  In this paper, for the discrete time status updating system with infinite
size, we derive the explicit expression of average age of information (AoI),
and the AoI's stationary distribution. Based on the discussions of difference
between finite and infinite size status updating systems, we successfully
characterize the random dynamics of system's AoI using a two-dimensional state
vector, which simultaneously tracks the real time AoI and the age of packet
currently under service. We constitute the two-dimensional age process and
completely solve all the stationary probabilities. Then, as one of the marginal
distributions, the stationary distribution of system's AoI is derived, and with
which the mean of the AoI is also determined.
