  Age of information (AoI) has been widely accepted as a measure quantifying
freshness of status information in real-time status update systems. In many of
such systems, multiple sources share a limited network resource and therefore
the AoIs defined for the individual sources should be correlated with each
other. However, there are not found any results studying the correlation of two
or more AoIs in a status update system with multiple sources. In this work, we
consider a multi-source system sharing a common service facility and provide a
framework to investigate joint performance of the multiple AoIs. We then apply
our framework to a simple pushout server with multiple sources and derive a
closed-form formula of the joint Laplace transform of the AoIs in the case with
independent M/G inputs. We further show some properties of the correlation
coefficient of AoIs in the two-source system.
