  We consider a status update system consisting of two independent sources and
one server in which packets of each source are generated according to the
Poisson process and packets are served according to an exponentially
distributed service time. We derive the moment generating function (MGF) of the
age of information (AoI) for each source in the system by using the stochastic
hybrid systems (SHS) under two existing source-aware packet management policies
which we term self-preemptive and non-preemptive policies. In the both
policies, the system (i.e., the waiting queue and the server) can contain at
most two packets, one packet of each source; when the server is busy and a new
packet arrives, the possible packet of the same source in the waiting queue is
replaced by the fresh packet. The main difference between the policies is that
in the self-preemptive policy, the packet under service is replaced upon the
arrival of a new packet from the same source, whereas in the non-preemptive
policy, this new arriving packet is blocked and cleared. We use the derived MGF
to find the first and second moments of the AoI and show the importance of
higher moments.
