Functional limit theorems for the number of busy servers in a $G/G/\infty$ queue

preprint2016arXivOpen access

We discuss weak convergence of the number of busy servers in a $G/G/\infty$ queue in the $J_1$ -topology on the Skorokhod space. We prove two functional limit theorems, with random and nonrandom centering, respectively, thereby solving two open problems stated in Mikosch and Resnick (2006}. A new integral representation for the limit Gaussian process is given.

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Functional limit theorems for the number of busy servers in a $G/G/\infty$ queue

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Functional limit theorems for the number of busy servers in a G/G/∞G/G/\inftyG/G/∞ queue

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Functional limit theorems for the number of busy servers in a $G/G/\infty$ queue