Advances in Decision Sciences

Advances in Decision Sciences / 2007 / Article
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Statistics and Applied Probability: A Tribute to Jeffrey J. Hunter

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Research Article | Open Access

Volume 2007 |Article ID 051801 | https://doi.org/10.1155/2007/51801

Don McNickle, "Correlations in Output and Overflow Traffic Processes in Simple Queues", Advances in Decision Sciences, vol. 2007, Article ID 051801, 13 pages, 2007. https://doi.org/10.1155/2007/51801

Correlations in Output and Overflow Traffic Processes in Simple Queues

Academic Editor: Paul Cowpertwait
Received11 Apr 2007
Accepted08 Aug 2007
Published24 Sep 2007

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.

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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.


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