  As an emerging metric for the timeliness of information delivery,
Age-of-Information (AoI) raises a special interest in the research area of
tolerance-critical communications, wherein sufficiently short blocklength is
usually adopted as an essential requirement. However, the interplay between AoI
and finite blocklength is scantly treated. This paper studies the occurrence of
high AoI, i.e., AoI outage, in TDMA systems with respect to the blocklength
allocation among users. A Markov Decision Process model is set up for the
problem, which enables a static state analysis, and therewith a policy
iteration approach to improve the AoI robustness is proposed. The burstiness of
outages is also analyzed to provide additional insights into this problem in
the finite blocklength (FBL) regime. It is shown that, different from average
AoI optimizations, a risk-sensitive approach is significantly beneficial for
AoI outage optimizations, on account of the FBL regime.
