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Evaluation of Steady-State Probabilities of Queueing System with Infinitely Many Servers for Different Input Flow Models

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Optimization Methods and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 130))

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Abstract

For the case of Poisson input flow in queueing system with infinitely many servers, the steady-state distribution of the number of customers can be evaluated due to the explicit formula (Poisson distribution). Five models of much more complicated input flows are considered. The combination of Poisson distribution (analytical part) with statistical simulation (statistical part) enables to evaluate the steady-state probabilities with the fast simulation method. Numerical examples demonstrate that the application of explicit analytical formula to the evaluation of small probabilities enables to reduce essentially the variance of the estimate while simulating the queueing system behavior in heavy traffic.

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Authors and Affiliations

  1. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnical Institute”, 37 Prospekt Peremogy, 03056, Kyiv, Ukraine

    Igor Kuznetsov & Alla Shumska

Authors
  1. Igor Kuznetsov
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  2. Alla Shumska
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Correspondence to Igor Kuznetsov .

Editor information

Editors and Affiliations

  1. Industrial & Systems Engineering, Texas A&M University, College Station, Texas, USA

    Sergiy Butenko

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  3. Methods of Discrete Optimization, V.M. Glushkov Institute of Cybernetics, Kyiv, Ukraine

    Volodymyr Shylo

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Kuznetsov, I., Shumska, A. (2017). Evaluation of Steady-State Probabilities of Queueing System with Infinitely Many Servers for Different Input Flow Models. In: Butenko, S., Pardalos, P., Shylo, V. (eds) Optimization Methods and Applications . Springer Optimization and Its Applications, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-319-68640-0_15

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