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Abstract
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Journal of Applied Mathematics and Stochastic Analysis 
Volume 6 (1993), Issue 3, Pages 189-216
doi:10.1155/S1048953393000176

Limit distributions for queues and random rooted trees

Lajos Takács

Case Western Reserve University, Cleveland 44106, Ohio, USA

Received 1 May 1993; Revised 1 July 1993

Abstract

In this paper several limit theorems are proved for the fluctuations of the queue size during the initial busy period of a queuing process with one server. These theorems are used to find the solutions of various problems connected with the heights and widths of random rooted trees.