Age-Optimal Service and Decision Processes in Internet of Things

We consider an Internet-of-Things (IoT) system in which a sensor observes a phenomenon of interest with exponentially distributed intervals and delivers updates to a monitor with random service times. At the monitor, the received updates are used to make decisions with deterministic or random intervals. For this system, we investigate the freshness of the received updates at decision epochs using the age upon decisions (AuDs) metric. With the first-come-first-served (FCFS) policy, theoretical results show that: 1) when the decisions are made with exponentially distributed intervals, the average AuD of the system is smaller when the service time (e.g., transmission time) is uniformly distributed than when it is exponentially distributed and would be the smallest if it is deterministic; 2) when the decisions are made periodically, the average AuD of the system is larger than, and decreases with decision rate to, the average AuD of the corresponding system with Poisson decision intervals; and 3) the probability of missing to use a received update for any decisions is decreasing with the decision rate and is the smallest if the service time is deterministic. When the last-come-first-served (LCFS) policy with preemption is used, we observe that systems with Poisson service processes perform the best while systems with periodic service processes perform the worst. For IoT-based monitoring systems, therefore, it is suggested to use deterministic monitoring schemes, deterministic transmitting schemes, and Poisson decision schemes so that the received updates are as fresh as possible at the time they are used to make decisions.