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

Part of: Special processes Limit theorems

Published online by Cambridge University Press:  28 March 2018

Alexander Iksanov ,
Wissem Jedidi  and
Fethi Bouzeffour
Alexander Iksanov*
Affiliation:
Taras Shevchenko National University of Kyiv and University of Wrocław
Wissem Jedidi*
Affiliation:
King Saud University and Université de Tunis El Manar
Fethi Bouzeffour*
Affiliation:
King Saud University
*
* Postal address: Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine. Email address: iksan@univ.kiev.ua
** Postal address: Department of Statistics & OR, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia. Email address: wissem_jedidi@yahoo.fr
*** Postal address: Department of Mathematics, College of Sciences, King Saud University, Riyadh, 11451, Saudi Arabia. Email address: fbouzaffour@ksu.edu.sa
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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.

Keywords

Functional limit theoremG/G/∞ queueperturbed random walktightness

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60K05: Renewal theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 15 - 29
Copyright
Copyright © Applied Probability Trust 2018 

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