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

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 2018 English Publisher:Cambridge University Press (CUP)Journal:Journal of Applied Probability, volume 55, pages 15-29 (issn: 0021-9002, eissn: 1475-6072,

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Authors: Alexander Iksanov; Wissem Jedidi; Fethi Bouzeffour;

doi: 10.1017/jpr.2018.2

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

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Abstract

Abstract We discuss weak convergence of the number of busy servers in a G/G/∞ queue in the J1-topology on the Skorokhod space. We prove two functional limit theorems with random and nonrandom centering, 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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