Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T02:06:20.025Z Has data issue: false hasContentIssue false
  • English
  • Français

The stress tensor and the energy 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

George M. Tsaklidis
George M. Tsaklidis*
Affiliation:
University of Thessaloniki
*
∗Postal address: Statistics and Operations Research Section, Mathematics Department, University of Thessaloniki, Thessaloniki 54006, Greece. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The set of the attainable structures of a continuous time homogeneous Markov system (HMS) with fixed size, is considered as a continuum and the evolution of the HMS in the Euclidean space corresponds to its motion. Taking account of the velocity field of the HMS, a suitable model of continuum–defined by its stress tensor–is proposed in order to explain the motion of the system. The adoption of this model (equivalently of its stress tensor) enables us to establish the concept of the energy of a structure of the HMS.

Keywords

Stochastic population systemscontinuous time homogeneous Markov systemcontinuum mechanics

MSC classification

Primary: 90B70: Theory of organizations, manpower planning
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 1 , March 1999 , pp. 21 - 29
Copyright
Copyright © Applied Probability Trust 1999 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bartholomew, D. J. (1982). Stochastic Models for Social Processes, 3rd edn. Wiley, New York.Google Scholar
Bartholomew, D. J., Forbes, A. F., and McClean, S. I. (1991). Statistical Techniques for Manpower Planning, 2nd edn. Wiley, Chichester.Google Scholar
Davies, G. S. (1973). Structural control in a graded manpower system. Management Sci. 20, 76–84.Google Scholar
Davies, G. S. (1978). Attainable and maintainable regions in Markov chain control. In Recent Theoretical Developments in Control, ed. Gregson, M. J. Academic Press, London, pp. 371–381.Google Scholar
Eringen, C. A. (1969). Mechanics of Continua. Wiley, New York.Google Scholar
Hasani, H. (1980). Markov renewal models for manpower systems. , University of London.Google Scholar
Isaacson, D. L., and Madsen, R. W. (1976). Markov chains theory and applications. Wiley, New York.Google Scholar
McClean, S. I. (1976). The two stage model for personnel behaviour. J. R. Statist. Soc. A 139, 205–217.Google Scholar
McClean, S. I. (1978). Continuous time stochastic models for a multigrade population. J. Appl. Prob. 15, 26–37.Google Scholar
McClean, S. I. (1980). A semi-Markovian manpower model in continuous time. J. Appl. Prob. 17, 846–852.Google Scholar
McClean, S. I. (1986a). Semi-Markov models for manpower planning. In Semi-Markov Models – Theory and Applications, ed. Janssen, J. Plenum, New York, pp. 238–300.Google Scholar
Mclean, S. I. (1986b). Extending the entropy stability measure for manpower planning. J. Operat. Res. Soc. 37, 1133–1138.Google Scholar
Mehlmann, A. (1979). Semi-Markovian manpower models in continuous time. J. Appl. Prob. 16, 416–422.Google Scholar
Tsaklidis, G. (1996). The evolution of the attainable structures of a continuous time homogeneous Markov system with fixed size. J. Appl. Prob. 33, 34–47.Google Scholar
Tsaklidis, G. (1997). The continuous time homogeneous Markov system with fixed size as a Newtonian fluid. Applied Stochastic Models and Data Anal. 13, 177–182.Google Scholar
Vajda, S. (1978). Mathematics of Manpower Planning. Wiley, New York.Google Scholar
Vassiliou, P.-C. G. (1984). Entropy as a measure of the experience distribution in a manpower system. J. Operat. Res. Soc. 35, 1021–1025.Google Scholar
Vassiliou, P.-C. G. (1993). The non-homogeneous Markov system in a stochastic environment in continuous time. In Proc. 6th Internat. Sympos. on Applied Stochastic Models and Data Analysis, ed. Janssen, J. and Skiadas, C. H. World Scientific, Singapore.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
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