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On a BMAP/G/1 Retrial System with Two Types of Search of Customers from the Orbit

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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

A single server retrial queueing model, in which customers arrive according to a batch Markovian arrival process (BMAP), is considered. An arriving batch, finding server busy, enters an orbit. Otherwise one customer from the arriving batch enters for service immediately while the rest join the orbit. The customers from the orbit try to reach the server subsequently and the inter-retrial times are exponentially distributed. Additionally, at each service completion epoch, two different search mechanisms are switched-on. Thus, when the server is idle, a competition takes place between primary customers, the customers coming by retrial and the two types of searches. It is assumed that if the type II search reaches the service facility ahead of the rest, all customers in the orbit are taken for service simultaneously, while in the other two cases, only a single customer is qualified to enter the service. We assume that the service times of the four types of customers namely, primary, repeated and those by the two types of searches are arbitrarily distributed with different distributions. Steady state analysis of the model is performed.

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Acknowledgments

This work has been financially supported by the Russian Science Foundation and the Department of Science and Technology (India) via grant No 16-49-02021 (INT/RUS/RSF/16) for the joint research project by the V.A. Trapeznikov Institute of Control Problems of the Russian Academy Sciences and the CMS College Kottayam.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Belarusian State University, 220030, Minsk, Belarus

    Alexander Dudin

  2. Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, India

    T. G. Deepak

  3. Department of Mathematics, CMS College, Kottayam, India

    Varghese C. Joshua & Achyutha Krishnamoorthy

  4. Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Vladimir Vishnevsky

Authors
  1. Alexander Dudin
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  2. T. G. Deepak
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  3. Varghese C. Joshua
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  4. Achyutha Krishnamoorthy
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  5. Vladimir Vishnevsky
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Correspondence to Alexander Dudin .

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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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Dudin, A., Deepak, T.G., Joshua, V.C., Krishnamoorthy, A., Vishnevsky, V. (2017). On a BMAP/G/1 Retrial System with Two Types of Search of Customers from the Orbit. 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_1

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  • DOI: https://doi.org/10.1007/978-3-319-68069-9_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68068-2

  • Online ISBN: 978-3-319-68069-9

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