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.