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Time to Start a Crowded Period in a Finite-Buffer Queue with Poisson Input Flow and General Processing Times

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Finite Difference Methods. Theory and Applications (FDM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

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Abstract

A finite-capacity queueing model with Poisson input flow and generally distributed processing times of jobs is considered. An idea of a crowded period is introduced, namely the time period in the system operation during which the number of jobs present in the system is continually greater than or equal the fixed level \(M>0\). A system of integral equations for the tail cumulative distribution function of the time to start a crowded period is derived, conditioned by the number of jobs present in the accumulating buffer before the start moment. A solution of the equivalent system written for Laplace transforms is found using the linear algebraic approach.

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Authors and Affiliations

  1. Institute of Mathematics, Silesian University of Technology, 23 Kaszubska Street, 44-100, Gliwice, Poland

    Wojciech M. Kempa

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  1. Wojciech M. Kempa
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Correspondence to Wojciech M. Kempa .

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Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Kempa, W.M. (2019). Time to Start a Crowded Period in a Finite-Buffer Queue with Poisson Input Flow and General Processing Times. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_37

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

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