Abstract
The data freshness at decision epochs of time-sensitive applications, e.g., auto-driving vehicles and autonomous underwater robots, 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 size.