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

2016/10/27 by Alexander Iksanov, Iksanov, Alexander, Wissem Jedidi +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1610.08662

openalex publication_date 2016/10/27 · openalex created_date 2016/11/04 · openalex updated_date 2026/07/28

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, 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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