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An M/M/1 Queue with n Undesired Services and a Desired Service

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Distributed Computer and Communication Networks (DCCN 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 601))

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Abstract

We study an M/M/1 queue with a set of services in undesired states and a desired state. Arrivals are according to a Poisson process with mean rate \(\lambda \). An arrival enters into desired service with probability \(\theta \), otherwise goes to one of the undesired services with complementary probability depending on the environmental factors. When the service time in undesired states exceeds a threshold random variable, the customer is pushed out of the system. Otherwise the customer, after recognizing that the current service is not the right one moves to desired service state. We discuss the case of n undesired services and a desired service.

A. Krishnamoorthy—Research is supported by the Department of Science and Technology, Government of India under grant INT/RUS/RMES/P-3/2014, dated 15/4/2015.

A.S. Manjunath—Research is supported by the University Grants Commission, Government of India, under Faculty Development Programme (Grant No. F.FIP/12thPlan/KLMG003TF05).

V.M. Vishnevsky—Research is supported by the Ministry of Education and Science of the Russian Federation under grant №14.613.21.0020, dated 22/10/2014 (RFMEFI61314X0020).

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References

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Authors and Affiliations

  1. Department of Mathematics, Cochin University of Science and Technology, Cochin, 682022, India

    A. Krishnamoorthy

  2. Department of Mathematics, Government College Kottayam, Kottayam, 686013, India

    A. S. Manjunath

  3. V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 65 Profsoyuznaya Street, Moscow, 117997, Russia

    V. M. Vishnevsky

Authors
  1. A. Krishnamoorthy
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  2. A. S. Manjunath
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  3. V. M. Vishnevsky
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Corresponding author

Correspondence to V. M. Vishnevsky .

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Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sc, Russian Academy of Sciences V.A. Trapeznikov Institute of Control Sc, Moscow, Russia

    Vladimir Vishnevsky

  2. V.A. Trapeznikov Inst. of Control Scienc, Russian Academy of Sciences V.A. Trapeznikov Inst. of Control Scienc, Moscow, Russia

    Dmitry Kozyrev

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Krishnamoorthy, A., Manjunath, A.S., Vishnevsky, V.M. (2016). An M/M/1 Queue with n Undesired Services and a Desired Service. In: Vishnevsky, V., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2015. Communications in Computer and Information Science, vol 601. Springer, Cham. https://doi.org/10.1007/978-3-319-30843-2_11

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  • DOI: https://doi.org/10.1007/978-3-319-30843-2_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30842-5

  • Online ISBN: 978-3-319-30843-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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