  In this paper, we consider the age of information (AoI) of a discrete time
status updating system, focusing on finding the stationary AoI distribution
assuming that the Ber/G/1/1 queue is used. Following the standard queueing
theory, we show that by invoking a two-dimensional state vector which tracks
the AoI and packet age in system simultaneously, the stationary AoI
distribution can be derived by analyzing the steady state of the constituted
two-dimensional stochastic process. We give the general formula of the AoI
distribution and calculate the explicit expression when the service time is
also geometrically distributed. The discrete and continuous AoI are compared,
we depict the mean of discrete AoI and that of continuous time AoI for system
with M/M/1/1 queue. Although the stationary AoI distribution of some continuous
time single-server system has been determined before, in this paper, we shall
prove that the standard queueing theory is still appliable to analyze the
discrete AoI, which is even stronger than the proposed methods handling the
continuous AoI.
