Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 3, Pages 189-216

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

Copyright © 1993 Lajos Takács. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.