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Transient Solution of a Heterogeneous Queuing System with Balking and Retention of Reneging Customers

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Computer Networks (CN 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1039))

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Abstract

We study a multiple heterogeneous servers queuing model with customers’ impatience and retention of impatient customers where the service is provided by multiple heterogeneous servers. The transient solution of the model is derived by using probability generating function technique. Some important measures of performance are studied. A numerical example is provided to study the stability analysis of the system. Further, a comparative analysis is performed between the heterogeneous servers queuing model and the homogeneous servers queuing model and it is found that the heterogeneous servers queuing model performs better. The stationary probabilities of the number of customers in the system are also derived. At the end, some particular cases of the model are discussed.

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Acknowledgments

Dr. Rakesh Kumar acknowledges the financial assistance provided by UGC, New Delhi, India under the Major Research Project vide letter no. F.-43-434/2014(SR) for preparation of this paper, and Prof. Rykov thanks Russian Fund of Fundamental Investigations for the support in framework of Grants No. 17-01-00633 and No. 17-07-00142.

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Authors and Affiliations

  1. School of Mathematics, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, India

    Rakesh Kumar & Sapana Sharma

  2. Department of Applied Mathematics and Computer Modeling, Gubkin Russian State University of Oil and Gas, Moscow, Russia

    Vladimir Rykov

Authors
  1. Rakesh Kumar
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  2. Sapana Sharma
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  3. Vladimir Rykov
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Correspondence to Rakesh Kumar .

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Editors and Affiliations

  1. Silesian University of Technology, Gliwice, Poland

    Piotr Gaj

  2. Silesian University of Technology, Gliwice, Poland

    Michał Sawicki

  3. Silesian University of Technology, Gliwice, Poland

    Andrzej Kwiecień

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Kumar, R., Sharma, S., Rykov, V. (2019). Transient Solution of a Heterogeneous Queuing System with Balking and Retention of Reneging Customers. In: Gaj, P., Sawicki, M., Kwiecień, A. (eds) Computer Networks. CN 2019. Communications in Computer and Information Science, vol 1039. Springer, Cham. https://doi.org/10.1007/978-3-030-21952-9_25

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  • DOI: https://doi.org/10.1007/978-3-030-21952-9_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-21951-2

  • Online ISBN: 978-3-030-21952-9

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