Age-upon-Decisions Minimizing Scheduling in Internet of Things: To be Random or to be Deterministic?

We consider an Internet of Things (IoT) system in which a sensor delivers updates to a monitor with exponential service time and first-come-first-served (FCFS) discipline. We investigate the freshness of the received updates and propose a new metric termed as \textit{Age upon Decisions (AuD)}, which is defined as the time elapsed from the generation of each update to the epoch it is used to make decisions (e.g., estimations, inferences, controls). Within this framework, we aim at improving the freshness of updates at decision epochs by scheduling the update arrival process and the decision making process. Theoretical results show that 1) when the decisions are made according to a Poisson process, the average AuD is independent of decision rate and would be minimized if the arrival process is periodic (i.e., deterministic); 2) when both the decision process and the arrive process are periodic, the average AuD is larger than, but decreases with decision rate to, the average AuD of the corresponding system with Poisson decisions (i.e., random); 3) when both the decision process and the arrive process are periodic, the average AuD can be further decreased by optimally controlling the offset between the two processes. For practical IoT systems, therefore, it is suggested to employ periodic arrival processes and random decision processes. Nevertheless, making periodical updates and decisions with properly controlled offset also is a promising solution if the timing information of the two processes can be accessed by the monitor.