Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 51801, 13 pages
doi:10.1155/2007/51801
Research Article
Correlations in Output and Overflow Traffic Processes in Simple Queues
Department of Management, University of Canterbury, Christchurch 8140, New Zealand
Received 11 April 2007; Accepted 8 August 2007
Academic Editor: Paul Cowpertwait
Copyright © 2007 Don McNickle. 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
We consider some simple Markov and Erlang queues with limited storage
space. Although the departure processes from some such systems are known to be
Poisson, they actually consist of the superposition of two complex correlated processes, the
overflow process and the output process. We measure the
cross-correlation between the counting processes for these two processes. It turns out
that this can be positive, negative, or even zero (without implying independence). The
models suggest some general principles on how big these correlations are, and when
they are important. This may suggest when renewal or moment approximations to similar
processes will be successful, and when they will not.