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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 519.872
I.N. Kuznetsov,1 A.A. Shumskaya2

THE EVALUATION OF STEADY-STATE PROBABILITIES OF QUEUEING SYSTEM
•/G /∞ FOR DIFFERENT INPUT FLOW MODELS

Abstract. We consider five input flow models of more complicated structure than the Poisson one, where steady-state probabilities of the queueing system •/G /∞ can be found explicitly (the Poisson distribution). For these models, the combination of Poisson distribution (analytical part) with statistical simulation (statistical part) allows us to evaluate the steady-state probabilities with the fast simulation method. The accuracy of the estimates is illustrated by numerical examples.

Keywords: queueing system, steady-state probabilities, nonstationary Poisson flow, regenerative process, semi-Markov process, cluster process, unbiased estimate, relative error.



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1 Physico-Technical Institute of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine,
e-mail: sea_hawk@icloud.com.

2 Physico-Technical Institute of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine,
e-mail: shumska-aa@ukr.net.

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