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On the Distributions of the State Sizes of the Continuous Time Homogeneous Markov System with Finite State Capacities

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  • George Vasiliadis

    (Aristotle University of Thessaloniki)

Abstract

In the present paper we study the evolution of a continuous time homogeneous Markov system whose states have finite capacities. We assume that the members of the system who overflow, due to the finite state capacities, leave the system. In order to investigate the variability of the state sizes we provide the evaluation of the intensity matrix for any time point and then we derive a formula concerning the derivate of the moments of the state sizes. As a consequence the distributions of the state sizes can be evaluated. Moreover, an alternative method of calculating the distributions of the state sizes by means of the interval transition probabilities is given. Finally we examine the distribution of the time needed for the leavers to leave the system. The theoretical results are illustrated by a numerical example.

Suggested Citation

  • George Vasiliadis, 2012. "On the Distributions of the State Sizes of the Continuous Time Homogeneous Markov System with Finite State Capacities," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 863-882, September.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-012-9284-9
    DOI: 10.1007/s11009-012-9284-9
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    References listed on IDEAS

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    1. G. Vasiliadis & G. Tsaklidis, 2009. "On the Distributions of the State Sizes of Closed Continuous Time Homogeneous Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 11(4), pages 561-582, December.
    2. G. J. Taylor & S. I. McClean & P. H. Millard, 2000. "Stochastic models of geriatric patient bed occupancy behaviour," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 163(1), pages 39-48.
    3. P.‐C. G. Vassiliou, 1997. "The evolution of the theory of non‐homogeneous Markov systems," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 13(3‐4), pages 159-176, September.
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    Cited by:

    1. P. -C. G. Vassiliou, 2022. "Limiting Distributions of a Non-Homogeneous Markov System in a Stochastic Environment in Continuous Time," Mathematics, MDPI, vol. 10(8), pages 1-16, April.

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