  We provide a characterization of the peak age of information (AoI) achievable
in a random-access system operating according to the frameless ALOHA protocol.
Differently from previous studies, our analysis accounts for the fact that the
number of terminals contending the channel may vary over time, as a function of
the duration of the previous contention period. The exact characterization of
the AoI provided in this paper, which is based on a Markovian analysis, reveals
the impact of some key protocol parameters such as the maximum length of the
contention period, on the average peak AoI. Specifically, we show that setting
this parameter so as to maximize the throughput may result in an AoI
degradation.
