  This paper studies the age of information (AoI) on an information updating
system such that multiple sources share one server to process packets of
updated information. In such systems, packets from different sources compete
for the server, and thus they may suffer from being interrupted, being
backlogged, and becoming stale. Therefore, in order to grasp structures of such
systems, it is crucially important to study a metric indicating a correlation
of different sources. In this paper, we aim to analyze the correlation of AoIs
on a single-server queueing system with multiple sources. As our contribution,
we provide the closed-form expression of the correlation coefficient of the
AoIs. To this end, we first derive the Laplace-Stieltjes transform of the
stationary distribution of each AoI for the multiple sources. Some nontrivial
properties on the systems are revealed from our analysis results.
