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Markov chains with marked transitions

Author

Listed:
  • He, Qi-Ming
  • Neuts, Marcel F.

Abstract

Several useful point processes such as the Markovian arrival process, the input and departure processes of finite-capacity Markovian queues, and various models for counters and biological phenomena are obtained by considering Markov chains with marked transitions. This point of view yields many examples of interesting dependent point processes and provides a unified formalism for their study. This paper presents some characterizations of Markov chains with marked transitions.

Suggested Citation

  • He, Qi-Ming & Neuts, Marcel F., 1998. "Markov chains with marked transitions," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 37-52, May.
    • Handle: RePEc:eee:spapps:v:74:y:1998:i:1:p:37-52
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    Citations

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    Cited by:

    1. Qi‐Ming He & Jingui Xie & Xiaobo Zhao, 2012. "Priority queue with customer upgrades," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 362-375, August.
    2. Jean-François Huchet & Xavier Richet, 2002. "Between Bureaucracy and Market: Chinese Industrial Groups in Search of New Forms of Corporate Governance," Post-Print hal-01331919, HAL.
    3. Marcel F. Neuts & Jian-Min Li, 1999. "Point Processes Competing for Runs: A New Tool for their Investigation," Methodology and Computing in Applied Probability, Springer, vol. 1(1), pages 29-53, July.
    4. Karumbathil Rasmi & Machuveettil Joseph Jacob & Alexander S. Rumyantsev & Achyutha Krishnamoorthy, 2021. "A Multi-Server Heterogeneous Queuing-Inventory System with Class-Dependent Inventory Access," Mathematics, MDPI, vol. 9(9), pages 1-23, May.
    5. Horváth, Gábor, 2015. "Efficient analysis of the MMAP[K]/PH[K]/1 priority queue," European Journal of Operational Research, Elsevier, vol. 246(1), pages 128-139.
    6. Ren, Jiandong, 2012. "A multivariate aggregate loss model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 402-408.
    7. Casale, Giuliano & Sansottera, Andrea & Cremonesi, Paolo, 2016. "Compact Markov-modulated models for multiclass trace fitting," European Journal of Operational Research, Elsevier, vol. 255(3), pages 822-833.
    8. Qi-Ming He & Jiandong Ren, 2016. "Analysis of a Multivariate Claim Process," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 257-273, March.
    9. Qi-Ming He & Jiandong Ren, 2016. "Parameter Estimation of Discrete Multivariate Phase-Type Distributions," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 629-651, September.
    10. Ruiz-Castro, Juan Eloy, 2020. "A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    11. Khayyati, Siamak & Tan, Barış, 2020. "Data-driven control of a production system by using marking-dependent threshold policy," International Journal of Production Economics, Elsevier, vol. 226(C).
    12. A. Gómez-Corral & M. E. Martos, 2009. "Marked Markovian Arrivals in a Tandem G-Network with Blocking," Methodology and Computing in Applied Probability, Springer, vol. 11(4), pages 621-649, December.
    13. Zhou, Wenhui & Zheng, Zhibin & Xie, Wei, 2017. "A control-chart-based queueing approach for service facility maintenance with energy-delay tradeoff," European Journal of Operational Research, Elsevier, vol. 261(2), pages 613-625.

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