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
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.
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.