  Consider a message processing system whose objective is to produce the most
current information as measured by the quantity known as "age of information".
We have argued in previous papers that if we are allowed to design the message
processing policy ad libitum, we should keep a small buffer and operate
according to a LIFO policy. In this small note we provide an analysis for the
AoI of the P_m system which uses a buffer of size m, a single server, operating
without service preemption and in a LIFO manner for stored messages. Analytical
expressions for the mean (or even distribution) of the AoI in steady-state are
possible but with the aid computer algebra. We explain the the analysis for
m=3.
