsth. 35, 141–146.CrossRefGoogle Scholar
Iosifescu, M. (1980) Finite Markov Processes and their Applications. Wiley, Chichester.Google Scholar
Leslie, P. H. (1945) On the use of matrices in certain population mathematics. Biometrika 33, 183–212.Google Scholar
Leslie, P. H. (1948) Some further notes on the use of matrices in population mathematics. Biometrika 35, 213–245.Google Scholar
Mehlmann, A. (1977) A note on the limiting behaviour of discrete-time Markovian manpower models with inhomogeneous independent Poisson input. J. Appl. Prob. 14, 611–613.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
Pollard, J. H. (1967) A note on certain discrete-time stochastic population models with Poisson immigration. J. Appl. Prob. 4, 209–213.Google Scholar
Pollard, J. H. (1973) Mathematical Models for the Growth of Human Populations. Cambridge University Press.Google Scholar
Prais, S. J. (1955) Measuring social mobility. J. R. Statist. Soc. A118, 56–66.Google Scholar
Tsaklidis, G. and Vassiliou, P.-C. G. (1988) Asymptotic periodicity of the variances and covariances of the state sizes in non-homogeneous Markov systems. J. Appl. Prob. 25, 21–33.Google Scholar
Vassiliou, P.-C. G. (1982) On the limiting behaviour of a non-homogeneous Markovian manpower model with independent Poisson input. J. Appl. Prob. 19, 433–438.CrossRefGoogle Scholar
Vassiliou, P.-C. G. (1986) Asymptotic variability of nonhomogeneous Markov systems under cyclic behaviour. Eur. J. Operat. Res. 27, 215–228.Google Scholar
Vassiliou, P.-C. G. and Georgiou, A. C. (1990) Asymptotically attainable structures in non-homogeneous Markov systems. Operat. Res. Google Scholar
Vassiliou, P.-C. G. and Gerontidis, I. (1985) Variances and covariances of the grade sizes in manpower systems. J. Appl. Prob. 22, 583–597.Google Scholar
Vassiliou, P.-C. G. and Tsantas, N. (1984a) Stochastic control in non-homogeneous Markov systems. Internat. J. Computer Math. 16, 139–155.Google Scholar
Vassiliou, P.-C. G. and Tsantas, N. (1984b) Maintainability of structures in nonhomogeneous Markov systems under cyclic behaviour and input control. SIAM J. Appl. Math. 44, 1014–1022.Google Scholar
Young, A. (1971) Demographic and ecological models for manpower planning, Aspects of Manpower Planning, ed Bartholomew, D. J. and Morris, B. R. English University Press, London.Google Scholar
Young, A. and Almond, G. (1961) Predicting distributions of staff. Computer Journal 3, 246–250.Google Scholar