arXiv math/05051272005-05math.PR

Asymptotic Analysis of Losses in the $GI/M/m/n$ Queueing System as $n$ Increases to Infinity

Vyacheslav M. Abramov

备注：: 23 pages, 12pt, 1 table, to apear in "Quality Technology and Quantitative Management"
发表信息：: Quality Technology and Quantitative Management, 4 (2007), 379-393
DOI：: 10.1080/16843703.2007.11673158

英文摘要：

The paper studies asymptotic behavior of the loss probability for the $GI/M/m/n$ queueing system as $n$ increases to infinity. The approach of the paper is based on applications of classic results of Takács (1967) and the Tauberian theorem with remainder of Postnikov (1979-1980) associated with the recurrence relation of convolution type. The main result of the paper is associated with asymptotic behavior of the loss probability. Specifically it is shown that in some cases (precisely described in the paper) where the load of the system approaches 1 from the left and $n$ increases to infinity, the loss probability of the $GI/M/m/n$ queue becomes asymptotically independent of the parameter $m$.

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