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

Igor Kuznetsov () and Alla Shumska ()
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Igor Kuznetsov: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnical Institute”
Alla Shumska: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnical Institute”

A chapter in Optimization Methods and Applications, 2017, pp 297-311 from Springer

Abstract: 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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-68640-0_15

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DOI: 10.1007/978-3-319-68640-0_15

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