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Asymptotically Attainable Structures in Nonhomogeneous Markov Systems

Author

Listed:
  • P.-C. G. Vassiliou

    (University of Thessaloniki, Thessaloniki, Greece)

  • A. C. Georgiou

    (University of Thessaloniki, Thessaloniki, Greece)

Abstract

In this paper, we provide and study a new aspect in the classical problem of the asymptotic behavior of a nonhomogeneous Markov system (NHMS). The set of asymptotically attainable structures is determined as the convex hull of k vertices, which are given. Also, the rate of convergence to asymptotically attainable structures is studied and conditions are provided for the convergence to be geometrically fast. Finally, an illustration of the results with data from manpower systems is provided.

Suggested Citation

  • P.-C. G. Vassiliou & A. C. Georgiou, 1990. "Asymptotically Attainable Structures in Nonhomogeneous Markov Systems," Operations Research, INFORMS, vol. 38(3), pages 537-545, June.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:3:p:537-545
    DOI: 10.1287/opre.38.3.537
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    Citations

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    Cited by:

    1. P.-C. G. Vassiliou, 2020. "Laws of Large Numbers for Non-Homogeneous Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1631-1658, December.
    2. Brecht Verbeken & Marie-Anne Guerry, 2024. "Attainability for Markov and Semi-Markov Chains," Mathematics, MDPI, vol. 12(8), pages 1-14, April.
    3. Andreas C. Georgiou & Alexandra Papadopoulou & Pavlos Kolias & Haris Palikrousis & Evanthia Farmakioti, 2021. "On State Occupancies, First Passage Times and Duration in Non-Homogeneous Semi-Markov Chains," Mathematics, MDPI, vol. 9(15), pages 1-17, July.
    4. Tim De Feyter & Marie-Anne Guerry & Komarudin, 2017. "Optimizing cost-effectiveness in a stochastic Markov manpower planning system under control by recruitment," Annals of Operations Research, Springer, vol. 253(1), pages 117-131, June.
    5. Tsantas, N., 1995. "Stochastic analysis of a non-homogeneous Markov system," European Journal of Operational Research, Elsevier, vol. 85(3), pages 670-685, September.
    6. Georgiou, A. C., 1999. "Aspirations and priorities in a three phase approach of a nonhomogeneous Markov system," European Journal of Operational Research, Elsevier, vol. 116(3), pages 565-583, August.
    7. Georgiou, Andreas C. & Thanassoulis, Emmanuel & Papadopoulou, Alexandra, 2022. "Using data envelopment analysis in markovian decision making," European Journal of Operational Research, Elsevier, vol. 298(1), pages 276-292.
    8. P.-C.G. Vassiliou, 2021. "Non-Homogeneous Markov Set Systems," Mathematics, MDPI, vol. 9(5), pages 1-25, February.

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