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On Markovian modelling of arrival processes

Author

Listed:
  • Gely Basharin

    (Peoples’ Friendship University of Russia (RUDN University))

  • Valeriy Naumov

    (Service Innovation Research Institute)

  • Konstantin Samouylov

    (Peoples’ Friendship University of Russia (RUDN University)
    Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences)

Abstract

Markovian arrival process (MAP) is a popular tool for modeling arrival processes of stochastic systems such as queueing systems, reliability systems and telecommunications networks. In this paper we show how properties of Markovian Arrival Processes can be derived from the general theory of Markov processes with a homogeneous second component. We also present a series of results on queueing systems with MAP arrivals which were published in RUDN University before 1990.

Suggested Citation

  • Gely Basharin & Valeriy Naumov & Konstantin Samouylov, 2018. "On Markovian modelling of arrival processes," Statistical Papers, Springer, vol. 59(4), pages 1533-1540, December.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:4:d:10.1007_s00362-018-1042-9
    DOI: 10.1007/s00362-018-1042-9
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    Cited by:

    1. Valeriy A. Naumov & Yuliya V. Gaidamaka & Konstantin E. Samouylov, 2019. "On Two Interacting Markovian Queueing Systems," Mathematics, MDPI, vol. 7(9), pages 1-12, September.
    2. Alka Choudhary & Srinivas R. Chakravarthy & Dinesh C. Sharma, 2021. "Analysis of MAP / PH /1 Queueing System with Degrading Service Rate and Phase Type Vacation," Mathematics, MDPI, vol. 9(19), pages 1-17, September.
    3. Valeriy Naumov & Konstantin Samouylov, 2021. "Resource System with Losses in a Random Environment," Mathematics, MDPI, vol. 9(21), pages 1-10, October.

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