  In Internet of Things (IoT), the decision timeliness of time-sensitive
applications is jointly affected by the statistics of update process and
decision process. This work considers an update-and-decision system with a
Poisson-arrival bufferless queue, where updates are delivered and processed for
making decisions with exponential or periodic intervals. We use
age-upon-decisions (AuD) to characterize timeliness of updates at decision
moments, and the missing probability to specify whether updates are useful for
decision-making. Our theoretical analyses 1) present the average AuDs and the
missing probabilities for bufferless systems with exponential or deterministic
decision intervals under different service time distributions; 2) show that for
service scheduling, the deterministic service time achieves a lower average AuD
and a smaller missing probability than the uniformly distributed and the
negative exponentially distributed service time; 3) prove that the average AuD
of periodical decision system is larger than and will eventually drop to that
of Poisson decision system along with the increase of decision rate; however,
the missing probability in periodical decision system is smaller than that of
Poisson decision system. The numerical results and simulations verify the
correctness of our analyses, and demonstrate that the bufferless systems
outperform the systems applying infinite buffer length.
