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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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