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Stationary Distribution of the Queueing Networks with Batch Negative Customer Arrivals

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Information Technologies and Mathematical Modelling - Queueing Theory and Applications (ITMM 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 564))

Abstract

Stationary functioning of a queueing network with batch negative customer arrivals is analyzed. Necessary and sufficient condition for ergodisity of the isolated node is established. Stationary product-form distribution of network states is found. Given network model is generalization of classic G-network model on the case of several types of negative customers.

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References

  1. Kurosh, A.G.: Course of Higher Algebra. Nauka, Moscow (1971). (in Russian)

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  2. Bocharov, P.P., Pechinkin, A.V.: Queueing Theory. RUDN, Moskow (1995). (in Russian)

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  3. Gikhman, I.I., Skorohod, A.V.: Introduction in Theory of Stochastic Processes. Nauka, Moskow (1977). (in Russian)

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  4. Klimenok, V.: On the Modification of Rouche’s Theorem for the Queueing Theory Problems. Queueing Syst. 38, 431–434 (2001)

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  5. Gelenbe, E.: Product-form queueing networks with negative and positive customers. J. Appl. Prob. 28, 656–663 (1991)

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Author information

Authors and Affiliations

  1. Francisk Skorina Gomel State University, Gomel, Belarus

    Yury Malinkovsky

  2. National Research Tomsk State University, Tomsk, Russia

    Yury Malinkovsky

Authors
  1. Yury Malinkovsky
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Correspondence to Yury Malinkovsky .

Editor information

Editors and Affiliations

  1. Applied Mathematics and Computer Science, Belarusian State University, Minsk, Russia

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Kemerovo State University, Anzhero-Sudzhensk, Russia

    Rafael Yakupov

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© 2015 Springer International Publishing Switzerland

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Malinkovsky, Y. (2015). Stationary Distribution of the Queueing Networks with Batch Negative Customer Arrivals. In: Dudin, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2015. Communications in Computer and Information Science, vol 564. Springer, Cham. https://doi.org/10.1007/978-3-319-25861-4_5

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  • DOI: https://doi.org/10.1007/978-3-319-25861-4_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25860-7

  • Online ISBN: 978-3-319-25861-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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