  Status update systems consist of sensors that take measurements of a physical
parameter and transmit them to a remote receiver. Age of Information (AoI) has
been studied extensively as a metric for the freshness of information in such
systems with and without an enforced hard or soft deadline. In this paper, we
propose three metrics for status update systems to measure the ability of
different queuing systems to meet a threshold requirement for the AoI. The {\em
overage probability} is defined as the probability that the age of the most
recent update packet held by the receiver is larger than the threshold. The
{\em stale update probability} is the probability that an update is stale,
i.e., its age has exceeded the deadline, when it is delivered to the receiver.
Finally, the {\em average overage} is defined as the time average of the
overage (i.e., age beyond the threshold), and is a measure of the average
``staleness'' of the update packets held by the receiver. We investigate these
metrics in three typical status update queuing systems -- M/G/1/1, M/G/1/$2^*$,
and M/M/1. Numerical results show the performances for these metrics under
different parameter settings and different service distributions. The
differences between the average overage and average AoI are also shown. Our
results demonstrate that a lower bound exists for the stale update probability
when the buffer size is limited. Further, we observe that the overage
probability decreases and the stale update probability increases as the update
arrival rate increases.
