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Heavy Outgoing Call Asymptotics for \({MMPP{\slash }}M{\slash }1{\slash }1\) Retrial Queue with Two-Way Communication

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2017)

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

Abstract

In this paper, we consider an MMPP/M/1/1 retrial queue where incoming fresh calls arrive at the server according to a Markov modulated Poisson process. Upon arrival, an incoming call either occupies the server if it is idle or joins an orbit if the server is busy. From the orbit, an incoming call retries to occupy the server and behaves the same as a fresh incoming call. The server makes an outgoing call in its idle time. Our contribution is to derive the asymptotics of the number of calls in retrial queue under the conditions of high rate of making outgoing calls and low rate of service time of outgoing calls.

A. Nazarov—The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008).

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Authors and Affiliations

  1. National Research Tomsk State University, Tomsk, Russia

    Anatoly Nazarov & Svetlana Paul

  2. Peoples Friendship University of Russia (RUDN University), Moscow, Russia

    Anatoly Nazarov

  3. Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba, Japan

    Tuan Phung-Duc

Authors
  1. Anatoly Nazarov
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  2. Tuan Phung-Duc
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  3. Svetlana Paul
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Corresponding author

Correspondence to Anatoly Nazarov .

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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Nazarov, A., Phung-Duc, T., Paul, S. (2017). Heavy Outgoing Call Asymptotics for \({MMPP{\slash }}M{\slash }1{\slash }1\) Retrial Queue with Two-Way Communication. 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_3

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  • DOI: https://doi.org/10.1007/978-3-319-68069-9_3

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  • 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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