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International Conference on Information Technologies and Mathematical Modelling

ITMM 2017: Information Technologies and Mathematical Modelling. Queueing Theory and Applications pp 243–255Cite as

Two-Way Communication M/M/1/1 Queue with Server-Orbit Interaction and Feedback of Outgoing Retrial Calls

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 800))

Abstract

The paper deals with two-way communication M/M/1/1 retrial queue where the server during its idle time makes outgoing calls of two types - to the customers in orbit and to the customers outside it. Durations of these calls follow two distinct exponential distributions. After completion of the outgoing call to a customer from orbit, this customer with probability p rejoins the orbit, and with its complementary probability leaves the service area. Using generating functions approach we derive explicit and recursive formulas for the stationary system state distribution and its factorial moments.

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Author information

Authors and Affiliations

  1. University of Forestry, 10 Kliment Ohridsky, 1756, Sofia, Bulgaria

    Velika Dragieva

  2. University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Tuan Phung-Duc

Authors
  1. Velika Dragieva
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  2. Tuan Phung-Duc
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Corresponding author

Correspondence to Velika Dragieva .

Editor information

Editors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Kazan National Research Technological University, Kazan, Russia

    Alexander Kirpichnikov

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Dragieva, V., Phung-Duc, T. (2017). Two-Way Communication M/M/1/1 Queue with Server-Orbit Interaction and Feedback of Outgoing Retrial Calls. In: Dudin, A., Nazarov, A., Kirpichnikov, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2017. Communications in Computer and Information Science, vol 800. Springer, Cham. https://doi.org/10.1007/978-3-319-68069-9_20

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  • DOI: https://doi.org/10.1007/978-3-319-68069-9_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68068-2

  • Online ISBN: 978-3-319-68069-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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