Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 51801, 13 pages
Research Article

Correlations in Output and Overflow Traffic Processes in Simple Queues

Don McNickle

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.


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.