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Numbers of Served and Lost Customers in Busy-Periods of M/M/1/n Systems with Balking

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Computational Science and Its Applications – ICCSA 2020 (ICCSA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12251))

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Abstract

In this work we analyze single server Markovian queueing systems with finite capacity and balking, that is M/M/1/n systems with balking. In these systems, the admission of customers is modulated by the state of the system at the instants of customer arrivals. Depending on the size of the queue upon arrival, customers that find place to join the system decide to enter the system with a certain probability. The number of customers in the system amounts to a Markov chain whose transition probabilities incorporate the balking probabilities. Using the Markovian regenerative property of the chain embedded at the instants of arrival or departure of customers, we characterize the joint probability distribution of the number of customers served and the number of customers lost in busy-periods, that is, during continuous occupation periods of the server. This is accomplished implementing a priori a recursive algorithmic procedure for computing the respective probability-generating function. Finally, a numerical illustration of the derived results is presented for different balking policies.

This research was partially supported by Fundação para a Ciência e a Tecnologia (FCT) through project UID/Multi/04621/2019.

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Author information

Authors and Affiliations

  1. University of Trás-os-Montes and Alto Douro, Vila Real, Portugal

    Fátima Ferreira

  2. Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    António Pacheco

  3. Escola Superior de Tecnologia e Gestão do Politécnico de Leiria, Leiria, Portugal

    Helena Ribeiro

  4. CEMAT, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    Fátima Ferreira, António Pacheco & Helena Ribeiro

Authors
  1. Fátima Ferreira
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  2. António Pacheco
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  3. Helena Ribeiro
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Corresponding author

Correspondence to Helena Ribeiro .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Chair- Center of ICT/ICE, Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Clayton School of Information Technology, Monash University, Clayton, VIC, Australia

    David Taniar

  7. Department of Information Science, Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

  11. Department of Neurology, University of Massachusetts Medical School, Worcester, MA, USA

    Yeliz Karaca

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Ferreira, F., Pacheco, A., Ribeiro, H. (2020). Numbers of Served and Lost Customers in Busy-Periods of M/M/1/n Systems with Balking. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science(), vol 12251. Springer, Cham. https://doi.org/10.1007/978-3-030-58808-3_12

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  • DOI: https://doi.org/10.1007/978-3-030-58808-3_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58807-6

  • Online ISBN: 978-3-030-58808-3

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