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• W1540996858 abstract "In this paper, we present a functional fluid limit theorem and a functional central limit theorem for a queue with an infinity of servers M/GI/∞. The system is represented by a point-measure valued process keeping track of the remaining processing times of the customers in service. The convergence in law of a sequence of such processes after rescaling is proved by compactness-uniqueness methods, and the deterministic fluid limit is the solution of an integrated equation in the space $mathcal{S}^{prime}$ of tempered distributions. We then establish the corresponding central limit theorem, that is, the approximation of the normalized error process by a $mathcal{S}^{prime}$-valued diffusion. We apply these results to provide fluid limits and diffusion approximations for some performance processes." @default.
• W1540996858 created "2016-06-24" @default.
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• W1540996858 date "2008-12-01" @default.
• W1540996858 modified "2023-10-06" @default.
• W1540996858 title "A functional central limit theorem for the M/GI/∞ queue" @default.
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• W1540996858 doi "https://doi.org/10.1214/08-aap518" @default.
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