Functional limit theorems for the number of busy servers in a   $G/G/\infty$ queue
  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. 
Alexander Iksanov, Wissem Jedidi and Fethi Bouzeffour
math.PR